Physics-Guided AI for Regional Landslide Susceptibility

A three-paper first-author research program develops, tests, and interprets physics-guided models for cross-region landslide-susceptibility mapping, with explicit analysis of training-sample variability.

Physics-guided learning · Cross-region evaluation · Training-sample variability

This project centers on three first-author papers that form a continuous research program. The 2021 study introduced a CNN–TRIGRS hybrid framework; the 2023 study systematically tested which physical module should be used and how model averaging addresses realization-to-realization variability; the 2024 study isolated the practical roles of spatial neighborhoods, data resolution, factor reduction, and data-driven nonlinearity. (Wei et al., 2021; Wei et al., 2023; Wei et al., 2024)

My role in the core research. Across these three papers, the published contribution statements list my roles in conceptualization, methodology, investigation—including field investigation—data curation, and writing the original drafts. (Wei et al., 2021; Wei et al., 2023; Wei et al., 2024)

Core research arc

2021 A hybrid framework integrating physical model and convolutional neural network Natural Hazards 109, 471–497 Introduced two explicit roles for physics: replacing discrete lithology with continuous safety factor and screening non-landslide samples. 2023 Comparison of hybrid data-driven and physical models at regional scales Acta Geotechnica 18, 4453–4476 Compared four physical modules, distinguished mean performance from variability caused by random training-sample selection, and tested model averaging in a larger validation region. 2024 Improving pixel-based regional landslide susceptibility mapping Geoscience Frontiers 15, 101782 Identified which data, spatial, physical, and algorithmic choices materially improved the two hybrid models.

Shared spatial test bed

The three studies use a deliberately spatial evaluation design in the Three Gorges Reservoir area. Zhuyuan supplies the training inventory, Qinglian serves as the principal cross-region test, and Wushan provides a substantially larger additional testing or validation region in the 2023 and 2024 studies. The regions differ in lithology, topography, inventory distribution, and conditioning-factor distributions. (Wei et al., 2021; Wei et al., 2023; Wei et al., 2024)

Maps of the Zhuyuan training region, Qinglian testing region, and Wushan additional testing region within Chongqing, with landslide inventories over elevation

Spatial evaluation design used in the 2024 study: Zhuyuan for training, Qinglian for cross-region testing, and Wushan for additional testing without local fine-tuning. Fig. 5 from (Wei et al., 2024).

Region	Role	Evidence used in the core papers
Zhuyuan	Training	85 landslide records in the 2021/2023 datasets; model fitting and within-region checks
Qinglian	Primary cross-region test	119 landslide records; includes geological units absent or scarcely represented in Zhuyuan
Wushan	Additional test/validation	2,954.7 km² and approximately 960 inventory records in the 2023 study

Region roles and inventory context reported across the three papers. (Wei et al., 2021; Wei et al., 2023; Wei et al., 2024)

2021 — CNN–TRIGRS framework

Research gap

The 2021 paper targeted two sources of cross-region failure. First, a categorical lithology channel can contain units in the testing region that do not occur in the training region; Qinglian’s $J_2s$ unit is the central example. Second, an incomplete landslide inventory can cause random down-sampling to select unrecorded unstable grids as non-landslide training samples. The authors describe this as the first comprehensive CNN–TRIGRS integration for regional LSM, while explicitly treating the implementation as a preliminary framework. (Wei et al., 2021)

CNN architecture and spatial samples

The data-driven module uses a multi-channel two-dimensional CNN. A sliding window converts the 12 conditioning-factor maps into $5\times5\times12$ samples, enabling the network to learn spatial relations among neighboring grids and channel-wise relations among conditioning factors. The architecture contains three convolutional stages followed by fully connected layers, without pooling; the paper reports 7,250 trainable parameters. (Wei et al., 2021)

The augmentation strategy responds to a specific sample-to-parameter imbalance: the Zhuyuan inventory provides 6,673 landslide grids, fewer than the number of trainable parameters. Successive $90^\circ$ rotations expand the spatial samples fourfold. Dropout and Min–Max normalization are also used, and binary cross-entropy supplies the training loss. Model outputs between 0 and 1 are later grouped into very-low, low, moderate, high, and very-high susceptibility classes using Jenks natural breaks. (Wei et al., 2021)

\[12@5\times5 \rightarrow 8@5\times5 \rightarrow 16@4\times4 \rightarrow 32@3\times3 \rightarrow 32 \rightarrow 8 \rightarrow 2\]

Schematic tensor labels reproduced from Fig. 1. The two outputs are the model's landslide and non-landslide class scores, and the reported susceptibility output lies between 0 and 1. The study does not evaluate whether these outputs are calibrated occurrence probabilities. The paper also does not fully specify the padding and reshaping operations, so this diagram should not be read as a complete implementation specification.

Why lithology was the first physics target

The 50-realization leave-one-factor-out experiment considered both the mean AUC and its spread. Omitting lithology produced the lowest mean and the widest range. River distance, road distance, and NDVI also produced comparatively broad distributions when removed. The authors interpreted these patterns as consistent with the roles of reservoir-level fluctuation, engineering activity, and vegetation cover in the study area, while noting that slope and curvature ranked lower than expected. Because the information was limited and the CNN can perform internal feature selection, all 12 factors were retained in the model. (Wei et al., 2021)

Factor removed	Mean AUC	Min–max AUC	Evidence in this experiment
Lithology	0.929	0.877–0.955	Lowest mean and widest range
Distance to rivers	0.932	0.892–0.948	One of the dominant factors identified by the authors
Distance to roads	0.932	0.889–0.959	One of the dominant factors identified by the authors
NDVI	0.936	0.884–0.955	One of the dominant factors identified by the authors
Curvature	0.943	0.909–0.961	Lower importance than the authors expected
Slope	0.946	0.918–0.962	Lower importance than the authors expected
TWI	0.957	0.943–0.966	Highest mean AUC after removal among the rows shown

Selected leave-one-factor-out results from Fig. 7. These rankings apply to this study area and experiment; they are not universal factor rankings. (Wei et al., 2021)

The two roles assigned to physics

TRIGRS computes a time- and depth-dependent infinite-slope safety factor:

\[F_s(Z,t)= \frac{\tan\phi'}{\tan\delta} + \frac{c'-\Psi(Z,t)\gamma_w\tan\phi'} {\gamma_s Z\sin\delta\cos\delta}\]

Variables. $c'$ and $\phi'$ are effective strength parameters; $\delta$ is slope angle; $Z$ is depth; $\Psi(Z,t)$ is pressure head; and $\gamma_w$ and $\gamma_s$ are the unit weights of water and soil. The study uses TRIGRS output as an explanatory feature and screening criterion rather than as the final susceptibility prediction.

The hybrid keeps 12 input channels but replaces lithology with the continuous $F_s$ map. For negative-sample screening, a $5\times5$ candidate window is retained only when the inventory label is 0 and its mean $F_s$ is greater than 2. The CNN remains the binary classifier. (Wei et al., 2021)

The transformation changes the geological encoding rather than the 30 m spatial resolution: eight categorical lithologic units are converted into grid-level continuous $F_s$ values for the 199,184 Qinglian grids. The paper reports an $F_s$ range of 0–11. These values are outputs of an explicitly parameterized physical model, not quantities learned by the CNN. (Wei et al., 2021)

\[Z(\delta)= \begin{cases} Z_{\max}\left(1-\dfrac{\delta}{40^\circ}\right), & \delta\le 40^\circ,\\[6pt] 0, & \delta>40^\circ. \end{cases}\]

Physical assumptions reported in the paper. Soil thickness decreases linearly from $Z_{\max}$ on flat terrain to zero at a $40^\circ$ slope; no soil is retained above that angle. The initial water table is placed 85% of the local soil thickness below the ground surface, soil properties are assigned by lithology, and the infinite-slope equation neglects inter-grid forces. Eq. (3) from (Wei et al., 2021).

The screening threshold and the physical-evaluation threshold serve different purposes. A candidate negative training window must have mean $F_s>2$, whereas the soil-depth sensitivity analysis later evaluates stand-alone TRIGRS classification at the grid-level threshold $F_s=1.2$. (Wei et al., 2021)

Flowchart of the 2021 CNN and CNN-TRIGRS hybrid models, including lithology replacement, safety-factor-based negative-sample screening, spatial training, and cross-region testing

The two integration points are visible in Steps 2–3: TRIGRS transforms lithology into grid-scale $F_s$ and pre-selects more likely stable negatives before CNN training. Fig. 3 from (Wei et al., 2021).

Evaluation design

Evaluation	Training data	Testing data	Purpose
Within-region	70% of a balanced Zhuyuan sample set	30% of that sample set	Check fitting when training and testing samples share the same region
Cross-region	Zhuyuan	Qinglian Town, evaluated area-wide	Measure spatial generalization without Qinglian training labels
Repeated cross-region	50 balanced training-set realizations from Zhuyuan	An area-wide Qinglian susceptibility prediction for each realization	Quantify variation caused by random training-sample selection

The underlying 30 m inventory contains 6,673 landslide and 193,674 non-landslide grids in Zhuyuan, and 17,326 landslide and 181,858 non-landslide grids in Qinglian. Twelve conditioning factors are used: elevation, slope, aspect, curvature, NDVI, lithology, land use, distance to roads, distance to rivers, annual precipitation, TWI, and SPI. (Wei et al., 2021)

Quantitative evidence

0.533 → 0.637Illustrative cross-region comparison: CNN versus hybrid without sample pre-selection

0.573 → 0.631Mean Qinglian AUC across 50 realizations: CNN versus screened hybrid

0.202 → 0.088Min–max AUC interval width across those realizations

In the within-region 70/30 experiment, CNN and hybrid AUC values were 0.936 and 0.941. In one Zhuyuan-to-Qinglian realization, they were 0.533 and 0.637. The repeated cross-region experiment below provides the more informative comparison because it does not depend on one random training set. (Wei et al., 2021)

Source note. Sec. 4.1 and Fig. 8 report the within-region CNN AUC as 0.936; the paper's conclusion reports 0.929. The section-specific value is used here.

Across 50 cross-region realizations, the hybrid without sample pre-selection increased mean AUC by 4.9% relative to CNN and reduced the min–max interval width by 24.8%. Adding $F_s$-based sample pre-selection increased mean AUC by a further 5.0% and reduced the hybrid interval width by 42.1%. (Wei et al., 2021)

AUC distributions of fifty Qinglian predictions from the CNN, the hybrid without sample pre-selection, and the hybrid with TRIGRS-based sample pre-selection

Fifty cross-region realizations separate the gain from replacing lithology with $F_s$ (CNN → unscreened hybrid) from the additional gain produced by negative-sample screening. Fig. 12 from (Wei et al., 2021).

Model	Min	25%	Mean	75%	Max
CNN	0.469	0.537	0.573	0.612	0.671
Hybrid, no pre-selection	0.504	0.577	0.601	0.634	0.656
Hybrid, with pre-selection	0.590	0.617	0.631	0.647	0.678

Spatial evidence beyond AUC

The cross-region failure was spatially structured. When the Zhuyuan-trained CNN was applied to Qinglian, most of the region was assigned very-low susceptibility, while moderate-to-very-high predictions were concentrated near rivers. The $J_2s$ unit absent from the training region formed a conspicuous failure area; the resulting AUC was 0.533. The authors attributed this pattern to the unlearned unit and the limited spatial differentiation provided by only eight categorical lithologic classes. (Wei et al., 2021)

Replacing lithology with $F_s$ improved transfer but did not eliminate variation between random training sets. One unscreened hybrid realization reached AUC 0.637 and placed 51.9% of observed landslide grids in the moderate-to-very-high classes; it identified many river-adjacent landslides but continued to underestimate areas farther from rivers. A second realization reached only 0.603 and classified 28.3% of landslide grids as moderate-to-very-high. These contrasting maps motivated the 50-realization analysis rather than selection of one favorable map. (Wei et al., 2021)

Qinglian landslide susceptibility map from an illustrative 2021 screened CNN-TRIGRS realization, with five susceptibility classes, landslide inventory outlines, and AUC 0.634

An illustrative screened-hybrid realization in Qinglian. Its AUC is 0.634; the statistical screening gain is established by the 50-realization distributions above, not by comparing this single map with a different unscreened realization. Fig. 13 from (Wei et al., 2021).

In this screened realization, 60.4% of observed landslide grids fell in the moderate-to-very-high classes, including 44.9% in the very-high class. The class-specific relative landslide density supplies a complementary check to AUC:

\[R_i= \frac{n_i/N_i}{\displaystyle\sum_j n_j/N_j}\times100,\]

$n_i$ is the number of landslide grids and $N_i$ is the total number of grids in class $i$. For Fig. 13, $R_i$ rises monotonically from 9.970 to 28.004 across the five susceptibility classes, indicating that mapped susceptibility and observed landslide density increase together. (Wei et al., 2021)

Sensitivity of physical output versus hybrid prediction

The raw TRIGRS output is sensitive to the assumed maximum soil depth. At the stand-alone threshold $F_s=1.2$, increasing $Z_{\max}$ from 10 to 30 m raised TPR from 2.9% to 39.7%, while FPR rose from 3.0% to 32.6%. The $Z_{\max}=20$ and 30 m configurations produced TPR/FPR ratios of 1.24 and 1.22; the 10 m configuration produced a ratio below 1 and classified nearly the entire region as safe. (Wei et al., 2021)

Configuration	Stand-alone physical result	Mean screened-hybrid AUC	Screened-hybrid min–max AUC
$Z_{\max}=10$ m	TPR 2.9%; FPR 3.0%; TPR/FPR < 1	0.626	0.556–0.659
$Z_{\max}=20$ m	TPR/FPR 1.24	0.631	0.590–0.678
$Z_{\max}=30$ m	TPR 39.7%; FPR 32.6%; TPR/FPR 1.22	0.624	0.590–0.657
CNN baseline	No TRIGRS classification	0.573	0.469–0.671

Across the three tested soil-depth assumptions, the screened-hybrid mean remained between 0.624 and 0.631 even though the stand-alone physical maps changed substantially. This experiment clarifies the intended role of physics: TRIGRS supplies structured information to the CNN as a feature and screening criterion rather than serving as the final calibrated susceptibility predictor. (Wei et al., 2021)

Original contribution and stated boundaries

The paper reports the first comprehensive attempt to combine CNN and TRIGRS for regional LSM. Physics is assigned two operational roles—feature construction and negative-sample screening—while CNN performs classification. (Wei et al., 2021)
The cross-region testing scheme and 50 realizations evaluate generalization and robustness rather than selecting one favorable result. (Wei et al., 2021)
Physics-based screening reduces the probability of drawing mislabeled negatives from an incomplete inventory; it does not reconstruct missing landslides. The field survey emphasized residential areas, so unstable or previously failed grids in remote areas could remain labeled as non-landslides. (Wei et al., 2021)
The paper describes the framework as preliminary. Future work proposed by the authors includes deeper/wider CNNs, transfer learning, and more complete inventories from radar, optical remote sensing, and field investigation. The framework was validated using Zhuyuan and Qinglian in Fengjie County. (Wei et al., 2021)

2023 — Physical-module selection and training-sample uncertainty

From one hybrid to four

The 2023 paper is organized around three questions: whether a simplified infinite-slope module can replace TRIGRS without sacrificing hybrid performance; whether compatibility between the physical module and the dominant landslide mechanism affects transfer performance; and whether model averaging can reduce the variability caused by random selection of non-landslide training samples. (Wei et al., 2023)

All four models replace geological strata with $F_s$ and use a physics-based stable-sample criterion, but their failure mechanisms and hydrological assumptions differ. This design separates two questions that are easily conflated: whether a physics-derived representation helps the CNN, and whether the selected physical formulation is appropriate for the dominant landslide type. (Wei et al., 2023)

The spatial transfer problem remains concrete in this dataset: $J_2s$ is absent from Zhuyuan but present in Qinglian, while $J_2xs$ occupies little of the training region—with only one recorded training landslide—but approximately one-fifth of the testing region. The paper also reports differences in elevation, terrain variability, road–inventory distance, and annual precipitation between the two towns. (Wei et al., 2023)

Hybrid	Physical module	Main physical assumption	How the grid-level $F_s$ is obtained
H1	TRIGRS	Richards-equation infiltration and grid runoff coupled to infinite-slope stability	Minimum computed $F_s$ across possible depths at the evaluated time
H2	ISSM, natural condition	Deep groundwater and no seepage within the sliding mass; infiltration/runoff ignored	Natural-condition infinite-slope equation
H3	ISSM, saturated condition	Water table at the surface, full saturation, and seepage parallel to the slope	Saturated infinite-slope equation
H4	Scoops3D	Bishop simplified analysis with spherical rotational trial surfaces, using the saturated soil parameters	Minimum across trial surfaces that affect each DEM grid

Sample construction and the 2023 CNN

The CNN receives $11\times11\times9$ samples. Nine channels represent elevation, slope, curvature, NDVI, geology or $F_s$, land use, distance to rivers, distance to roads, and annual precipitation. All landslide-grid samples are retained. An equal number of non-landslide samples is drawn after physics-based screening, and rotation is used for augmentation. The screening rule retains candidates whose center grid and eight neighbors have an average $F_s>1$. A realization therefore means a separately trained model built from a different random negative subset—not repeated evaluation of one fixed network. Mean AUC describes cross-region discrimination, while range and SD describe training-sample-selection variability. (Wei et al., 2023)

The 2023 CNN is both wider and deeper than the 2021 network. Three parallel branches learn channel weights and spatial patterns at different scales: $1\times1\rightarrow3\times3$, $1\times1\rightarrow5\times5$, and $3\times3$ max pooling followed by $1\times1$ convolution. Their feature maps are concatenated, passed through 32- and 64-filter convolutional stages, flattened, and processed by dense layers of 128, 64, 32, 16, and 8 units before the class output. The reported network contains 1,033,266 weights and biases and is trained with binary cross-entropy, back-propagation, and Adam. Fig. 4 does not separately draw the final two-unit output layer, so this is reported architecture rather than executable reconstruction code. (Wei et al., 2023)

Across all four physical modules, soil depth again decreases linearly to zero as slope increases from $0^\circ$ to $40^\circ$, and properties are assigned by geological stratum. TRIGRS alone uses an initial water table at 85% of soil depth. Table 3 reports natural soil unit weights of 21–22 kN/m³, natural cohesion of 32.8–42 kPa, and friction angles of $16^\circ$–$17.7^\circ$ across the eight units; the corresponding saturated ranges are 21.5–22.5 kN/m³, 26.2–39 kPa, and $13^\circ$–$15.2^\circ$. These stratum-wise assignments are inputs to the physical modules, not calibrated spatial fields. (Wei et al., 2023)

For the two simplified infinite-slope modules, the paper uses:

\[F_s^{\mathrm{natural}} = \frac{c'}{\gamma_s Z_{\max}\sin\delta\cos\delta} + \frac{\tan\phi'}{\tan\delta}\] \[F_s^{\mathrm{saturated}} = \frac{c'}{\gamma_{\mathrm{sat}} Z_{\max}\sin\delta\cos\delta} + \frac{\gamma'\tan\phi'}{\gamma_{\mathrm{sat}}\tan\delta}\]

Variables. $Z_{\max}$ is maximum soil depth; $\gamma_s$, $\gamma_{\mathrm{sat}}$, and $\gamma'$ are the natural, saturated, and submerged unit weights of soil. The two equations differ primarily in their groundwater and saturation assumptions.

Four physical modules compared in the 2023 hybrid-model study: TRIGRS, infinite-slope stability under natural and saturated conditions, and three-dimensional Scoops3D

The four physical modules differ in hydrological assumptions and failure-surface representation. Fig. 6 from (Wei et al., 2023).

Diagnosing the CNN-only transfer failure

In one realization, CNN AUC decreased from 0.812 over the Zhuyuan training region to 0.615 in Qinglian. The geology-specific diagnostic is more revealing: within Qinglian’s $J_2s$-only area, the paper reports a mean AUC of 0.574, and 10% of the realizations fell below 0.5. The $J_2s$ unit is absent from training, while $J_2xs$ covers little of Zhuyuan—with one recorded training landslide—but roughly one-fifth of Qinglian. (Wei et al., 2023)

Source note. Sec. 4.2/Fig. 12 and Fig. 15 contain non-identical 100-realization CNN summaries. Fig. 15 values are used below to keep the direct cross-model comparison internally consistent. (Wei et al., 2023)

Physical-model performance before hybridization

The three two-dimensional modules produced similar stand-alone AUC values in Qinglian, whereas Scoops3D produced approximately 0.45. The authors relate the lower Scoops3D performance to failure-mode applicability: the study inventory is dominated by shallow landslides, while Scoops3D searches spherical rotational surfaces suited to deep-seated failures. (Wei et al., 2023)

Physical module	Mean $F_s$	SD of $F_s$	Stand-alone AUC
TRIGRS	2.601	2.789	0.568
Natural ISSM	2.615	2.826	0.569
Saturated ISSM	2.211	2.881	0.587
Scoops3D	1.407	0.454	≈0.45

Values from Fig. 14. Scoops3D is labeled 0.455 in the figure and 0.452 in the accompanying text, so the table reports approximately 0.45. (Wei et al., 2023)

Added process detail did not automatically produce a stronger regional physical predictor. The authors explain the similar TRIGRS, natural-ISSM, and saturated-ISSM AUC values by the difficulty of obtaining accurate regional soil properties and depths, unrepresented spatiotemporal input uncertainty, and omitted effects of engineering construction and vegetation on infiltration and runoff. This is the authors’ interpretation of the comparison, not an independent causal experiment. (Wei et al., 2023)

Scoops3D produced a more spatially concentrated $F_s$ field and the smallest $F_s$ SD because it considers interactions among soil columns. That physically more structured output did not yield the best susceptibility discrimination: its spherical rotational surfaces were less compatible with the shallow colluvial landslides that dominate the inventory. The comparison therefore tests physical applicability rather than treating physical-model complexity as a proxy for hybrid quality. (Wei et al., 2023)

One hundred realizations: accuracy and robustness are different criteria

AUC distributions over one hundred realizations for CNN and the H1, H2, and H3 physics-guided CNN models

The three shallow-slope hybrids have nearly identical mean AUC, but H3 has the narrowest min–max range and the smallest SD. Values in the table below are transcribed from Fig. 15. (Wei et al., 2023)

Model	Min	Q1	Mean	Q3	Max	SD
CNN	0.472	0.559	0.596	0.635	0.693	0.049
H1: CNN + TRIGRS	0.550	0.666	0.686	0.711	0.739	0.038
H2: CNN + natural ISSM	0.563	0.666	0.685	0.712	0.735	0.036
H3: CNN + saturated ISSM	0.598	0.675	0.684	0.700	0.723	0.021
H4: CNN + Scoops3D	0.518	0.591	0.618	0.646	0.700	0.045

The paper attributes H3’s smaller variability to its impact on negative-sample screening under the shared $F_s>1$ criterion. H1 and H2 did not effectively remove candidate negatives because the minimum values in their physical-module $F_s$ maps exceeded the cutoff. H3 did remove candidates and therefore reduced the chance of sampling unstable grids as negatives. H4 improved mean AUC through the continuous $F_s$ representation, but its SD of 0.045 remained close to the CNN value of 0.049 because its $F_s$ field also did not effectively pre-screen negatives. (Wei et al., 2023)

Among H1–H3, H3 was recommended because its realization distribution had the highest minimum, narrowest range, and smallest SD—not because it had the highest mean, which was slightly larger for H1. In the separate H3–H4 comparison, the paper explains H3’s advantage by the saturated infinite-slope module’s greater suitability for the shallow landslides that dominate the inventory, compared with Scoops3D’s spherical rotational surfaces. (Wei et al., 2023)

Model averaging in Qinglian and Wushan

\[\overline{\mathbf{Y}} = \frac{1}{m} \sum_{r=1}^{m}a_r\mathbf{Y}_r, \qquad a_r=1\]

The study uses a uniform element-wise average of independently trained susceptibility matrices.

Three Qinglian susceptibility maps from independently trained H3 realizations with visibly different spatial patterns and AUC values of 0.717, 0.685, and 0.639

Three independently trained H3 realizations produce different spatial patterns even though the architecture and physical module are unchanged. Their AUC values are 0.717, 0.685, and 0.639. Fig. 17 from (Wei et al., 2023).

The averaging rationale is not majority voting over class labels. It is an element-wise average of continuous susceptibility fields. Under the paper’s error–ambiguity explanation, averaging effectiveness depends jointly on the accuracy and spatial diversity of the individual realizations. (Wei et al., 2023)

In Qinglian, 20 random H3 realizations ranged from 0.626 to 0.723. Averaging subsets of 5, 10, 15, and all 20 realizations yielded AUC values of 0.708, 0.709, 0.705, and 0.705. These averages exceeded most, but not the best, individual Qinglian realization. (Wei et al., 2023)

Threshold-specific TPR/FPR ratios provide a second evaluation of the five-realization H3 average. At every listed susceptibility-class threshold, H3 has the largest ratio among CNN, saturated ISSM, and the hybrid average:

Classification threshold	CNN	Saturated ISSM	H3 average
Very high	1.445	1.398	2.106
High	1.279	1.251	1.885
Moderate	1.203	1.179	1.528
Low	1.075	1.113	1.216

TPR/FPR ratios from Table 4; the lower bound of each susceptibility class is used as the binary threshold. At the very-high threshold, H3 has FPR 0.179 and TPR 0.377, giving 2.106. (Wei et al., 2023)

Wushan provides a second, substantially larger transfer test. Its area is 2,954.7 km²—approximately 12 times the training area—and the study reports about 960 landslides. Five H3 realizations trained without Wushan data produced AUC values of 0.760, 0.785, 0.817, 0.683, and 0.703; their uniform average reached 0.834, exceeding all five. (Wei et al., 2023)

Wushan is not simply a larger holdout. Its geological and topographic conditions differ substantially from Zhuyuan, and many inventory records lie along the Three Gorges Reservoir banks. No Wushan data were used for training. In the paper’s visual assessment, the high and very-high zones of the averaged map capture almost all mapped records. (Wei et al., 2023)

Wushan landslide susceptibility map produced by averaging five H3 realizations and ROC curves for the five individual realizations and their average

Wushan validation: the averaged map and ROC curve combine five H3 realizations without Wushan model training. Fig. 20 from (Wei et al., 2023).

Original contribution and stated limitations

The paper shows that choosing a physically based module requires both physical-module performance and compatibility with the dominant landslide mechanism; adding a more three-dimensional model does not automatically improve the hybrid. (Wei et al., 2023)
It evaluates mean performance and realization-to-realization variability separately, then tests uniform model averaging as a way to address variation caused by random training-sample selection. (Wei et al., 2023)
The formal limitations state that spatial variability of soil properties and temporal changes in conditioning factors and inventories were not considered. Proposed next steps include failure-probability or reliability-index screening, multi-temporal data, and transfer learning. (Wei et al., 2023)

2024 — Key design elements in pixel-based mapping

What the 2024 study isolates

The 2024 paper moves from proposing a hybrid to dissecting why it performs as it does. Rather than treating hybrid-model performance as a single aggregate gain, it examines five design levers through a sequence of controlled comparisons: physics-derived explanatory-factor nonlinearity, pixel spatial neighborhoods, data-driven algorithmic nonlinearity, model-parameter count, and data quantity and quality. (Wei et al., 2024)

Controlled experiment	What is changed	What is held conceptually fixed
Physics-derived representation	Geological class versus saturated-ISSA $F_s$	Single-pixel LR framework
Factor reduction	Starting with nine factors; one factor removed at each step after coefficient refitting	Hybrid Model I and 30 m inputs
Input resolution	1,000 m versus 30 m land cover	Elevation, land cover, and $F_s$
Spatial context	Single-pixel versus local-area samples from 90 to 390 m	Selected factors and cross-region test
Algorithmic nonlinearity	LR versus compact CNN at common local-area sizes	Same physical module and factor channels
Data scarcity	Training pool reduced from 100% to 1%	Three-factor, 270 m configurations
New-region transfer	Direct application in Wushan	No Wushan-label fine-tuning or calibration

Hybrid Model I combines logistic regression with saturated infinite-slope stability analysis; Hybrid Model II combines a deliberately compact CNN with the same physical module. The common data pipeline merges factor maps into a multichannel image, converts geology into $F_s$, discretizes the data to 30 m pixels, reconstructs single-pixel or local-area samples with a sliding window, screens candidate negatives using sample-average $F_s$, and down-samples the retained negatives to match the landslide-sample count. (Wei et al., 2024)

The physical module is the saturated infinite-slope stability analysis:

\[F_s = \frac{c'}{H\gamma_{\mathrm{sat}}\sin\delta\cos\delta} + \frac{\gamma'\tan\phi'}{\gamma_{\mathrm{sat}}\tan\delta}\]

Variables. $c'$ and $\phi'$ are effective cohesion and friction angle; $\delta$ is slope angle; $H$ is soil thickness; and $\gamma_{\mathrm{sat}}$ and $\gamma'$ are saturated and submerged soil unit weights. The resulting $F_s$ is used as a nonlinear explanatory factor in both hybrid models.

The more general ISSA formulation contains the groundwater-depth ratio $k=h_w/H$. The paper sets $k=1$ for the saturated condition because regional water-table depths are difficult to obtain and the preceding comparison found limited change in average hybrid performance across the tested saturation assumptions. (Wei et al., 2024)

Controlled model and sample design

The distinction between a single pixel and a local area is explicit in the regression model. For $c$ explanatory factors, single-pixel LR uses one value per factor:

\[\operatorname{logit}(p) = \ln\left(\frac{p}{1-p}\right) = \sum_{k=1}^{c}w_kx_k+w_0.\]

For an $n\times n$ local area, each factor at each neighboring grid receives its own coefficient:

\[\operatorname{logit}(p) = \ln\left(\frac{p}{1-p}\right) = \sum_{i=1}^{n}\sum_{j=1}^{n}\sum_{k=1}^{c}w_{ijk}x_{ijk}+w_0.\]

The sample shapes are $1\times1\times c$ and $n\times n\times c$, respectively. In both cases the target is the landslide probability of the center grid. Eqs. (3)–(4) from (Wei et al., 2024).

Comparison of single-pixel and local-area samples: a single value per factor versus a spatial tensor of neighboring grids whose center grid is the prediction target

Single-pixel and local-area sample construction. The local-area LR assigns a separate coefficient to every factor at every location in the neighborhood. Fig. 4 from (Wei et al., 2024).

The CNN is intentionally constrained to make the LR–CNN comparison interpretable: one convolutional stage, one dense output stage, and parallel $1\times1$ and $3\times3$ filters. The resulting feature maps are flattened and passed to a sigmoid output trained with binary cross-entropy. Weight sharing and local connectivity allow the $9\times9\times3$ CNN configuration to use fewer reported parameters than local-area LR—163 versus 244—despite its greater algorithmic nonlinearity. (Wei et al., 2024)

Physics-derived factors and factor reduction

In the Table 3 comparison, where testing AUC is calculated after excluding the $J_2s^2$ area because that unit is absent from the training region, replacing geological information with $F_s$ increased LR training AUC from 0.623 to 0.695 and testing AUC from 0.648 to 0.682. Because the explanatory factors were Min–Max normalized and no multicollinearity was found, the fitted coefficients can be compared directly: the coefficient of $F_s$ was $-1.604$, versus $-0.232$ for the original geological/lithological factor. The negative $F_s$ coefficient is consistent with lower susceptibility at higher stability. (Wei et al., 2024)

The physics-derived feature addresses two distinct problems. First, $J_2s^2$ is absent from the training region, so ordinary LR cannot learn a category–response relation for that unit; continuous $F_s$ provides a representation in the same numerical domain across both regions. Second, $F_s$ is a nonlinear combination of slope geometry, soil strength, unit weight, and saturation assumptions. The paper’s XOR illustration is conceptual rather than a landslide-data experiment: it shows how a constructed nonlinear feature can make a previously inseparable input space linearly separable. (Wei et al., 2024)

The step-wise deletion procedure is itself part of the experimental contribution. At each step, LR is refitted, the coefficients of all remaining factors are recalculated, and the factor with the smallest absolute fitted coefficient is removed. The deletion order is curvature → NDVI → annual precipitation → distance to roads → slope → distance to rivers. This leaves elevation, land cover, and $F_s$; the next deletion removes $F_s$, followed by elevation. (Wei et al., 2024)

Step	Factors retained	Training AUC	Testing AUC	Factor removed next
1	9	0.695	0.685	Curvature
2	8	0.695	0.685	NDVI
3	7	0.695	0.686	Annual precipitation
4	6	0.694	0.683	Distance to roads
5	5	0.690	0.687	Slope
6	4	0.687	0.690	Distance to rivers
7	3: elevation + land cover + $F_s$	0.690	0.691	$F_s$
8	2: elevation + land cover	0.679	0.675	Elevation
9	1: land cover	0.651	0.636	—

Steps 1–7 maintain testing AUC between 0.683 and 0.691. Removing $F_s$ in Step 8 reduces it to 0.675, supporting the three-factor minimum reported by the paper. (Wei et al., 2024)

Source note. Table 3 excludes the $J_2s^2$ area for comparison with ordinary LR and reports testing AUC 0.682; the subsequent Table 4 step-wise Hybrid I experiment reports full-region testing AUC 0.685 at Step 1. These are experiment-specific values rather than a rounding difference.

Data resolution and spatial neighborhood

Using the three-factor Hybrid I, 1,000 m land-cover data produced training/testing AUC values of 0.647/0.655; 30 m data produced 0.690/0.691, a reported 5.5% testing-AUC increase. The fitted land-cover coefficient also changed from 0.666 at 1,000 m to $-3.916$ at 30 m. The paper treats this as evidence that resolution materially changes how the model uses land cover; the coefficient sign is not given an additional physical interpretation. (Wei et al., 2024)

For spatial context, single-pixel Hybrid I begins at 0.691. Local-area samples raise its AUC to approximately 0.72, which the paper summarizes as an approximately 4.2% increase. Hybrid Model I reaches its highest plotted value, 0.727, at 210 m and obtains 0.726 at 270 m. Hybrid Model II reaches its maximum of 0.739 at 270 m. The authors adopt 270 m as the common sample size for the subsequent controlled comparison and Wushan application. (Wei et al., 2024)

Sample side length	Hybrid I: LR + ISSA	Hybrid II: CNN + ISSA
30 m	0.691	Not plotted
90 m	0.716	0.718
150 m	0.726	0.729
210 m	0.727	0.733
270 m	0.726	0.739
330 m	0.721	0.731
390 m	0.719	0.727

The section text lists sample sizes through 330 m, whereas Fig. 11 also plots 390 m; the table follows the values shown in Fig. 11. (Wei et al., 2024)

The inventory’s mean landslide area is 56,287.1 m², corresponding to an equivalent square side of 237.2 m. The authors offer this scale correspondence—and the irregular, elongated shape of real landslides—as a possible explanation for the strong performance near 270 m. They also note that increasingly large windows can introduce information redundant to the stability of the center slope. (Wei et al., 2024)

Testing AUC of the logistic-regression and CNN hybrid models for sample spatial sizes from 30 to 390 metres

Hybrid Model I rises from 0.691 for a single 30 m pixel to about 0.72 with local-area samples. Hybrid Model II is higher than Hybrid Model I at every common tested local-area size. Fig. 11 from (Wei et al., 2024).

At the common 270 m configuration, replacing LR with CNN increases AUC from 0.726 to 0.739, a difference of 0.013. By comparison, adding spatial context raises Hybrid I from 0.691 to roughly 0.72. Under the tested configurations, the paper therefore concludes that pixel-neighborhood information has a larger effect than increasing data-driven algorithmic nonlinearity. Its XOR example with a four-neuron hidden layer is a conceptual demonstration of algorithmic nonlinearity, not an additional landslide-data result. (Wei et al., 2024)

Model complexity, training quantity, and Wushan

The full training pool contains 52,696 samples. As the selected proportion decreases, testing AUC initially remains stable and then declines. Hybrid Model I falls earlier and more rapidly: at 20%, 5%, and 1% of the available pool, its AUC values are 0.720, 0.697, and 0.619, compared with 0.732, 0.722, and 0.632 for Hybrid Model II. The paper does not infer a universal minimum training percentage from this experiment. (Wei et al., 2024)

Testing AUC of Hybrid Models I and II as the selected training pool is reduced from 100 percent to 1 percent

Training-data-quantity experiment. Hybrid Model II remains more stable as the sample pool becomes small. Fig. 14 from (Wei et al., 2024).

For the three-factor, 270 m ($9\times9$) local-area configuration, Hybrid Model I has $9\times9\times3+1=244$ fitted coefficients. The compact CNN has 163 reported parameters. The paper associates its greater sample-efficiency with weight sharing and local connectivity; the comparison is specific to this deliberately compact architecture rather than to CNNs in general. (Wei et al., 2024)

Transfer to Wushan without local calibration

Wushan does not provide the same categorical geological-stratum product used in Zhuyuan and Qinglian. The study instead uses an engineering geological map, estimates soil properties from its lithological descriptions, and runs ISSA to generate the common $F_s$ representation. Both models then use elevation, 30 m land cover, $F_s$, and 270 m local-area samples. No Wushan landslide labels are used to fine-tune or calibrate either model. (Wei et al., 2024)

The resulting AUC values are 0.745 for Hybrid Model I and 0.756 for Hybrid Model II. At the highest listed quantile threshold, their absolute metrics are nearly identical:

Model	Threshold	Accuracy	Precision	Recall	FPR	F1
Hybrid I	0.757	0.803	0.039	0.604	0.195	0.073
Hybrid II	0.764	0.803	0.039	0.605	0.195	0.074

Threshold-specific values from Table 8. They complement, but are not interchangeable with, threshold-independent AUC. (Wei et al., 2024)

The paper discusses low precision and comparatively high FPR in relation to inventory incompleteness. Field surveys emphasize roads and populated areas, so some highly susceptible remote areas without mapped records may not be genuine false predictions. It also notes that landslide polygons can include runout zones that may have been stable before failure. (Wei et al., 2024)

Wushan susceptibility maps produced by Hybrid Model I and Hybrid Model II without local label fine-tuning, with AUC values of 0.745 and 0.756

Direct Wushan application without local-label fine-tuning: Hybrid Model I (left) and Hybrid Model II (right). Fig. 18 from (Wei et al., 2024).

Original contribution and stated limitations

The paper separates the effects of physics-derived explanatory factors, neighborhood information, algorithmic nonlinearity, parameter count, input quantity, and spatial resolution instead of treating hybrid performance as a single undifferentiated gain. (Wei et al., 2024)
It shows that the LR hybrid can retain cross-region AUC close to that of the compact CNN hybrid while offering greater practicality and interpretability; the compact CNN provides a marginal AUC increase and greater stability as training data are reduced. (Wei et al., 2024)
The methods state several modeling assumptions: saturated condition $k=1$; seepage parallel to the slope; neglected inter-pixel forces; identical estimated soil parameters within each geological unit; and a linear relation between LR predictors and log odds. These are stated assumptions rather than results of the ablation experiments. (Wei et al., 2024)
The discussion notes that field inventories may underrepresent remote areas, mapped polygons may include runout zones that were stable before failure, and higher-resolution inventories and factors could improve evaluation. It proposes InSAR, LiDAR, UAV imagery, and image recognition as possible routes to a more complete inventory. Wushan is evaluated without local calibration. (Wei et al., 2024)

Synthesis across the three studies

Scientific question	2021	2023	2024
How should physics enter the model?	Use $F_s$ as a continuous feature and sample-screening criterion	Compare four candidate physical modules and their failure assumptions	Quantify the weight and practical value of the physics-derived factor
How should transfer be evaluated?	Train in Zhuyuan and test in Qinglian	Add 100 realizations and Wushan validation	Repeat Wushan evaluation with LR and compact CNN hybrids
How are data and model variability investigated?	Quantify the effect of random negative-sample selection over 50 balanced training-set realizations	Compare 100 realizations, select the module with lower realization-to-realization variability, and average susceptibility matrices	Hold the physical module fixed while testing training-data quantity, parameter count, spatial context, and input resolution
What is the practical model-design lesson?	In the tested Zhuyuan-to-Qinglian transfer, $F_s$ improved the geological representation and reduced negative-sample-selection uncertainty	Match the physical module to the dominant failure mode; greater model complexity alone does not ensure better hybrid performance	Under the tested LR and compact-CNN configurations, spatial-neighborhood information produced a larger AUC gain than additional data-driven nonlinearity; training quantity and input resolution also affected performance

Related collaborative work addresses dense regional prediction and probabilistic calibration of physically based slope models. These studies complement the core papers but solve distinct methodological problems.

Dense probability-field prediction with U-Net

U-Net changes the mapping from “local area → center-pixel probability” to “local multi-channel area → complete probability matrix.” The model uses $16\times16\times10$ inputs, an encoder–decoder structure, skip connections, and overlapping output averaging. Across 20 realizations, mean AUC was 0.868 in the training region and 0.661 in the cross-region evaluation; averaging 20 cross-region matrices yielded 0.684. (Tan et al., 2025)

Three-panel U-Net landslide susceptibility framework showing spatial sampling, encoder-decoder learning with skip connections, and probability-map reconstruction

U-Net sampling, encoder–decoder architecture, and regional probability-map reconstruction. Fig. 1 from (Tan et al., 2025).

Spatial calibration of the physical model

A DCT–Bayesian method represents a spatially varying friction-angle field with retained DCT coefficients and estimates them from stable/unstable observations. In the Qinglian case, calibration raised AUC from 0.516 to 0.842, with TPR 0.588 and FPR 0.026. The spatial field is inferred rather than directly measured. (Luo et al., 2022)

Calibrated regional results showing factor of safety, failure probability, inferred friction angle, and ROC curves

MAP-estimated safety, failure probability, friction-angle field, and ROC comparison. Fig. 18 from (Luo et al., 2022).

Efficient Bayesian calibration with PCE

For coupled hydro-mechanical models, polynomial-chaos expansion approximates repeated numerical responses inside Bayesian MCMC:

\[\widehat{F}(\boldsymbol{\theta}) = d_0\Psi_0(\boldsymbol{\theta}) + \sum_{i=1}^{U-1}d_i\Psi_i(\boldsymbol{\theta})\]

In the 2023 numerical example, the complete proposed method—including surrogate training—required 1.69 h, compared with 207.5 h for Bayesian estimation using the numerical model directly. Pore-pressure responses were most informative for hydraulic parameters, while displacement responses were more informative for stiffness and strength. (Zhang et al., 2023)

Two-stage workflow for constructing polynomial-chaos surrogate models and using them in Bayesian MCMC parameter estimation

PCE surrogate construction followed by Bayesian parameter estimation. The numerical example uses model responses with 3% artificial Gaussian noise. Fig. 2 from (Zhang et al., 2023).

Earlier PCE-based probabilistic back-analysis produced posterior statistics and 95% prediction intervals close to direct numerical-model back-analysis for the same synthetic slope response. (Wu et al., 2018)

Numerical-model and PCE-based back-analysis pore-pressure responses with 95 percent prediction intervals and synthetic data

Numerical-model and PCE-based back-analysis intervals in the 2018 numerical example. Fig. 7 from (Wu et al., 2018).

The DCT-inferred regional friction-angle field cannot be checked directly because the actual field is unknown. The two PCE studies demonstrate their methods through numerical examples rather than field deployments. (Luo et al., 2022; Zhang et al., 2023; Wu et al., 2018)

References

2025

China Civ. Eng. J.
Study on regional landslide susceptibility assessment method based on U-Net semantic segmentation network and its cross-generalization ability

Lin Tan, Lulu Zhang, Xin Wei, and 3 more authors

China Civil Engineering Journal, 2025

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3 citations

Current regional landslide susceptibility assessment (LSA) methods based on the raster / grid / pixel unit suffer from such problems as insufficient consideration of spatial correlation of raster units and poor cross-generalization ability, and to address these problems, a LSA method based on the U-Net semantic segmentation network is proposed. With the Zhuyuan Town and the Qinglian Town in Fengjie County taken as the study areas, ten landslide conditioning factors, including elevation, lithology and normalized difference vegetation index, are selected. By forming a dataset with these conditioning factors and landslide inventory, the U-Net model is established for LSA. The model averaging method is applied to several prediction matrices, and the accuracy and uncertainty are quantified by the receiver operating characteristic (ROC) curves and the area under the curve (AUC). To further enhance the cross-generalization ability affected by different lithologies across regions, a lithology scoring method is proposed, and the model is applied to Qinglian Town to assess its cross-generalization ability. The results show that: (1) The U-Net model presents reliable performance and effectively captures the spatial correlation of raster units, and the optimized network architecture enables more accurate susceptibility assessment. The landslide susceptibility map in Zhuyuan Town agrees well with the landslide inventory, whose assessment is better than that of Qinglian Town. (2) The model averaging method can effectively reduce the uncertainty of predictions. Stable and reliable assessment results can be obtained by averaging a small number of predictions, without the necessity of seeking the optimal result from a single random realization. As the number of predictions involving in model averaging increases, the AUC presents a convergent trend. (3) The lithology scoring method standardizes the data distribution of the training and test areas, and in combination with the model averaging method, it can be used to ensure the cross-generalization ability of the model.
@article{tan2024study, title = {Study on regional landslide susceptibility assessment method based on U-Net semantic segmentation network and its cross-generalization ability}, author = {Tan, Lin and Zhang, Lulu and Wei, Xin and Liu, Dongsheng and Du, Chunlan and Li, Hai}, journal = {China Civil Engineering Journal}, volume = {58}, number = {6}, pages = {103--116}, year = {2025}, doi = {10.15951/j.tmgcxb.23110923}, citations = {3} }

2024

Geosci. Front.
Improving pixel-based regional landslide susceptibility mapping

Xin Wei, Paolo Gardoni, Lulu Zhang, and 4 more authors

Geoscience Frontiers. Previously listed as an ESI Highly Cited Paper, 2024

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52 citations

Regional landslide susceptibility mapping (LSM) is essential for risk mitigation. While deep learning algorithms are increasingly used in LSM, their extensive parameters and scarce labels (limited landslide records) pose training challenges. In contrast, classical statistical algorithms, with typically fewer parameters, are less likely to overfit, easier to train, and offer greater interpretability. Additionally, integrating physics-based and data-driven approaches can potentially improve LSM. This paper makes several contributions to enhance the practicality, interpretability, and cross-regional generalization ability of regional LSM models: (1) Two new hybrid models, composed of data-driven and physics-based modules, are proposed and compared. Hybrid Model I combines the infinite slope stability analysis (ISSA) with logistic regression, a classical statistical algorithm. Hybrid Model II integrates ISSA with a convolutional neural network, a representative of deep learning techniques. The physics-based module constructs a new explanatory factor with higher nonlinearity and reduces prediction uncertainty caused by incomplete landslide inventory by pre-selecting non-landslide samples. The data-driven module captures the relation between explanatory factors and landslide inventory. (2) A step-wise deletion process is proposed to assess the importance of explanatory factors and identify the minimum necessary factors required to maintain satisfactory model performance. (3) Single-pixel and local-area samples are compared to understand the effect of pixel spatial neighborhood. (4) The impact of nonlinearity in data-driven algorithms on hybrid model performance is explored. Typical landslide-prone regions in the Three Gorges Reservoir, China, are used as the study area. The results show that, in the testing region, by using local-area samples to account for pixel spatial neighborhoods, Hybrid Model I achieves roughly a 4.2% increase in the AUC. Furthermore, models with 30 m resolution land-cover data surpass those using 1000 m resolution data, showing a 5.5% improvement in AUC. The optimal set of explanatory factors includes elevation, land-cover type, and safety factor. These findings reveal the key elements to enhance regional LSM, offering valuable insights for LSM practices.
@article{wei2024improving, title = {Improving pixel-based regional landslide susceptibility mapping}, author = {Wei, Xin and Gardoni, Paolo and Zhang, Lulu and Tan, Li and Liu, Dongsheng and Du, Chunli and Li, Hui}, journal = {Geoscience Frontiers}, volume = {15}, number = {4}, pages = {101782}, year = {2024}, publisher = {Elsevier}, doi = {10.1016/j.gsf.2024.101782}, citations = {52}, }

2023

Acta Geotech.
Comparison of hybrid data-driven and physical models for landslide susceptibility mapping at regional scales

Xin Wei, Lulu Zhang, Paolo Gardoni, and 5 more authors

Acta Geotechnica, 2023

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80 citations

Landslide susceptibility mapping (LSM) is essential for the spatial prediction of landslides and risk prevention. Physically based LSM models are confined by oversimplifications of physical processes and limited information about soil properties. Data-driven LSM models may give reliable results only when the training and the testing data have high similarity, and application in regions with different geological conditions is often inapplicable. This paper proposes four hybrid data-driven and physical models and compares these models in terms of cross-regional generalization ability and prediction uncertainty. The effects of physical module performance on the hybrid model are analyzed. For the physical modules of the four hybrid models, two-dimensional (2D) physically based models, TRIGRS and the infinite-slope stability models (ISSMs), and the three-dimensional (3D) physically based model, Scoops3D, are adopted. The data-driven modules all adopt the convolutional neural network (CNN) model. Two towns in the Three-Gorge Reservoir area of China are used as the training and testing areas. The results show that all hybrid models have better generalization ability than using the data-driven module exclusively. The prediction uncertainty is significantly reduced by pre-selecting training samples using the physical module. The optimal hybrid model is the one that integrates CNN and ISSM (under the saturated condition). It is then applied to a new region (Wushan County) to further validate the generalization ability. It can make accurate predictions without calibrating the trained model using new data from the validation area. Finally, the effectiveness of model averaging for improving the prediction performance is verified. Using model averaging, the AUC value in the validation area yields 0.834, which is even higher than the original realizations, with AUC values ranging from 0.683 to 0.817. Therefore, the optimal hybrid model can be directly used for LSM in the Three-Gorge Reservoir, and the findings can provide valuable guidance for generalization ability improvement and prediction uncertainty reduction of LSM models in other countries and regions.
@article{wei2023comparison, title = {Comparison of hybrid data-driven and physical models for landslide susceptibility mapping at regional scales}, author = {Wei, Xin and Zhang, Lulu and Gardoni, Paolo and Chen, Yangming and Tan, Lin and Liu, Dongsheng and Du, Chunlan and Li, Hai}, journal = {Acta Geotechnica}, volume = {18}, number = {8}, pages = {4453--4476}, year = {2023}, publisher = {Springer}, doi = {10.1007/s11440-023-01841-4}, citations = {80} }
Rock Mech. Bull.
Polynomial chaos surrogate and bayesian learning for coupled hydro-mechanical behavior of soil slope

Lulu Zhang, Fang Wu, Xin Wei, and 4 more authors

Rock Mechanics Bulletin, 2023

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20 citations

As rainfall infiltrates into soil slopes, the hydraulic and mechanical behaviors of soils are interacted. In this study, an efficient probabilistic parameter estimation method for coupled hydro-mechanical behavior in soil slope is proposed. This method integrates the Polynomial Chaos Expansion (PCE) method, the coupled hydro-mechanical modeling, and the Bayesian learning method. A coupled hydro-mechanical numerical model is established for the simulation of behaviors of unsaturated soil slope under rainfall infiltration, following by training a cheap-to-run PCE surrogate to replace it. Probabilistic estimation of soil parameters is conducted based on the Bayesian learning technique with the Markov Chain Monte Carlo (MCMC) simulation. A numerical example of an unsaturated slope under rainfall infiltration is presented to illustrate the proposed method. The effects of measurement durations and response types on parameter estimation are addressed. The result shows that with the increase of measurement duration, the uncertainties of soil parameters are significantly reduced. The uncertainties of hydraulic properties are reduced significantly using the pore water pressure data, while the uncertainties of soil strength parameters are reduced greatly using the measured displacement data.
@article{zhang2023polynomial, title = {Polynomial chaos surrogate and bayesian learning for coupled hydro-mechanical behavior of soil slope}, author = {Zhang, Lulu and Wu, Fang and Wei, Xin and Yang, Hao-Qing and Fu, Shixiao and Huang, Jinsong and Gao, Liang}, journal = {Rock Mechanics Bulletin}, volume = {2}, number = {1}, pages = {100023}, year = {2023}, publisher = {Elsevier}, citations = {20} }

2022

Georisk
Probabilistic model calibration of spatial variability for a physically-based landslide susceptibility model

Junyao Luo, Lulu Zhang, Hao-Qing Yang, and 3 more authors

Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards, 2022

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27 citations

Physically-based landslide susceptibility models have been widely used to predict rainfall-triggered landslides. Calibration of these models is mainly conducted by tuning various inputs, but spatially varying soil properties are not considered. In this study, an efficient probabilistic model calibration method is proposed, which integrates discrete cosine transform (DCT) representation of spatial variability with Bayesian parameter estimation to characterise the spatial variation of soil properties in a physically-based landslide susceptibility model. The efficacy of DCT inversion in representing fields with binary information about landslide occurrence and non-occurrence is investigated. To illustrate the capability and feasibility of the proposed method, a hypothetical example and a case study of a 2014 regional rainfall-triggered landslide event in Qinglian Town, Chongqing, China are presented. The results demonstrate that the location, size and shape of landslide have little influence on the DCT inversion. Considering spatial variation in model calibration can significantly improve model prediction performance for regional rainfall-induced landslides. The topography of the landslide initiation area may affect the influence of the model calibration if the field observations do not agree with the fundamental physics underlying the stability equation used in the model.
@article{luo2022probabilistic, title = {Probabilistic model calibration of spatial variability for a physically-based landslide susceptibility model}, author = {Luo, Junyao and Zhang, Lulu and Yang, Hao-Qing and Wei, Xin and Liu, Dongsheng and Xu, Jiabao}, journal = {Georisk: Assessment and Management of Risk for Engineered Systems and Geohazards}, volume = {16}, number = {4}, pages = {728--745}, year = {2022}, publisher = {Taylor \& Francis}, doi = {10.1080/17499518.2021.1988986}, citations = {27} }

2021

Nat. Hazards
A hybrid framework integrating physical model and convolutional neural network for regional landslide susceptibility mapping

Xin Wei, Lulu Zhang, Junyao Luo, and 1 more author

Natural Hazards, 2021

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89 citations

Landslide susceptibility mapping (LSM) is critical for risk assessment and mitigation. Generalization ability and prediction uncertainty are the current challenges for LSM but have been rarely investigated. The generalization ability refers to the ability of trained models to assess the landslide susceptibility of new areas and make accurate predictions. The prediction uncertainty mainly comes from the possibility of wrongly selecting the unstable landslide samples as stable ones from incomplete landslide inventory. This paper proposes a hybrid model by integrating the convolutional neural network (CNN) with physical model transient rainfall infiltration and grid-based regional slope-stability analysis (TRIGRS) to address the challenges above by combining the advantages of the two approaches. CNN is the main structure of the hybrid model and serves as a binary classifier to capture the spatial and inter-channel correlation among landslide conditioning factors and landslide inventory. TRIGRS characterizes the differences among grids caused by lithology by converting originally spatially discrete and banded lithology information into spatially continuous safety factors (Fs) within a fixed range and pre-selects training samples to ensure the correctness of the selected non-landslide grids. Two towns (Zhuyuan and Qinglian) in Fengjie, Chongqing, China, are used as the study area. A landslide inventory and landslide conditioning factor maps with 30 m resolution consist of the database. The performance of CNN and the proposed hybrid model is compared using the receiver operating characteristic curve and relative landslide density index (R-index). The superiority of the hybrid model and the effect of pre-selection of training samples are investigated. The results reveal that the generalization ability is enhanced and the prediction uncertainty is reduced by the proposed hybrid model.
@article{wei2021novel, title = {A hybrid framework integrating physical model and convolutional neural network for regional landslide susceptibility mapping}, author = {Wei, Xin and Zhang, Lulu and Luo, Junyao and Liu, Dongsheng}, journal = {Natural Hazards}, volume = {109}, pages = {471--497}, year = {2021}, publisher = {Springer}, doi = {10.1007/s11069-021-04844-0}, citations = {89} }

2018

Chin. J. Geotech. Eng.
Probabilistic back analysis method for unsaturated soil slopes with fluid-solid coupling process based on polynomial chaos expansion

Fang Wu, Lulu Zhang, Wentao Zheng, and 1 more author

Chinese Journal of Geotechnical Engineering, 2018

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4 citations

The seepage and stress-deformation in an unsaturated slope under rainfall infiltration are interacted with high nonlinearity. Numerical models are commonly adopted to solve the coupled governing equations. Tremendous computational cost of numerical modeling is the main obstacle for probabilistic back analysis with field monitoring data. A probabilistic back analysis method based on polynomial chaos expansion (PCE) is proposed in this study. PCE approximation is used to construct the explicit functions between unsaturated soil parameters and model responses to replace the original numerical model. The PCE surrogate model is adopted in parameter posterior inference with Markov chain Monte Carlo (MCMC) simulation based on the Bayesian theory. An example of unsaturated soil slope under rainfall infiltration is presented to illustrate the efficiency of the proposed method. The statistics of posterior distribution and 95% uncertainty bounds obtained using the PCE-based method are close to the results of the traditional back analysis based on the original numerical model. In addition, the proposed new method can significantly improve the efficiency of model calibration.
@article{wu2018probabilistic, title = {Probabilistic back analysis method for unsaturated soil slopes with fluid-solid coupling process based on polynomial chaos expansion}, author = {Wu, Fang and Zhang, Lulu and Zheng, Wentao and Wei, Xin}, journal = {Chinese Journal of Geotechnical Engineering}, volume = {40}, number = {12}, pages = {2215--2221}, year = {2018}, doi = {10.11779/CJGE201812008}, citations = {4} }

Core research arc

Shared spatial test bed

2021 — CNN–TRIGRS framework

Research gap

CNN architecture and spatial samples

Why lithology was the first physics target

The two roles assigned to physics

Evaluation design

Quantitative evidence

Spatial evidence beyond AUC

Sensitivity of physical output versus hybrid prediction

Original contribution and stated boundaries

2023 — Physical-module selection and training-sample uncertainty

From one hybrid to four

Sample construction and the 2023 CNN

Diagnosing the CNN-only transfer failure

Physical-model performance before hybridization

One hundred realizations: accuracy and robustness are different criteria

Model averaging in Qinglian and Wushan

Original contribution and stated limitations

2024 — Key design elements in pixel-based mapping

What the 2024 study isolates

Controlled model and sample design

Physics-derived factors and factor reduction

Data resolution and spatial neighborhood

Model complexity, training quantity, and Wushan

Transfer to Wushan without local calibration

Original contribution and stated limitations

Synthesis across the three studies

Related collaborative extensions

Dense probability-field prediction with U-Net

Spatial calibration of the physical model

Efficient Bayesian calibration with PCE

References

2025

2024

2023

2022

2021

2018