A Novel Deep Learning Approach for Emulating Computationally Expensive Postfire Debris Flows

TL;DR

This work tackles the high computational cost of physics-based debris-flow models by developing a deep learning-based surrogate using a modified U-Net. The model operates on patch-level terrain data and includes a benchmark upstream context plus a six-parameter input to predict peak flow depth, enabling rapid uncertainty quantification via Monte Carlo methods. Training relies on Titan2D simulations generated with Latin Hypercube Sampling, achieving maximum pointwise errors below 10% and near-perfect landscape-wide agreement (Pearson ≈ 0.999) on both Montecito and Oak Creek sites. The patch-predict-stitch framework and probabilistic hazard outputs significantly reduce computation time while providing robust probabilistic hazard maps, offering a scalable, generalizable tool for geophysical flow analysis and hazard assessment.

Abstract

Traditional physics-based models of geophysical flows, such as debris flows and landslides that pose significant risks to human lives and infrastructure are computationally expensive, limiting their utility for large-scale parameter sweeps, uncertainty quantification, inversions or real-time applications. This study presents an efficient alternative, a deep learning-based surrogate model built using a modified U-Net architecture to predict the dynamics of runoff-generated debris flows across diverse terrain based on data from physics based simulations. The study area is divided into smaller patches for localized predictions using a patch-predict-stitch methodology (complemented by limited global data to accelerate training). The patches are then combined to reconstruct spatially continuous flow maps, ensuring scalability for large domains. To enable fast training using limited expensive simulations, the deep learning model was trained on data from an ensemble of physics based simulations using parameters generated via Latin Hypercube Sampling and validated on unseen parameter sets and terrain, achieving maximum pointwise errors below 10% and robust generalization. Uncertainty quantification using Monte Carlo methods are enabled using the validated surrogate, which can facilitate probabilistic hazard assessments. This study highlights the potential of deep learning surrogates as powerful tools for geophysical flow analysis, enabling computationally efficient and reliable probabilistic hazard map predictions.

Figures (10)

• Figure 1: Study Areas for Model training and evaluation. (A) The study area near Montecito, California, USA. (B) The study area encompassing the Middle Fork of Oak Creek, near Independence, California, USA. The satellite image on the left shows the study regions. The red box highlights the region with the corresponding DEMs used for deep learning model evaluation on the right. The satellite images are sourced from Google Maps googlemaps_montecitogooglemaps_oakcreek.
• Figure 2: Schematic representation of the modified U-Net architecture, which integrates dual input sets: spatial features (e.g., elevation and max flow height) through the encoder-decoder framework and physical model parameters via fully connected layers. Skip connections ensure spatial feature preservation for accurate predictions of maximum flow depth in the output.
• Figure 3: Comparison of model predictions with and without benchmark simulations. (A) Predictions without incorporating a benchmark simulation. (B) Predictions with a benchmark simulation included as an additional input channel, improving model performance. The absolute error plots highlight a reduction in errors when benchmark simulations are used, demonstrating the increased model performance from the upstream context.
• Figure 4: Comparison of patch data and model predictions across three arbitrary Titan2D simulations. Each subplot depicts patches extracted from Titan2D simulations alongside corresponding model predictions. Error is defined at each point as the absolute value of the difference between the Titan2d simulations and the model prediction.
• Figure 5: Comparison between the Titan2D simulation and model prediction over the entire study. Error refers to absolute error at each point.