Geosciences, Vol. 16, Pages 55: Learning Debris Flow Dynamics with a Deep Learning Fourier Neural Operator: Application to the Rendinara–Morino Area

Geosciences doi: 10.3390/geosciences16020055

Authors:
Mauricio Secchi
Antonio Pasculli
Massimo Mangifesta
Nicola Sciarra

Accurate numerical simulation of debris flows is essential for hazard assessment and early-warning design, yet high-fidelity solvers remain computationally expensive, especially when large ensembles must be explored under epistemic uncertainty in rheology, initial conditions, and topography. At the same time, field observations are typically sparse and heterogeneous, limiting purely data-driven approaches. In this work, we develop a deep-learning Fourier Neural Operator (FNO) as a fast, physics-consistent surrogate for one-dimensional shallow-water debris-flow simulations and demonstrate its application to the Rendinara–Morino system in central Italy. A validated finite-volume solver, equipped with HLLC and Rusanov fluxes, hydrostatic reconstruction, Voellmy-type basal friction, and robust wet–dry treatment, is used to generate a large ensemble of synthetic simulations over longitudinal profiles representative of the study area. The parameter space of bulk density, initial flow thickness, and Voellmy friction coefficients is systematically sampled, and the resulting space–time fields of flow depth and velocity form the training dataset. A two-dimensional FNO in the (x,t) domain is trained to learn the full solution operator, mapping topography, rheological parameters, and initial conditions directly to h(x,t) and u(x,t), thereby acting as a site-specific digital twin of the numerical solver. On a held-out validation set, the surrogate achieves mean relative L2 errors of about 6–7% for flow depth and 10–15% for velocity, and it generalizes to an unseen longitudinal profile with comparable accuracy. We further show that targeted reweighting of the training objective significantly improves the prediction of the velocity field without degrading depth accuracy, reducing the velocity error on the unseen profile by more than a factor of two. Finally, the FNO provides speed-ups of approximately 36× with respect to the reference solver at inference time. These results demonstrate that combining physics-based synthetic data with operator-learning architectures enables the construction of accurate, computationally efficient, and site-adapted surrogates for debris-flow hazard analysis in data-scarce environments.

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Mauricio Secchi www.mdpi.com