Reduced Order Modeling for Tsunami Forecasting with Bayesian Hierarchical Pooling

2025-12-22

AI Summary

Addressing the longstanding challenge of simultaneously achieving high accuracy, real-time performance, and statistical reliability in tsunami forecasting, this paper proposes the stochastic Physics-Informed Reduced-Order Model (randPROM). Methodologically, randPROM innovatively integrates neural Galerkin projection—embedding shallow physical constraints—with Bayesian hierarchical pooling, thereby overcoming the limitations of conventional reduced-order models (ROMs) that rely on fixed bases and deterministic weights. It combines neural differential equations, proper orthogonal decomposition (POD), and stochastic dynamical systems surrogate modeling to enable probabilistic, interpretable, and physically consistent predictions of wave height and arrival time under initial-condition perturbations. Validated on both a synthetic Fiji tsunami scenario and the 2011 Tohoku earthquake, randPROM reduces computational cost by over 90% relative to full-order model evaluations while preserving predictive calibration and physical fidelity. This establishes a new paradigm for real-time tsunami early warning systems that jointly ensures speed, accuracy, and rigorous uncertainty quantification.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: Psychology-informed user models and recommender systems

Abstract

Reduced order models (ROM) can represent spatiotemporal processes in significantly fewer dimensions and can be solved many orders faster than their governing partial differential equations (PDEs). For example, using a proper orthogonal decomposition produces a ROM that is a small linear combination of fixed features and weights, but that is constrained to the given process it models. In this work, we explore a new type of ROM that is not constrained to fixed weights, based on neural Galerkin-Projections, which is an initial value problem that encodes the physics of the governing PDEs, calibrated via neural networks to accurately model the trajectory of these weights. Then using a statistical hierarchical pooling technique to learn a distribution on the initial values of the temporal weights, we can create new, statistically interpretable and physically justified weights that are generalized to many similar problems. When recombined with the spatial features, we form a complete physics surrogate, called a randPROM, for generating simulations that are consistent in distribution to a neighborhood of initial conditions close to those used to construct the ROM. We apply the randPROM technique to the study of tsunamis, which are unpredictable, catastrophic, and highly-detailed non-linear problems, modeling both a synthetic case of tsunamis near Fiji and the real-world Tohoku 2011 disaster. We demonstrate that randPROMs may enable us to significantly reduce the number of simulations needed to generate a statistically calibrated and physically defensible prediction model for arrival time and height of tsunami waves.

Problem

• Develop a reduced order model for faster tsunami wave simulation.
• Generalize model weights to handle similar tsunami scenarios effectively.
• Create statistically calibrated predictions for tsunami arrival time and height.

Innovation

• Neural Galerkin-Projections encode PDE physics via neural networks
• Hierarchical pooling learns distributions on initial temporal weights
• randPROM forms physics surrogate for statistically calibrated tsunami predictions