Bayesian Physics Informed Neural Networks for Data Assimilation and Spatio-Temporal Modelling of Wildfires
arXiv:2212.00970 · doi:10.1016/j.spasta.2023.100746
Abstract
We apply the Physics Informed Neural Network (PINN) to the problem of wildfire fire-front modelling. We use the PINN to solve the level-set equation, which is a partial differential equation that models a fire-front through the zero-level-set of a level-set function. The result is a PINN that simulates a fire-front as it propagates through the spatio-temporal domain. We show that popular optimisation cost functions used in the literature can result in PINNs that fail to maintain temporal continuity in modelled fire-fronts when there are extreme changes in exogenous forcing variables such as wind direction. We thus propose novel additions to the optimisation cost function that improves temporal continuity under these extreme changes. Furthermore, we develop an approach to perform data assimilation within the PINN such that the PINN predictions are drawn towards observations of the fire-front. Finally, we incorporate our novel approaches into a Bayesian PINN (B-PINN) to provide uncertainty quantification in the fire-front predictions. This is significant as the standard solver, the level-set method, does not naturally offer the capability for data assimilation and uncertainty quantification. Our results show that, with our novel approaches, the B-PINN can produce accurate predictions with high quality uncertainty quantification on real-world data.
arXiv commentAccepted for publication in Spatial Statistics
References in corpus (16)
- Adam: A Method for Stochastic Optimization
- Variational Inference: A Review for Statisticians
- Artificial Neural Networks for Solving Ordinary and Partial Differential Equations
- Aleatoric and Epistemic Uncertainty in Machine Learning: An Introduction to Concepts and Methods
- B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data
- Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations
- On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks
- Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
- Adversarial Uncertainty Quantification in Physics-Informed Neural Networks
- Physics-Informed Neural Networks for Multiphysics Data Assimilation with Application to Subsurface Transport
- Coupled atmosphere-wildland fire modeling with WRF-Fire
- A Physics Informed Neural Network for Time-Dependent Nonlinear and Higher Order Partial Differential Equations
- Wasserstein Generative Adversarial Uncertainty Quantification in Physics-Informed Neural Networks
- Towards Data Assimilation in Level-Set Wildfire Models Using Bayesian Filtering
- A Bayesian Spatio-Temporal Level Set Dynamic Model and Application to Fire Front Propagation
- Physics-Informed Machine Learning Simulator for Wildfire Propagation