Model-Agnostic Knowledge Guided Correction for Improved Neural Surrogate Rollout

Bharat Srikishan, Daniel O'Malley, Mohamed Mehana, Nicholas Lubbers, Nikhil Muralidhar

Keywords: deep learning, knowledge guided machine learning, scientific machine learning, computational fluid dynamics, reinforcement learning

TL;DR: We propose a novel model-agnostic, cost-aware method which combines a neural surrogate, decision model, and simulator to significantly reduce rollout error when performing time-series PDE prediction.

Abstract: Modeling the evolution of physical systems is critical to many applications in science and engineering. As the evolution of these systems is governed by partial differential equations (PDEs), there are a number of computational simulations which resolve these systems with high accuracy. However, as these simulations incur high computational costs, they are infeasible to be employed for large-scale analysis. A popular alternative to simulators are neural network surrogates which are trained in a data-driven manner and are much more computationally efficient. However, these surrogate models suffer from high rollout error when used autoregressively, especially when confronted with training data paucity. Existing work proposes to improve surrogate rollout error by either including physical loss terms directly in the optimization of the model or incorporating computational simulators as `differentiable layers' in the neural network. Both of these approaches have their challenges, with physical loss functions suffering from slow convergence for stiff PDEs and simulator layers requiring gradients which are not always available, especially in legacy simulators. We propose the Hybrid PDE Predictor with Reinforcement Learning (HyPER) model: a model-agnostic, RL based, cost-aware model which combines a neural surrogate, RL decision model, and a physics simulator (with or without gradients) to reduce surrogate rollout error significantly. In addition to reducing in-distribution rollout error by **47%-78%**, HyPER learns an intelligent policy that is adaptable to changing physical conditions and resistant to noise corruption. Code available at https://github.com/scailab/HyPER.

Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)

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Submission Number: 11738