mlsanityData to 14 Oct 2026

Reinforcement Learning Closures for Underresolved Partial Differential Equations using Synthetic Data

arXiv 2505.11308 ↗First posted 16 May 2025cs.LG physics.comp-phcited by 0

On the map: Deep reinforcement learning methods → RL theory and sample complexity

Abstract (arXiv)

Partial Differential Equations (PDEs) describe phenomena ranging from turbulence and epidemics to quantum mechanics and financial markets. Despite recent advances in computational science, solving such PDEs for real-world applications remains prohibitively expensive because of the necessity of resolving a broad range of spatiotemporal scales. In turn, practitioners often rely on coarse-grained approximations of the original PDEs, trading off accuracy for reduced computational resources. To mitigate the loss of detail inherent in such approximations, closure models are employed to represent unresolved spatiotemporal interactions. We present a framework for developing closure models for PDEs using synthetic data acquired through the method of manufactured solutions. These data are used in conjunction with reinforcement learning to provide closures for coarse-grained PDEs. We illustrate the efficacy of our method using the one-dimensional and two-dimensional Burgers' equations and the two-dimensional advection equation. Moreover, we demonstrate that closure models trained for inhomogeneous PDEs can be effectively generalized to homogeneous PDEs. The results demonstrate the potential for developing accurate and computationally efficient closure models for systems with scarce data.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods. Builds on 25 of its 51 references that are in the map. First posted on arXiv 16 May 2025.

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25 of 51 references.

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  1. 2024Closure Discovery for Coarse-Grained Partial Differential Equations Using Grid-based Reinforcement Learning1 Feb

Other references · 24

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  1. 2021Tianshou: a Highly Modularized Deep Reinforcement Learning Librarycited by 143
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