mlsanityData to 7 Oct 2026

Closure Discovery for Coarse-Grained Partial Differential Equations Using Grid-based Reinforcement Learning

arXiv 2402.00972 ↗First posted 1 Feb 2024cs.LG cs.MA physics.comp-phcited by 2

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Abstract (arXiv)

Reliable predictions of critical phenomena, such as weather, wildfires and epidemics often rely on models described by Partial Differential Equations (PDEs). However, simulations that capture the full range of spatio-temporal scales described by such PDEs are often prohibitively expensive. Consequently, coarse-grained simulations are usually deployed that adopt various heuristics and empirical closure terms to account for the missing information. We propose a novel and systematic approach for identifying closures in under-resolved PDEs using grid-based Reinforcement Learning. This formulation incorporates inductive bias and exploits locality by deploying a central policy represented efficiently by a Fully Convolutional Network (FCN). We demonstrate the capabilities and limitations of our framework through numerical solutions of the advection equation and the Burgers' equation. Our results show accurate predictions for in- and out-of-distribution test cases as well as a significant speedup compared to resolving all scales.

Key facts. Cited by 2 papers in the map (data through 7 Oct 2026). Builds on 33 of its 51 references that are in the map. First posted on arXiv 1 Feb 2024.

Builds on

33 of 51 references.

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Citing papers per year: 2025: 2.

2 papers.

  1. 2025Optimal Lattice Boltzmann Closures through Multi-Agent Reinforcement Learningcited by 2
  2. 2025Reinforcement Learning Closures for Underresolved Partial Differential Equations using Synthetic Datacited by 0