Learning to Solve PDE-constrained Inverse Problems with Graph Networks

2022/06/01 by Qingqing Zhao, David B. Lindell, Zhao, Qingqing +3 · 4 citations
Computer Science · Materials Science · Physics and Astronomy · #Computational Physics and Python Applications #FOS: Computer and information sciences #Machine Learning (cs.LG) #Machine Learning in Materials Science #Model Reduction and Neural Networks

paper · pdf · doi:10.48550/arxiv.2206.00711

openalex publication_date 2022/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Learned graph neural networks (GNNs) have recently been established as fast and accurate alternatives for principled solvers in simulating the dynamics of physical systems. In many application domains across science and engineering, however, we are not only interested in a forward simulation but also in solving inverse problems with constraints defined by a partial differential equation (PDE). Here we explore GNNs to solve such PDE-constrained inverse problems. Given a sparse set of measurements, we are interested in recovering the initial condition or parameters of the PDE. We demonstrate that GNNs combined with autodecoder-style priors are well-suited for these tasks, achieving more accurate estimates of initial conditions or physical parameters than other learned approaches when applied to the wave equation or Navier-Stokes equations. We also demonstrate computational speedups of up to 90x using GNNs compared to principled solvers. Project page: https://cyanzhao42.github.io/LearnInverseProblem

Cited by

• 3DID: Direct 3D Inverse Design for Aerodynamics with Physics-Aware Optimization
• Semantic Joint Source Channel Coding for Distributed Subsurface Imaging in Multi-Agent Systems
• MaNGO - Adaptable Graph Network Simulators via Meta-Learning
• Numerical PDE solvers outperform neural PDE solvers

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