Differentiable Implicit Solver on Graph Neural Networks for Forward and Inverse Problems
Keywords: Graph Neural Networks, Differentiable solvers, Implicit schemes, Numerical modelling, Inverse problems
TL;DR: We integrated graph neural networks (GNNs), the finite-volume method, implicit time-stepping to develop a fully differentiable modeling pipeline and applied it to forward and inverse problems of geoscience.
Abstract: Partial differential equations (PDEs) on unstructured grids can be solved using message passing on a graph neural network (GNN). Implicit time-stepping schemes are often favored, especially for parabolic PDEs, due to their stability properties. In this work, we develop a fully differentiable implicit solver for unstructured grids. We evaluate its performance across four key tasks: a) forward modeling of stiff evolutionary and static problems; b) the inverse problem of estimating equation coefficients; c) the inverse problem of estimating the right-hand side; and d) graph coarsening to accelerate forward modeling. The increased stability and differentiability of our solver enable excellent results in reducing the complexity of forward modeling and efficiently solving related inverse problems. This makes it a promising tool for geoscience and other physics-based applications.
Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)
Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.
Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2025/AuthorGuide.
Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.
No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.
Submission Number: 10796
Loading