Automatic Differentiation with Constraints in Forward and Inverse Problems
Approximate solutions of partial differential equations (PDEs) on unstructured grids can be represented on a graph. Numerical optimization involving stiff evolutionary and static PDEs often requires solving a large system of equations, which can be treated as a constraint. In this work, we present a fully differentiable graph-based implicit solver that incorporates this constraint. We evaluate its performance across four key tasks: a) linear and nonlinear forward modeling of evolutionary and static problems, b) solving inverse problems to estimate equation coefficients, c) solving inverse problems to estimate the right-hand side, and d) learnable graph coarsening to accelerate forward mod...
| Authors | Nikolay Yavich, Alexander Ryabov, Viacheslav Naumov et al. |
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| Primary category | cs.AI |
| Published | 20 October 2026 |
| Last updated at source | 20 October 2026 |
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