Efficient Message Passing for Partial Differential Equation Priors
Prior information for real-world physical quantities is most elegantly expressed via partial differential equations (PDEs). In this paper, we propose a novel way to solve PDEs using probabilistic inference on a factor graph. In general, factor graphs provide a natural way to encode prior knowledge into a model as explicit factors; here, this knowledge is provided by a governing PDE, which narrows the solution space, while observed data further shape the posterior over the parameters. The approximate parameter posterior is inferred using message passing based on moment matching, without posterior sampling or global gradient-based optimization. We demonstrate our approach on the first-order...
| Authors | Anna Kazachkova, Leonhard Hennicke, Rainer Schlosser et al. |
|---|---|
| Primary category | cs.LG |
| Published | 26 September 2026 |
| Last updated at source | 26 September 2026 |
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