OCL-PDE: A Generative Framework for PDE Inverse Problems with Observation-Complementary Latents

Abstract:Partial differential equation (PDE) inverse problems are often ill-posed, making fine-scale details difficult to recover. We address this problem by introducing a learned observation-complementary latent representation that preserves reconstruction-relevant information and is combined with the observation to reconstruct the unknown field. Building on this representation, we propose OCL-PDE, a generative framework that encourages the observation to guide large-scale structure and the latent to supply complementary fine-scale details. OCL-PDE is built on a physics-aware autoencoder (AE) and conditional Flow Matching, supporting inverse reconstruction as well as forward PDE prediction. Experiments demonstrate improved reconstruction accuracy and fine-detail recovery compared with the evaluated baselines.

Machine Learning (cs.LG)

arXiv:2610.06259 [cs.LG]

(or arXiv:2610.06259v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.06259 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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