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arXiv Machine Learning By Ryoichiro Agata, Tomohisa Okazaki

Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks

Read the original on arXiv Machine Learning →

arXiv:2605. 07060v3 Announce Type: replace-cross Abstract: Physics-informed neural networks (PINNs) provide a mesh-free framework for solving PDE-constrained inverse problems, but their extension to Bayesian inversion still faces a fundamental difficulty: prior distributions are typically defined in the weight space of neural networks, whereas physically meaningful prior assumptions are more naturally expressed in function space.

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