Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks
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. In this study, we introduce a unified framework, termed functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks (fpBPINN), to incorporate functional priors into Bayesian PINN-based inversion. We consider two complementary approaches. The first is a functional-prior-i...
| Authors | Ryoichiro Agata, Tomohisa Okazaki |
|---|---|
| Primary category | physics.geo-ph |
| Published | 8 May 2026 |
| Last updated at source | 13 August 2026 |
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