| Abstract |
In this talk, we present a unified learning framework for inverse problems governed by wave and elliptic partial differential equations (PDEs), where the forward operator is unknown and no ground-truth interior data is available.
The key idea is to embed a physics-based forward solver directly into the training loop, enabling learning from boundary measurement data alone. This removes the need for supervised training pairs and allows simultaneous recovery of unknown quantities.
The framework is applied to three representative problems:
(1) a nonlinear photoacoustic model where the sound speed depends on the unknown initial pressure,
(2) a wave inverse problem with spatially varying unknown sound speed, connected to Calderón-type structures,
(3) an elliptic inverse problem based on the Dirichlet-to-Neumann map, where theoretical uniqueness is available.
Numerical results demonstrate robustness under noise. This work suggests a general paradigm for solving PDE inverse problems via physics-informed self-supervised learning. |
