IP-Basis PINNs: Efficient Multi-Query Inverse Parameter Estimation
This work addresses efficiency challenges for researchers and practitioners using PINNs for inverse parameter estimation, though it is incremental as it builds on prior foundational work.
The paper tackles the computational expense of solving inverse problems with Physics-Informed Neural Networks (PINNs) in multi-query scenarios by introducing IP-Basis PINNs, a meta-learning framework that achieves significant speedup per query over standard PINNs while maintaining robust performance with scarce and noisy data.
Solving inverse problems with Physics-Informed Neural Networks (PINNs) is computationally expensive for multi-query scenarios, as each new set of observed data requires a new, expensive training procedure. We present Inverse-Parameter Basis PINNs (IP-Basis PINNs), a meta-learning framework that extends the foundational work of Desai et al. (2022) to enable rapid and efficient inference for inverse problems. Our method employs an offline-online decomposition: a deep network is first trained offline to produce a rich set of basis functions that span the solution space of a parametric differential equation. For each new inverse problem online, this network is frozen, and solutions and parameters are inferred by training only a lightweight linear output layer against observed data. Key innovations that make our approach effective for inverse problems include: (1) a novel online loss formulation for simultaneous solution reconstruction and parameter identification, (2) a significant reduction in computational overhead via forward-mode automatic differentiation for PDE loss evaluation, and (3) a non-trivial validation and early-stopping mechanism for robust offline training. We demonstrate the efficacy of IP-Basis PINNs on three diverse benchmarks, including an extension to universal PINNs for unknown functional terms-showing consistent performance across constant and functional parameter estimation, a significant speedup per query over standard PINNs, and robust operation with scarce and noisy data.