IP-Basis PINNs: Efficient Multi-Query Inverse Parameter Estimation

• URL: http://arxiv.org/abs/2509.07245v1
• Date: Mon, 08 Sep 2025 21:43:41 GMT
• Title: IP-Basis PINNs: Efficient Multi-Query Inverse Parameter Estimation
• Authors: Shalev Manor, Mohammad Kohandel,
• Abstract summary: We present Inverse- Basis PINNs (IP-Basis PINNs) to enable rapid and efficient inference for inverse problems.<n>Our method employs an offline-online decomposition: a deep network is first trained offline to produce a rich set of basis functions.<n>We demonstrate the efficacy of IP-Basis PINNs on three diverse benchmarks.
• Score: 0.764671395172401
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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