IP-Basis PINNs: Efficient Multi-Query Inverse Parameter Estimation
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| Format: | Preprint |
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2025
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| _version_ | 1866909778273370112 |
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| author | Manor, Shalev Kohandel, Mohammad |
| author_facet | Manor, Shalev Kohandel, Mohammad |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_07245 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | IP-Basis PINNs: Efficient Multi-Query Inverse Parameter Estimation Manor, Shalev Kohandel, Mohammad Machine Learning 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. |
| title | IP-Basis PINNs: Efficient Multi-Query Inverse Parameter Estimation |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2509.07245 |