Inverse Neural Operator for ODE Parameter Optimization
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arXiv
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| Autori principali: | , , , , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866911508766654464 |
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| author | Liu, Zhi-Song Peng, Wenqing Toropainen, Helmi Kheder, Ammar Rupp, Andreas Froning, Holger Lin, Xiaojie Boy, Michael |
| author_facet | Liu, Zhi-Song Peng, Wenqing Toropainen, Helmi Kheder, Ammar Rupp, Andreas Froning, Holger Lin, Xiaojie Boy, Michael |
| contents | We propose the Inverse Neural Operator (INO), a two-stage framework for recovering hidden ODE parameters from sparse, partial observations. In Stage 1, a Conditional Fourier Neural Operator (C-FNO) with cross-attention learns a differentiable surrogate that reconstructs full ODE trajectories from arbitrary sparse inputs, suppressing high-frequency artifacts via spectral regularization. In Stage 2, an Amortized Drifting Model (ADM) learns a kernel-weighted velocity field in parameter space, transporting random parameter initializations toward the ground truth without backpropagating through the surrogate, avoiding the Jacobian instabilities that afflict gradient-based inversion in stiff regimes. Experiments on a real-world stiff atmospheric chemistry benchmark (POLLU, 25 parameters) and a synthetic Gene Regulatory Network (GRN, 40 parameters) show that INO outperforms gradient-based and amortized baselines in parameter recovery accuracy while requiring only 0.23s inference time, a 487x speedup over iterative gradient descent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_11854 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Inverse Neural Operator for ODE Parameter Optimization Liu, Zhi-Song Peng, Wenqing Toropainen, Helmi Kheder, Ammar Rupp, Andreas Froning, Holger Lin, Xiaojie Boy, Michael Machine Learning We propose the Inverse Neural Operator (INO), a two-stage framework for recovering hidden ODE parameters from sparse, partial observations. In Stage 1, a Conditional Fourier Neural Operator (C-FNO) with cross-attention learns a differentiable surrogate that reconstructs full ODE trajectories from arbitrary sparse inputs, suppressing high-frequency artifacts via spectral regularization. In Stage 2, an Amortized Drifting Model (ADM) learns a kernel-weighted velocity field in parameter space, transporting random parameter initializations toward the ground truth without backpropagating through the surrogate, avoiding the Jacobian instabilities that afflict gradient-based inversion in stiff regimes. Experiments on a real-world stiff atmospheric chemistry benchmark (POLLU, 25 parameters) and a synthetic Gene Regulatory Network (GRN, 40 parameters) show that INO outperforms gradient-based and amortized baselines in parameter recovery accuracy while requiring only 0.23s inference time, a 487x speedup over iterative gradient descent. |
| title | Inverse Neural Operator for ODE Parameter Optimization |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2603.11854 |