Inverse Neural Operator for ODE Parameter Optimization

• URL: http://arxiv.org/abs/2603.11854v1
• Date: Thu, 12 Mar 2026 12:20:23 GMT
• Title: Inverse Neural Operator for ODE Parameter Optimization
• Abstract summary: Inverse Neural Operator (INO) is a framework for recovering hidden ODE parameters from sparse, partial observations.<n>INO outperforms gradient-based and amortized baselines in parameter recovery accuracy while requiring only 0.23s inference time.
• Score: 6.148294495010685
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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