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.
@article{arxiv.2603.11854,
title = {Inverse Neural Operator for ODE Parameter Optimization},
author = {Zhi-Song Liu and Wenqing Peng and Helmi Toropainen and Ammar Kheder and Andreas Rupp and Holger Froning and Xiaojie Lin and Michael Boy},
journal= {arXiv preprint arXiv:2603.11854},
year = {2026}
}