Inverse Neural Operator for ODE Parameter Optimization

TL;DR

The paper introduces INO, a two-stage neural framework that efficiently recovers ODE parameters from sparse data, outperforming traditional methods in accuracy and speed, especially in stiff regimes.

Contribution

The paper presents a novel two-stage approach combining a spectral-regularized neural surrogate and an amortized velocity model for fast, stable ODE parameter inference.

Findings

Outperforms gradient-based methods in accuracy.

Achieves 487x faster inference than iterative gradient descent.

Effective on real-world and synthetic benchmarks.

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.