Inverse Neural Operator for ODE Parameter Optimization

2026-03-12

AI Summary

This work addresses the challenge of recovering unknown parameters of implicit ordinary differential equations (ODEs) from sparse, partially observed data by proposing a two-stage framework termed INO. First, a conditional Fourier Neural Operator with cross-attention (C-FNO) reconstructs complete system trajectories. Subsequently, an Amortized Drift Model (ADM) directly guides an initial parameter guess toward the true values in parameter space, circumventing backpropagation through surrogate models. The approach incorporates spectral regularization to suppress high-frequency artifacts and effectively mitigates Jacobian instability during gradient-based inversion in stiff systems. Evaluated on the POLLU (25-parameter) and GRN (40-parameter) benchmarks, INO significantly outperforms existing methods, achieving inference in only 0.23 seconds—487 times faster than iterative gradient descent.

Technology Category

• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

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.

Problem

• ODE parameter recovery
• sparse observations
• inverse problem
• parameter estimation
• hidden dynamics

Innovation

• Inverse Neural Operator
• Conditional Fourier Neural Operator
• Amortized Drifting Model
• ODE parameter recovery
• spectral regularization