Inverse Neural Operator for ODE Parameter Optimization
This addresses parameter optimization in stiff ODE systems like atmospheric chemistry, offering a faster and more accurate solution, though it is incremental as it builds on neural operator methods.
The paper tackles the problem of recovering hidden ODE parameters from sparse, partial observations by proposing the Inverse Neural Operator (INO), a two-stage framework that outperforms baselines in accuracy and achieves a 487x speedup with 0.23s inference time.
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.