Algorithmic Differential Inversion for Regularized Training of Neural Differential Equations

Speaker: Gero Kauerauf, RWTH Aachen

Abstract

Training Neural Differential Equations often causes severe trajectory ill- conditioning and solver slowdowns. We present a matrix-free algorithmic differential inversion approach that efficiently computes and regularizes trajectory condition numbers during training. By expressing global linear solves as sequential step-level inverse sweeps, our method bypasses dense matrix storage or global iterative linear solves entirely. Experiments demonstrate order-of-magnitude cost reductions and accelerated trajectory integration.