[2510.21852] Interpretable Diagnostics and Adaptive Data Assimilation for Neural ODEs via Discrete Empirical Interpolation

Computer Science > Machine Learning arXiv:2510.21852 (cs) [Submitted on 22 Oct 2025 (v1), last revised 2 Apr 2026 (this version, v2)] Title:Interpretable Diagnostics and Adaptive Data Assimilation for Neural ODEs via Discrete Empirical Interpolation Authors:Hojin Kim, Romit Maulik View a PDF of the paper titled Interpretable Diagnostics and Adaptive Data Assimilation for Neural ODEs via Discrete Empirical Interpolation, by Hojin Kim and Romit Maulik View PDF HTML (experimental) Abstract:We present a framework that leverages the Discrete Empirical Interpolation Method (DEIM) for interpretable deep learning and dynamical system analysis. Although DEIM efficiently approximates nonlinear terms in projection-based reduced-order models (POD-ROM), its fixed interpolation points are repurposed for identifying dynamically representative spatial structures in learned models. We apply DEIM as an interpretability tool to examine the learned dynamics of a pre-trained Neural Ordinary Differential Equation (NODE) for two-dimensional vortex-merging and backward-facing step flows. DEIM trajectories reveal physically meaningful structures in NODE predictions and expose failure modes when extrapolating to unseen flow configurations. Building on this diagnostic capability, we further introduce a DEIM-guided data assimilation strategy that injects sparse, dynamically representative corrections into the NODE rollout. By allocating a limited nudging budget to DEIM-identified sampling locations, ...