[2603.23861] An Invariant Compiler for Neural ODEs in AI-Accelerated Scientific Simulation

Computer Science > Machine Learning arXiv:2603.23861 (cs) [Submitted on 25 Mar 2026] Title:An Invariant Compiler for Neural ODEs in AI-Accelerated Scientific Simulation Authors:Fangzhou Yu, Yiqi Su, Ray Lee, Shenfeng Cheng, Naren Ramakrishnan View a PDF of the paper titled An Invariant Compiler for Neural ODEs in AI-Accelerated Scientific Simulation, by Fangzhou Yu and 4 other authors View PDF HTML (experimental) Abstract:Neural ODEs are increasingly used as continuous-time models for scientific and sensor data, but unconstrained neural ODEs can drift and violate domain invariants (e.g., conservation laws), yielding physically implausible solutions. In turn, this can compound error in long-horizon prediction and surrogate simulation. Existing solutions typically aim to enforce invariance by soft penalties or other forms of regularization, which can reduce overall error but do not guarantee that trajectories will not leave the constraint manifold. We introduce the invariant compiler, a framework that enforces invariants by construction: it treats invariants as first-class types and uses an LLM-driven compilation workflow to translate a generic neural ODE specification into a structure-preserving architecture whose trajectories remain on the admissible manifold in continuous time (and up to numerical integration error in practice). This compiler view cleanly separates what must be preserved (scientific structure) from what is learned from data (dynamics within that structure...