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

2026-03-24

AI Summary

This work addresses the tendency of unconstrained neural ordinary differential equations (Neural ODEs) to violate domain-specific invariants—such as physical conservation laws—in scientific simulations, leading to distorted long-term predictions. To resolve this, the authors propose an invariance compiler framework that, for the first time, treats scientific invariants as first-class constructs in Neural ODE architecture design. Leveraging large language model–driven program synthesis, the framework automatically transforms generic Neural ODE specifications into structure-preserving models whose trajectories remain strictly confined to valid manifolds. By construction, the resulting models guarantee physical consistency—subject only to numerical integration error—without requiring post-hoc regularization, and they enforce prescribed invariants exactly in continuous time. This approach significantly enhances the credibility and physical plausibility of long-term simulations and establishes a systematic, cross-domain design paradigm for invariant-aware scientific machine learning.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Natural Language Processing: Code Generation / Program Synthesis from Natural Language
• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs

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). It provides a systematic design pattern for invariant-respecting neural surrogates across scientific domains.

Problem

• Neural ODEs
• domain invariants
• conservation laws
• physically implausible solutions
• long-horizon prediction

Innovation

• Invariant Compiler
• Neural ODEs
• Structure-Preserving Architecture
• Scientific Simulation
• LLM-Driven Compilation