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

arXiv: https://arxiv.org/abs/2603.23861 · HTML: https://mlsanity.com/paper/2603.23861/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 26 of its 70 references that are in the map.
- First posted on arXiv 25 Mar 2026.

## Builds on (most cited first, 26 of 26)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gauges](https://mlsanity.com/paper/2104.13478/) (2021)
- [Hamiltonian Neural Networks](https://mlsanity.com/paper/1906.01563/) (2019)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Interaction Networks for Learning about Objects, Relations and Physics](https://mlsanity.com/paper/1612.00222/) (2016)
- [Lagrangian Neural Networks](https://mlsanity.com/paper/2003.04630/) (2020)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning](https://mlsanity.com/paper/1907.04490/) (2019)
- [A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groups](https://mlsanity.com/paper/2104.09459/) (2021)
- [E(n) Equivariant Normalizing Flows](https://mlsanity.com/paper/2105.09016/) (2021)
- [Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraints](https://mlsanity.com/paper/2010.13581/) (2020)
- [Do Differentiable Simulators Give Better Policy Gradients?](https://mlsanity.com/paper/2202.00817/) (2022)
- [Neural Manifold Ordinary Differential Equations](https://mlsanity.com/paper/2006.10254/) (2020)
- [Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems](https://mlsanity.com/paper/2107.08024/) (2021)
- [A Probabilistic Graphical Model Foundation for Enabling Predictive Digital Twins at Scale](https://mlsanity.com/paper/2012.05841/) (2020)
- [GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systems](https://mlsanity.com/paper/2109.00092/) (2021)
- [Neural Dynamics on Complex Networks](https://mlsanity.com/paper/1908.06491/) (2019)
- [Learning Poisson systems and trajectories of autonomous systems via Poisson neural networks](https://mlsanity.com/paper/2012.03133/) (2020)
- [Neural Ordinary Differential Equations on Manifolds](https://mlsanity.com/paper/2006.06663/) (2020)
- [Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamics](https://mlsanity.com/paper/2210.06036/) (2022)
- [Autonomous Discovery of Unknown Reaction Pathways from Data by Chemical Reaction Neural Network](https://mlsanity.com/paper/2002.09062/) (2020)
- [SINDy-BVP: Sparse Identification of Nonlinear Dynamics for Boundary Value Problems](https://mlsanity.com/paper/2005.10756/) (2020)
- [FINDE: Neural Differential Equations for Finding and Preserving Invariant Quantities](https://mlsanity.com/paper/2210.00272/) (2022)
- [Fixed-Time Stable Gradient Flows: Applications to Continuous-Time Optimization](https://mlsanity.com/paper/1808.10474/) (2018)
- [Semi-Explicit Neural DAEs: Learning Long-Horizon Dynamical Systems with Algebraic Constraints](https://mlsanity.com/paper/2505.20515/) (2025)

## Abstract (arXiv)

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.