mlsanityData to 14 Oct 2026

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

arXiv 2603.23861 ↗First posted 25 Mar 2026cs.LGcited by 0

Not on the map. Why?

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.

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

26 of 70 references.

References · 26

  1. 2018Neural Ordinary Differential Equationscited by 3,779
  2. 2021Convex optimizationcited by 2,515
  3. 2021Geometric Deep Learning: Grids, Groups, Graphs, Geodesics, and Gaugescited by 1,167
  4. 2019Hamiltonian Neural Networkscited by 712
  5. 2019AI Feynman: a Physics-Inspired Method for Symbolic Regressioncited by 548
  6. 2016Interaction Networks for Learning about Objects, Relations and Physicscited by 509
  7. 2020Lagrangian Neural Networkscited by 398
  8. 2019Augmented Neural ODEscited by 397
  9. 2019Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learningcited by 212
  10. 2021A Practical Method for Constructing Equivariant Multilayer Perceptrons for Arbitrary Matrix Groupscited by 187
  11. 2021E(n) Equivariant Normalizing Flowscited by 165
  12. 2020Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraintscited by 105
14 more
  1. 2022Do Differentiable Simulators Give Better Policy Gradients?cited by 89
  2. 2020Neural Manifold Ordinary Differential Equationscited by 81
  3. 2021Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systemscited by 67
  4. 2020A Probabilistic Graphical Model Foundation for Enabling Predictive Digital Twins at Scalecited by 58
  5. 2021GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systemscited by 49
  6. 2019Neural Dynamics on Complex Networkscited by 38
  7. 2020Learning Poisson systems and trajectories of autonomous systems via Poisson neural networkscited by 38
  8. 2020Neural Ordinary Differential Equations on Manifoldscited by 31
  9. 2022Guaranteed Conservation of Momentum for Learning Particle-based Fluid Dynamicscited by 30
  10. 2020Autonomous Discovery of Unknown Reaction Pathways from Data by Chemical Reaction Neural Networkcited by 27
  11. 2020SINDy-BVP: Sparse Identification of Nonlinear Dynamics for Boundary Value Problemscited by 22
  12. 2022FINDE: Neural Differential Equations for Finding and Preserving Invariant Quantitiescited by 12
  13. 2018Fixed-Time Stable Gradient Flows: Applications to Continuous-Time Optimizationcited by 10
  14. 2025Semi-Explicit Neural DAEs: Learning Long-Horizon Dynamical Systems with Algebraic Constraintscited by 4

Built on by

Not cited yet.