An Invariant Compiler for Neural ODEs in AI-Accelerated Scientific Simulation
arXiv:2603.23861v1 Announce Type: new 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 cleanl
arXiv:2603.23861v1 Announce Type: new 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.
Executive Summary
This article presents an invariant compiler for Neural ODEs, a framework that enforces invariants in continuous-time models by construction. By treating invariants as first-class types and utilizing an LLM-driven compilation workflow, the compiler translates a generic neural ODE specification into a structure-preserving architecture. This approach cleanly separates scientific structure from learned dynamics within that structure, providing a systematic design pattern for invariant-respecting neural surrogates. The invariant compiler addresses a critical issue in AI-accelerated scientific simulation, where unconstrained neural ODEs can drift and violate domain invariants, leading to physically implausible solutions and compounded error in long-horizon prediction.
Key Points
- ▸ Invariant compiler framework for Neural ODEs
- ▸ LLM-driven compilation workflow for structure-preserving architecture
- ▸ Clean separation of scientific structure and learned dynamics
Merits
Strength
The invariant compiler framework addresses a critical issue in AI-accelerated scientific simulation, ensuring physically plausible solutions and reducing error in long-horizon prediction.
Demerits
Limitation
The compiler's performance and scalability may be affected by the complexity of the neural ODE specification and the LLM-driven compilation workflow.
Expert Commentary
The invariant compiler framework is a significant contribution to the field of AI-accelerated scientific simulation, addressing a critical issue in Neural ODEs. By leveraging LLMs and treating invariants as first-class types, the compiler provides a systematic design pattern for invariant-respecting neural surrogates. While the compiler's performance and scalability may be affected by the complexity of the neural ODE specification, this limitation is outweighed by the framework's potential to improve the accuracy and reliability of AI-accelerated simulations. As the field continues to evolve, the invariant compiler framework is likely to become a crucial tool for researchers and practitioners seeking to develop more accurate and reliable models.
Recommendations
- ✓ Further research is needed to fully evaluate the performance and scalability of the invariant compiler framework in various scientific domains.
- ✓ The framework should be applied to real-world scientific simulations to demonstrate its effectiveness and potential impact on AI-accelerated scientific simulation.
Sources
Original: arXiv - cs.LG
