TNODEV: Toolbox for Neural ODE Verification

2026-06-15

AI Summary

Existing formal verification methods for neural ordinary differential equations (neural ODEs) suffer from limited accuracy and scalability, supporting only single-shot reachability analysis. This work proposes the first end-to-end verification framework for neural ODEs, integrating continuous-time mixed-monotonicity theory, interval-based reachability analysis, a counterexample-guided iterative refinement loop for input sets, and a parallel scheduling mechanism. The framework further introduces three heuristic strategies for input set partitioning. It supports diverse neural ODE architectures and safety specifications, demonstrating significant improvements over state-of-the-art tools NNV 2.0 and CORA on benchmark problems. Experimental results show that the approach substantially enhances both the precision and efficiency of verifying safety set inclusion and classification robustness for neural ODEs.

Abstract

Neural ordinary differential equations (neural ODE) have started to appear in safety critical settings such as continuous-time controllers for cyber-physical systems and classifiers integrated into automated decision pipelines, raising the question of whether their behavior can be formally verified. Existing tools dedicated to neural ODE provide only a single reachability call without iterative input set refinement, limiting the precision of their verdicts to whatever one reachability call can deliver. We present TNODEV, the first sound formal verifier for neural ODE that integrates a falsification checker, a fast interval-based reachability backend based on continuous-time mixed monotonicity, a verification and refinement loop with three input-set splitting heuristics, and a parallel scheduler in a single end-to-end pipeline. TNODEV supports safe-set inclusion verification on pure neural ODE, neural ODE in closed loop with a neural network controller and general neural ODE (GNODE), with the safe set specified either as an interval or as the half-space intersection induced by a target classification label. We evaluate TNODEV on a range of benchmarks across safe-set inclusion and classification-robustness properties, including a direct reachability comparison against NNV~2.0 and CORA and a verification comparison against NNV2.0 on MNIST general neural ODE classifiers.

Problem

• Neural ODE
• formal verification
• reachability analysis
• safety-critical systems
• input set refinement

Innovation

• Neural ODE
• formal verification
• reachability analysis
• input-set refinement
• mixed monotonicity