$S^3$: A Smooth Simulation Surrogate for Optimizing Discrete Abstractions of Dynamical Systems

2026-08-16

AI Summary

This study addresses the challenge of balancing soundness and conservatism in discrete abstractions of dynamic systems by proposing Smooth Simulation Surrogate ($S^3$). By integrating Taylor model reachability analysis, $S^3$ constructs a differentiable objective function to approximate inverse simulation metrics, enabling gradient-based optimization of abstraction parameters while theoretically guaranteeing soundness. Compared to conventional approaches, $S^3$ significantly reduces abstraction conservatism without compromising soundness and achieves superior computational efficiency. Consequently, this work establishes a novel paradigm for high-precision system verification that effectively reconciles safety guarantees with accuracy requirements.

Abstract

Intelligent systems are increasingly deployed in safety-critical settings with black-box controllers, including neural networks. The properties and behaviors of these end-to-end systems can be studied with abstraction-based methods that replace them with simpler finite models. Constructing such abstractions requires balancing the soundness of over-approximating the dynamical system against conservatism, which manifests as spurious or excessive nondeterministic behaviors. Bi-simulation theory provides principled metrics for characterizing these relationships, but does not prescribe how to construct sound abstractions with minimal conservatism. We fill this gap with a smooth simulation surrogate ($S^3$) --- a differentiable objective that approximates the reverse simulation metric used to quantify conservatism. Combined with Taylor model-based reachability, $S^3$ enables gradient-based optimization of abstraction parameters while preserving soundness by construction. We evaluate this optimization pipeline on three case studies. Our results show that $S^3$ is strongly correlated with the reverse simulation metric, is computationally faster, and serves as an effective objective for reducing abstraction conservatism.

Problem

• Discrete Abstraction
• Dynamical Systems
• Conservatism
• Bi-simulation
• Soundness

Innovation

• Smooth Simulation Surrogate
• Differentiable Optimization
• Discrete Abstraction
• Reverse Simulation Metric
• Taylor Model Reachability