Transformer-Accelerated Interpolated Data-Driven Reachability Analysis from Noisy Data

TL;DR

This paper introduces a novel data-driven reachability analysis method called IRA, which leverages multi-resolution interpolation and Transformer acceleration to improve scalability and provide rigorous guarantees from noisy data.

Contribution

The paper proposes IRA and TA-IRA, combining multi-resolution interpolation with Transformer-based acceleration, enabling scalable, data-driven reachability analysis with theoretical guarantees from noisy measurements.

Findings

IRA achieves significant computational savings in reachability analysis.

TA-IRA provides finite-sample coverage certificates using Transformer models.

Numerical experiments confirm the theoretical guarantees and efficiency improvements.

Abstract

Data-driven reachability analysis provides guaranteed outer approximations of reachable sets from input-state measurements, yet each propagation step requires a matrix-zonotope multiplication whose cost grows with the horizon length, limiting scalability. We observe that data-driven propagation is inherently step-size sensitive, in the sense that set-valued operators at different discretization resolutions yield non-equivalent reachable sets at the same physical time, a property absent in model-based propagation. Exploiting this multi-resolution structure, we propose Interpolated Reachability Analysis (IRA), which computes a sparse chain of coarse anchor sets sequentially and reconstructs fine-resolution intermediate sets in parallel across coarse intervals. We derive a fully data-driven coarse-noise over-approximation that removes the need for continuous-time system knowledge, prove deterministic outer-approximation guarantees for all interpolated sets, and establish conditional tightness relative to the fine-resolution chain. To replace the remaining matrix-zonotope multiplications in the fine phase, we further develop Transformer-Accelerated IRA (TA-IRA), where an encoder-decoder Transformer is calibrated via split conformal prediction to provide finite-sample pointwise and path-wise coverage certificates. Numerical experiments on a five-dimensional linear system confirm the theoretical guarantees and demonstrate significant computational savings.