Interpretable AI-Assisted Early Reliability Prediction for a Two-Parameter Parallel Root-Finding Scheme

TL;DR

This paper introduces an interpretable AI framework that predicts the stability of a root-finding solver early in its iteration process, enabling timely decisions to improve computational efficiency.

Contribution

It presents a novel AI-assisted reliability diagnostic method combining proxy stability profiling and machine learning for early prediction in parameterized root-finding schemes.

Findings

Reliable early prediction achieved with high R^2 scores at few iterations

Predictive accuracy improves significantly with larger horizons

Inference costs are negligible, enabling real-time application

Abstract

We propose an interpretable AI-assisted reliability diagnostic framework for parameterized root-finding schemes based on kNN-LLE proxy stability profiling and multi-horizon early prediction. The approach augments a numerical solver with a lightweight predictive layer that estimates solver reliability from short prefixes of iteration dynamics, enabling early identification of stable and unstable parameter regimes. For each configuration in the parameter space, raw and smoothed proxy profiles of a largest Lyapunov exponent (LLE) estimator are constructed, from which contractivity-based reliability scores summarizing finite-time convergence are derived. Machine learning models predict the reliability score from early segments of the proxy profile, allowing the framework to determine when solver dynamics become diagnostically informative. Experiments on a two-parameter parallel root-finding scheme show reliable prediction after only a few iterations: the best models achieve R^2=0.48 at horizon T=1, improve to R^2=0.67 by T=3, and exceed R^2=0.89 before the characteristic minimum-location scale of the stability profile. Prediction accuracy increases to R^2=0.96 at larger horizons, with mean absolute errors around 0.03, while inference costs remain negligible (microseconds per sample). The framework provides interpretable stability indicators and supports early decisions during solver execution, such as continuing, restarting, or adjusting parameters.