Interpretable AI-Assisted Early Reliability Prediction for a Two-Parameter Parallel Root-Finding Scheme
This addresses the problem of early reliability prediction for numerical solvers, enabling decisions like continuing or adjusting parameters, but it is incremental as it builds on existing methods for stability profiling.
The paper tackles the problem of predicting the reliability of a two-parameter parallel root-finding scheme early during solver execution, using an interpretable AI-assisted framework that estimates reliability from short iteration dynamics. The result shows reliable prediction after only a few iterations, with R^2 reaching 0.67 by T=3 and exceeding 0.89 before the stability profile's minimum-location scale, and accuracy improves to R^2=0.96 at larger horizons with mean absolute errors around 0.03.
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.