Physics-constrained prediction of first-passage-time distributions in a strongly nonlinear stochastic Φ6 oscillator

Abstract

Accurate reconstruction of first-passage-time (FPT) distributions is essential for time-dependent reliability analysis of nonlinear stochastic systems but is costly when repeated large-scale Monte Carlo simulations are required. This study proposes a physics-constrained hybrid surrogate for a stochastic ${\Phi }^6$ oscillator. An energy-based three-parameter form represents the FPT density. Target-specific, dimensionally consistent features are derived using the Buckingham $\pi$ theorem. Ridge regression predicts the three density parameters, and separate Gaussian process models correct their residuals. The model is evaluated on fixed in-distribution (ID) and directional out-of-distribution (OOD) test sets generated by directional extrapolation. For the 69 samples yielding admissible predictions from both models, the hybrid model increases the median PDF-level $R^2$ from 0.9185 to 0.9633. It reduces the median Kolmogorov–Smirnov statistic, AD-type discrepancy, and Wasserstein $W_1$ distance from 0.0719 to 0.0463, from 1.9625 to 0.4224, and from 3.6966 s to 1.6214 s, respectively. The ridge baseline and hybrid model yield admissible parameter triplets for 81 and 82 of 100 test samples, respectively. These results demonstrate improved FPT distribution reconstruction on the common admissible subset, while the remaining inadmissible predictions indicate that parameter admissibility can be further improved.