Self-induced stochastic resonance (SISR) is the emergence of coherent oscillations in slow-fast excitable systems driven solely by noise, without external periodic forcing or proximity to a bifurcation. This work presents a physics-informed machine learning framework for modeling and predicting SISR in the stochastic FitzHugh-Nagumo neuron. We embed the governing stochastic differential equations and SISR-asymptotic timescale-matching constraints directly into a Physics-Informed Neural Network (PINN) based on a Noise-Augmented State Predictor architecture. The composite loss integrates data fidelity, dynamical residuals, and barrier-based physical constraints derived from Kramers' escape theory. The trained PINN accurately predicts the dependence of spike-train coherence on noise intensity, excitability, and timescale separation, matching results from direct stochastic simulations with substantial improvements in accuracy and generalization compared with purely data-driven methods, while requiring significantly less computation. The framework provides a data-efficient and interpretable surrogate model for simulating and analyzing noise-induced coherence in multiscale stochastic systems.

翻译：自诱导随机共振（SISR）是指仅由噪声驱动、无需外部周期强迫或接近分岔点的慢-快可激发系统中出现相干振荡的现象。本研究提出了一种基于物理信息的机器学习框架，用于建模和预测随机FitzHugh-Nagumo神经元中的SISR。我们将控制随机微分方程和SISR渐近时间尺度匹配约束直接嵌入到基于噪声增强状态预测器架构的物理信息神经网络（PINN）中。复合损失函数整合了数据保真度、动力学残差以及基于Kramers逃逸理论推导的势垒物理约束。训练后的PINN能够准确预测脉冲序列相干性对噪声强度、可激发性和时间尺度分离的依赖关系，其结果与直接随机模拟相匹配，相比纯数据驱动方法在精度和泛化能力上均有显著提升，同时计算需求大幅降低。该框架为模拟和分析多尺度随机系统中噪声诱导的相干性提供了一个数据高效且可解释的代理模型。