用物理约束神经网络模拟噪声引发的神经元同步振荡。
Self-induced stochastic resonance: A physics-informed machine learning approach
- 将随机微分方程与逃逸理论约束嵌入神经网络，实现物理可解释建模。
- 准确预测噪声强度、兴奋性与时间尺度对放电相干性的影响。
- 数据效率高、计算量小，适合多尺度随机系统分析。
自诱导随机共振（SISR）是慢-快激发系统在仅由噪声驱动下自发产生有序振荡的现象，无需外部周期激励或接近分岔点。本文提出一种基于噪声增强状态预测器的物理信息神经网络（PINN）框架，用于建模和预测随机福克-赫尔姆霍兹神经元中的SISR。通过直接嵌入控制方程及基于克兰默斯逃逸理论的渐近时间尺度匹配约束，构建包含数据保真度、动力学残差与屏障型物理约束的复合损失函数。训练后的PINN能精确预测尖峰序列相干性随噪声强度、兴奋性及时间尺度分离度的变化规律，其精度与泛化能力显著优于纯数据驱动方法，且计算开销大幅降低。该框架为多尺度随机系统中噪声诱导相干性的仿真与分析提供了高效可解释的代理模型。
原文摘要 · Abstract (English)
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.
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