发表机构
Occidental College（西方学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对FitzHugh-Nagumo系统，用参数条件傅里叶神经算子作为快速可微代理，在两种动力学状态下实现高精度、高速度的模拟，可用于神经调节相关的参数扫描。
AI 中文摘要
FitzHugh-Nagumo（FHN）系统是神经元电压动力学的简化模型，可捕捉孤立动作电位及大脑节律性放电背后的激活-抑制结构。探索其5维生理参数空间对神经调节和将电压记录映射回生物物理学具有重要意义，但传统有限差分求解器使快速参数扫描成本高昂。我们训练参数条件傅里叶神经算子（FNO）作为FHN电压和恢复场的快速可微代理，用于一维空间域，通过特征-wise线性调制（FiLM）将每个傅里叶层条件化为参数向量λ=(D_u, D_v, a, b, τ)。我们应用一次分岔分析界定模型跨越的两种不同状态：振荡（紧张性放电）和可激发（动作电位传播），并为每种状态训练一个算子。在振荡状态下，该代理在两个场上均达到低于0.1%的相对L²误差，运行速度比有限差分基线快近三个数量级，在参数空间上均匀泛化，并在训练范围外外推至低个位数百分比误差。在可激发状态下，同一算子准确再现放电阈值和c∝√D_u传导速度定律，并复制完整的传播脉冲，完全捕捉可激发分岔结构，而非仅平滑插值场。
英文摘要
The FitzHugh-Nagumo (FHN) system serves as a simplified model of neuronal voltage dynamics, capturing the activator-inhibitor structure behind both isolated action potentials and the rhythmic spiking seen across the brain. Exploring its 5D physiological parameter space is important for neuromodulation and mapping voltage recordings back to biophysics, yet classical finite-difference solvers make rapid parameter sweeps expensive. We train parameter-conditioned Fourier Neural Operators (FNOs) as fast, differentiable surrogates for the FHN voltage and recovery fields on a one-dimensional spatial domain, conditioning each Fourier layer on the parameter vector $λ= (D_u, D_v, a, b, τ)$ via feature-wise linear modulation (FiLM). We apply a single bifurcation analysis that delimits the two distinct regimes the model spans, oscillatory (tonic firing) and excitable (action-potential propagation), and we train one operator in each. In the oscillatory regime the surrogate attains sub-$0.1\%$ relative $L^2$ error on both fields, runs nearly three orders of magnitude faster than the finite-difference baseline, generalizes uniformly across the parameter space, and extrapolates to low single-digit percentage errors outside of the training bounds. In the excitable regime the same operator accurately reproduces the firing threshold and the $c \propto \sqrt{D_u}$ conduction-velocity law and replicates full traveling pulses, fully capturing the excitable bifurcation structure rather than just smoothly interpolating fields.
CommentsHuman Brain & AI @ International Joint Conferences on Artificial Intelligence (IJCAI) 2026
