忆阻 FitzHugh--Nagumo 神经网络的连续数据同化
Continuous Data Assimilation for Memristive FitzHugh--Nagumo Neural Networks
- Towson University（托森大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究忆阻 FitzHugh--Nagumo 神经网络的连续数据同化，提出仅向膜电位方程添加反馈的 nudging 算法，证明指数收敛和能量类唯一性，并给出噪声误差界。
AI中文摘要：
在本研究中，我们研究了一类具有忆阻反馈和线性突触耦合的部分扩散 FitzHugh--Nagumo 神经网络的连续数据同化。这里实施的 nudging 算法仅向膜电位方程添加反馈项，而恢复变量和忆导变量仍未被观测。我们获得了加权能量估计，这些估计给出了在全膜电位或粗膜电位观测下，数据同化解指数收敛到参考解的充分条件。此外，我们证明了在一维和二维中的能量类唯一性。在三维中，唯一性判据是膜电位初始数据的 L^4 可积性。我们还建立了局部平方可积强迫的观测噪声估计，当噪声能量最终有界时，产生渐近误差界。
英文摘要：
In this study, we investigate continuous data assimilation for a class of partly diffusive FitzHugh--Nagumo neural networks with memristive feedback and linear synaptic coupling. The nudging algorithm implemented here only adds a feedback term to the membrane-potential equations, while the recovery and memductance variables remain unobserved. We obtain weighted energy estimates that give sufficient conditions for exponential convergence of the data-assimilated solution to the reference solution under full or coarse membrane potential observations. Moreover, we prove energy-class uniqueness in dimensions one and two. In dimension three, the uniqueness criterion is an \(L^4\) membrane-potential initial data. We also establish an observational-noise estimate for locally square-integrable forcing, yielding an asymptotic error bound when the noise energy is eventually bounded.
