模拟神经形态电路的算子理论框架
An Operator-Theoretic Framework to Simulate Neuromorphic Circuits
AI总结：
本文提出一种算子理论分裂框架，将神经形态电路分解为LTI无损耗与静态电阻部分，实现时域和频域分离计算，并通过百神经元FitzHugh-Nagumo网络验证其可扩展性。
摘要：
分裂算法在凸优化中已得到充分确立，旨在解决大规模问题。利用此类算法模拟非线性电路网络的行为，为神经形态系统的模拟与设计提供了可扩展的方法。针对由线性电容和电感以及非线性电阻元件构成的电路，我们提出一种分裂方法，将网络分解为其LTI无损耗分量和静态电阻分量。这种分裂在物理和算法上均具有优势，并允许在时域和频域中分别进行计算。为展示该方法的可扩展性，我们模拟了一个由一百个神经元组成的网络，这些神经元采用著名的FitzHugh-Nagumo电路建模，并具有全对全扩散耦合。
英文摘要：
Splitting algorithms are well-established in convex optimization and are designed to solve large-scale problems. Using such algorithms to simulate the behavior of nonlinear circuit networks provides scalable methods for the simulation and design of neuromorphic systems. For circuits made of linear capacitors and inductors with nonlinear resistive elements, we propose a splitting that breaks the network into its LTI lossless component and its static resistive component. This splitting has both physical and algorithmic advantages and allows for separate calculations in the time domain and in the frequency domain. To demonstrate the scalability of this approach, a network made from one hundred neurons modeled by the well-known FitzHugh-Nagumo circuit with all-to-all diffusive coupling is simulated.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
