用于能量计算的非线性深度电阻网络的快速仿真

中文摘要 AI 辅助

深度电阻网络是电子能量系统，其计算由非线性电路的稳态电压完成。非线性器件能够实现表达力强的输入输出变换，但在仿真和训练过程中，电路平衡点的计算成本高昂。最近的坐标下降求解器相对于SPICE类电路仿真器实现了大幅加速，但仅适用于理想二极管模型所建模的非线性。这种数学简化对于实际模拟电路是不够的。在此，我们将坐标下降仿真扩展到实际的单调非线性，包括肖克利二极管、反向并联二极管对和分段线性电流-电压特性。在相邻电压固定的情况下，每个节点更新仍然是标量基尔霍夫定律求解。单指数特性允许闭式朗伯W更新，而更一般的单调特性可以用标量求根方法处理。在具有一到三个隐藏层且隐藏宽度从64到1024的网络中，该求解器复现了匹配的SPICE稳态电压，90%的验证样本的相对L1误差低于1.1×10⁻⁴，同时实现了高达1.7×10³的加速比。我们进一步在MNIST上训练了一个1568×100×20的双肖克利网络，测试误差达到约3.0%，并将每轮训练时间减少了约4.4×10²倍。总之，这些结果为包含实际非线性器件的大规模模拟能量系统的电路级设计和训练建立了一条实用途径。

英文摘要

Deep resistive networks are electronic energy-based systems in which computation is performed by the steady-state voltages of nonlinear circuits. Nonlinear devices enable expressive input-output transformations, but make the circuit equilibria costly to compute during simulation and training. Recent coordinate-descent solvers have achieved large speedups over SPICE-class circuit simulators, but only for nonlinearities modeled as ideal-diode models. This mathematical simplification is not sufficient for practical analog circuits. Here we extend coordinate-descent simulation to realistic monotone nonlinearities, including Shockley diodes, antiparallel diode pairs, and piecewise-linear current-voltage characteristics. With neighboring voltages fixed, each node update remains a scalar Kirchhoff-law solve. Single-exponential characteristics admit closed-form Lambert-(W) updates, while more general monotone characteristics can be handled with scalar root-finding methods. Across networks with one to three hidden layers and hidden widths from 64 to 1024, the solver reproduces matched SPICE steady-state voltages with relative $L_1$ errors below $1.1\times10^{-4}$ for 90% of validation samples, while achieving speedups up to $(1.7\times10^3)$. We further train a $1568\times100\times20$ double-Shockley network on MNIST, reaching about 3.0% test error and reducing the per-epoch training time by roughly $4.4\times10^2$. Together, these results establish a practical route to the circuit-level design and training of large-scale analog energy-based systems incorporating realistic nonlinear devices.

发表机构

• Université Paris-Saclay（巴黎萨克雷大学）
• CNRS, Centre de Nanosciences et de Nanotechnologies（法国国家科学研究中心，纳米科学与技术中心）
• Laboratoire Albert Fert, CNRS, Thales, Université Paris-Saclay（阿尔贝·费尔实验室，法国国家科学研究中心，泰雷兹集团，巴黎萨克雷大学）

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