基于PINN的非线性电路直流工作点求解方法  

PINN-based method for solving DC operating points in nonlinear circuits

作　　者：蔡固顺[1] 刘锦辉[1,2] 张馨丹 黄钊 王泉 CAI Gushun;LIU Jinhui;ZHANG Xindan;HUANG Zhao;WANG Quan(School of Computer Science and Technology,Xidian University,Xi’an 710126,China;Shaanxi Province Key Laboratory of Smart Human Computer Interaction and Wearable Technology,Xi’an 710126,China;Guangzhou Institute of Technology,Xidian University,Guangzhou 510530,China)

机构地区：[1]西安电子科技大学计算机科学与技术学院,陕西西安710126 [2]陕西省智能人机交互与可穿戴技术重点实验室,陕西西安710126 [3]西安电子科技大学广州研究院,广东广州510530

出　　处：《西安电子科技大学学报》2024年第6期91-103,共13页Journal of Xidian University

基　　金：陕西省重点研发计划(2024GX-YBXM-107);广州市基础研究计划(2023A04J0402)。

摘　　要：物理信息神经网络是一种新型深度学习模型,但是却无法很好解决高阶非线性方程在电路直流分析中难以求解的问题。为此,提出了一种基于物理信息神经网络的新型学习仿真模型,用于实现对非线性电路直流工作点的高效仿真分析与精确求解。特别地,文中同时将非线性器件的优安特性方程与修正节点分析方程作为损失函数的正则化项,通过将节点导纳矩阵与独立电源值作为先验知识直接代入物理信息神经网络中进行训练,得到直流工作点学习仿真模型,以有效预测节点电压值,实现对不同器件模型的非线性求解。在3种典型的非线性器件上验证了所提出的物理信息神经网络学习模型。仿真结果表明,所提出的物理信息神经网络学习模型与理论值相比,最大相对误差不超过4.30%,有效解决了传统数值算法在求解非线性电路直流工作点时难以收敛的问题。相比于Gmin法和源步进法,所提物理信息神经网络模型的平均预测精度分别提高了0.11%和0.23%。在需要更少样本的情况下,具有更好的学习效率与稳定性。The Physical-informed Neural Network(PINN)is a new type of deep learning model,but it cannot effectively solve the problem that high-order nonlinear equations are difficult to solve in circuit DC analysis.To address this problem,this paper proposes a novel and PINN-based learning simulation model to achieve an efficient simulation analysis and accurate solutions of DC operating points in nonlinear circuits.Specifically,the nonlinear device IV characteristic equation and modified node analysis(MNA)equation are simultaneously exploited as a regularization term for the loss function,and the node admittance matrix and independent power supply values are directly substituted into the PINN as prior knowledge for training to obtain the final DC operating point learning simulation model,thereby effectively predicting the node voltage value and completing the nonlinear solution of different device models.To validate the proposed PINN learning model,we conduct experiments on three typical nonlinear devices.The simulation results show that the maximum relative error of the proposed PINN learning model is less than 4.30%compared with the theoretical values,thus effectively solving the problem that the traditional numerical algorithms converge with difficulty when solving the DC operating points in nonlinear circuits.As compared with Gmin and source-stepping methods,the average prediction accuracy of the proposed PINN model increases by 0.11%and 0.23%,respectively.This illustrates that our method has a higher learning efficiency and a good stability while requiring fewer samples.

关 键 词：物理信息神经网络 非线性器件 电路直流分析 预测模型 

分 类 号：TP391.9[自动化与计算机技术—计算机应用技术]