综述：合金设计中物理模型与人工智能的集成与发展

王晨充, 徐伟

Overview: Integration and Development of Physical Models and Artificial Intelligence in Alloy Design

WANG Chenchong, XU Wei

图10 机制指导人工智能的方法与应用

Fig.10 Methods and applications of mechanism guided artificial intelligence (PINN—physics-informed neural network, NN—neural network, PDE—partial differential equation, MSE—mean squared error. x—spatial variable, t—temporal variable, w—weight, b—bias, σ—activation function, u—solution of the partial differential equation and also the output of the neural network, L—differential operator, g—known function on the right-hand side of the partial differential equation, θ—parameter set of the partial differential equation, R—residual value, ε—threshold. MSE{u, BC, IC}—mean squared error of the solution u when considering boundary conditions (BC) and initial conditions (IC), MSER is the mean squared error based on the R)