Abstract
The problem of electro-thermal coupling is widely present in the integrated circuit (IC). The accuracy and efficiency of traditional solution methods, such as the finite element method (FEM), are tightly related to the quality and density of mesh construction. Recently, PINN (physics-informed neural network) was proposed as a method for solving differential equations. This method is mesh free and generalizes the process of solving PDEs regardless of the equations’ structure. Therefore, an experiment is conducted to explore the feasibility of PINN in solving electro-thermal coupling problems, which include the electrokinetic field and steady-state thermal field. We utilize two neural networks in the form of sequential training to approximate the electric field and the thermal field, respectively. The experimental results show that PINN provides good accuracy in solving electro-thermal coupling problems.
Highlights
The resolution of multi-physics problems comes down to the computation of partial differential equation (PDE) solutions
We propose to use the Physics-Informed Neural Network (PINN) to solve a Joule heating problem, which consists of a coupling problem of the electrokinetic field and steady-state thermal field
The two deep neural networks whose loss functions are defined in Equation (4) are employed to study the electro-thermal coupling issue
Summary
The resolution of multi-physics problems comes down to the computation of partial differential equation (PDE) solutions. The discretization represents the domain well for low-dimensional problems, but not for high-dimensional ones, as the number of elements increases exponentially with the dimensionality These methods only solve the PDEs at discrete points, and require interpolation or slope behavior for other points or other fields; this property makes the solution of the state variables at the interpolated points less accurate [1], the derivatives of the state variables. Deep learning has recently achieved great success in the fields of science and business [2,3,4] Due to these advances, many scientists have been working to embrace deep learning in the computation of physical problems. Wang et al [11]
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