A physics-inspired neural network to solve partial differential equations - application in diffusion-induced stress.

Area of Science:

• Materials Science
• Computational Mechanics
• Electrochemistry

Background:

• Diffusion-induced stress is critical for lithium- and sodium-ion battery durability.
• Traditional numerical methods struggle with the complexity of these problems.

Purpose of the Study:

• To develop a novel computational approach for analyzing diffusion-induced stress.
• To apply a physics-inspired neural network to solve coupled PDEs for mechanical equilibrium and mass transport.

Main Methods:

• Utilized a physics-inspired neural network within the DeepXDE framework.
• Developed whole loss functions incorporating PDE, initial, and boundary condition residuals.
• Employed time-space coordinates as input for ANNs, outputting displacement and solute concentration.

Main Results:

• Successfully solved spatiotemporal evolution of displacement and solute concentration in an elastic sphere.
• Validated results against analytical solutions and COMSOL finite element simulations.
• Demonstrated the network's capability for both decoupled and coupled diffusion-stress problems.

Conclusions:

• The physics-inspired neural network offers a viable alternative to traditional numerical methods.
• This approach provides a new pathway for analyzing stress evolution in battery electrodes during cycling.