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A deep difference collocation method and its application in elasticity problems
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AI
DOI：10.1016/j.ijsolstr.2024.112692.png)
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Abstract
En 中文
Based on the coordinate transformation and difference scheme, a deep difference collocation method (DDCM) that solves the partial differential equations (PDEs) via a square domain is proposed in this paper. In most of deep learning-based methods such as physics-informed neural networks (PINNs), boundary losses and calculation of the items of PDEs in a physical domain using automatic differentiation will result in time-consuming training. DDCM utilizes a difference approximation approach to expedite the computation of neural network derivatives, enhancing training efficiency. It is adaptable to irregular physical domains via coordinate transformation and provides versatility in enforcing boundary conditions, enabling partial or total elimination of boundary losses. This research covers the analysis of 2D and 3D elastic problems along with the Kirchhoff plate bending problem. The validity of the introduced method is verified by comparing the obtained results to those from theoretical solutions, Finite Element Method (FEM), and Boundary Element Method (BEM). In comparison with PINN, the proposed methodology demonstrates a notably enhanced computational efficiency in solving PDEs, and exhibits commendable stability under a specified computational memory constraint.
Keywords:
Deep learning
Partial differential equations
Kirchhoff plate
Coordinate transformation
Finite difference approximation
Journal
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3.8
Papers:
1.1W
Citations:
3.1W