Linel2D-Net: A deep learning approach to solving 2D linear elastic boundary value problems on image domains

Area of Science:

• Computational mechanics
• Applied physics
• Machine learning for engineering

Background:

• Solving physical boundary value problems (BVPs) is crucial but computationally intensive.
• Traditional numerical methods like finite difference methods (FDM) suffer from slow convergence and high computational cost.
• There is a need for efficient, non-iterative methods to solve complex engineering problems.

Purpose of the Study:

• To present an efficient data-driven deep neural network (DNN) approach for solving 2D linear elastic BVPs.
• To develop a U-Net-based surrogate model capable of non-iterative BVP solutions.
• To demonstrate the model's accuracy and applicability in engineering simulations.

Main Methods:

• Utilized a U-Net architecture as a surrogate model.
• Trained the model on a dataset of reference solutions obtained from Finite Difference Methods (FDM).
• Focused on 2D linear elasticity problems to emulate material behavior.

Main Results:

• The DNN approach provides an efficient, non-iterative solution for arbitrary 2D linear elastic BVPs.
• The U-Net surrogate model accurately emulates linear elastic material behavior.
• Achieved significant improvements in throughput compared to conventional methods.

Conclusions:

• The proposed data-driven DNN method offers a powerful and efficient alternative for solving linear elastic BVPs.
• This approach has broad applications in deformable modeling and complex simulations.
• Highlights the potential of machine learning in accelerating scientific and engineering computations.