Enhancing PINN Performance Through Lie Symmetry Group
This work addresses the challenge of solving PDEs for scientific computing applications, representing an incremental improvement by combining existing mathematical concepts with deep learning methods.
This paper tackles the problem of solving partial differential equations (PDEs) by integrating Lie symmetry groups into Physics-Informed Neural Networks (PINNs), resulting in enhanced accuracy and efficiency. Numerical experiments show progressive improvements across three distinct cases, though specific numerical gains are not quantified.
This paper presents intersection of Physics informed neural networks (PINNs) and Lie symmetry group to enhance the accuracy and efficiency of solving partial differential equation (PDEs). Various methods have been developed to solve these equations. A Lie group is an efficient method that can lead to exact solutions for the PDEs that possessing Lie Symmetry. Leveraging the concept of infinitesimal generators from Lie symmetry group in a novel manner within PINN leads to significant improvements in solution of PDEs. In this study three distinct cases are discussed, each showing progressive improvements achieved through Lie symmetry modifications and adaptive techniques. State-of-the-art numerical methods are adopted for comparing the progressive PINN models. Numerical experiments demonstrate the key role of Lie symmetry in enhancing PINNs performance, emphasizing the importance of integrating abstract mathematical concepts into deep learning for addressing complex scientific problems adequately.