A framework based on symbolic regression coupled with eXtended Physics-Informed Neural Networks for gray-box learning of equations of motion from data

2023/07/25 by Elham Kiyani, Khemraj Shukla, George Em Karniadakis +1 · 30 citations
Engineering · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Artificial intelligence #Artificial neural network #Computer science #Domain (mathematical analysis) #Fluid Dynamics and Turbulent Flows #Lattice Boltzmann Simulation Studies #Mathematical analysis #Mathematics #Matrix norm #Model Reduction and Neural Networks #Noise (video) #Nonlinear system #Norm (philosophy) #Physics #Symbolic regression #Test data

paper · open access · doi:10.1016/j.cma.2023.116258

published in Computer Methods in Applied Mechanics and Engineering 415, 116258 (Elsevier BV)

openalex publication_date 2023/07/25 · openalex created_date 2023/07/26 · openalex updated_date 2026/08/01

Citations

• Understanding deep learning (still) requires rethinking generalization
• Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems
• When and why PINNs fail to train: A neural tangent kernel perspective

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