Conditional physics informed neural networks

DOI10.1016/J.CNSNS.2021.106041zbMath1485.65086arXiv2104.02741OpenAlexW3198835738MaRDI QIDQ2247060

Akira Kato, Markus Gusenbauer, Alexander Kovacs, Lukas Exl, Tetsuya Shoji, Noritsugu Sakuma, Masao Yano, Markus Hovorka, Johann Fischbacher, Alexander Kornell, Thomas Schrefl, Harald Oezelt, Leoni Breth, Akihito Kinoshita

Publication date: 16 November 2021

Published in: Communications in Nonlinear Science and Numerical Simulation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2104.02741

zbMATH Keywords

ordinary differential equationsRitz methodeigenvalue problemsmicromagneticsartificial neural network

Mathematics Subject Classification ID

Artificial neural networks and deep learning (68T07) Numerical solution of eigenvalue problems involving ordinary differential equations (65L15)

Related Items (6)

Scientific machine learning through physics-informed neural networks: where we are and what's next ⋮ Data-driven synchronization-avoiding algorithms in the explicit distributed structural analysis of soft tissue ⋮ Physics-informed neural networks combined with polynomial interpolation to solve nonlinear partial differential equations ⋮ Error convergence and engineering-guided hyperparameter search of PINNs: towards optimized I-FENN performance ⋮ Application of machine learning regression models to inverse eigenvalue problems ⋮ Physics-informed ConvNet: learning physical field from a shallow neural network

Uses Software

• SciPy
• Python
• Adam
• PyDEns
• DeepXDE
• scikit-optimize
• SciANN
• SimNet
• DeepONet
• hp-VPINNs

Cites Work

• Factorization method in quantum mechanics
• The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
• SciANN: a Keras/Tensorflow wrapper for scientific computations and physics-informed deep learning using artificial neural networks
• Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
• Magnetization Curve of the Infinite Cylinder
• DeepXDE: A Deep Learning Library for Solving Differential Equations
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