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Physics-informed neural networks for solving nonlinear diffusivity and Biot’s equations
- Source :
- Kadeethum, T, Jørgensen, T M & Nick, H 2020, ' Physics-informed neural networks for solving nonlinear diffusivity and Biot’s equations ', P L o S One, vol. 15, no. 5, e0232683 . https://doi.org/10.1371/journal.pone.0232683, PLoS ONE, PLoS ONE, Vol 15, Iss 5, p e0232683 (2020)
- Publication Year :
- 2020
-
Abstract
- This paper presents the potential of applying physics-informed neural networks for solving nonlinear multiphysics problems, which are essential to many fields such as biomedical engineering, earthquake prediction, and underground energy harvesting. Specifically, we investigate how to extend the methodology of physics-informed neural networks to solve both the forward and inverse problems in relation to the nonlinear diffusivity and Biot's equations. We explore the accuracy of the physics-informed neural networks with different training example sizes and choices of hyperparameters. The impacts of the stochastic variations between various training realizations are also investigated. In the inverse case, we also study the effects of noisy measurements. Furthermore, we address the challenge of selecting the hyperparameters of the inverse model and illustrate how this challenge is linked to the hyperparameters selection performed for the forward one.
- Subjects :
- FOS: Computer and information sciences
Computer Science - Machine Learning
Momentum
Inverse
010103 numerical & computational mathematics
01 natural sciences
Machine Learning (cs.LG)
Computational Engineering, Finance, and Science (cs.CE)
Mathematical and Statistical Techniques
Computer Science - Computational Engineering, Finance, and Science
Hyperparameter
Multidisciplinary
Partial differential equation
Artificial neural network
Physics
Classical Mechanics
Partial Differential Equations
Numerical Analysis (math.NA)
Inverse problem
Deformation
010101 applied mathematics
Physical Sciences
Medicine
Algorithms
Research Article
Optimization
Computer and Information Sciences
Neural Networks
Science
Multiphysics
Fluid Mechanics
Research and Analysis Methods
Continuum Mechanics
Differential Equations
FOS: Mathematics
Applied mathematics
Computer Simulation
Mathematics - Numerical Analysis
0101 mathematics
Fluid Flow
Damage Mechanics
Stochastic Processes
Biot number
Biology and Life Sciences
Fluid Dynamics
Nonlinear system
Nonlinear Dynamics
Time Domain Analysis
Neural Networks, Computer
Mathematical Functions
Mathematics
Neuroscience
Subjects
Details
- Language :
- English
- Database :
- OpenAIRE
- Journal :
- Kadeethum, T, Jørgensen, T M & Nick, H 2020, ' Physics-informed neural networks for solving nonlinear diffusivity and Biot’s equations ', P L o S One, vol. 15, no. 5, e0232683 . https://doi.org/10.1371/journal.pone.0232683, PLoS ONE, PLoS ONE, Vol 15, Iss 5, p e0232683 (2020)
- Accession number :
- edsair.doi.dedup.....8123fe1d40b774ace3b351d188abd398