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Physics-informed neural networks for solving nonlinear diffusivity and Biot's equations.

Teeratorn Kadeethum1,2, Thomas M Jørgensen1, Hamidreza M Nick2

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Summary
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Physics-informed neural networks show promise for solving complex nonlinear multiphysics problems. This study explores their application to forward and inverse problems, assessing accuracy and hyperparameter effects.

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Area of Science:

  • Computational Science
  • Applied Mathematics
  • Engineering Physics

Background:

  • Nonlinear multiphysics problems are crucial in diverse scientific and engineering fields.
  • Solving these problems often requires advanced computational techniques.
  • Physics-informed neural networks (PINNs) offer a novel approach by integrating physical laws into neural network training.

Purpose of the Study:

  • To investigate the application of PINNs for solving nonlinear multiphysics problems.
  • To extend PINN methodology to address both forward and inverse problems related to nonlinear diffusivity and Biot's equations.
  • To analyze the impact of training data size, hyperparameters, and noisy measurements on PINN accuracy.

Main Methods:

  • Utilizing physics-informed neural networks (PINNs) to model nonlinear diffusivity and Biot's equations.
  • Implementing PINNs for both forward (predicting system behavior) and inverse (estimating parameters) problems.
  • Systematically varying training dataset sizes and hyperparameter configurations.
  • Evaluating the influence of stochastic variations and measurement noise on model performance.

Main Results:

  • PINNs demonstrate potential for solving nonlinear multiphysics forward and inverse problems.
  • Accuracy is sensitive to the size of training data and hyperparameter choices.
  • Stochastic variations and noisy measurements impact the reliability of inverse problem solutions.
  • Hyperparameter selection for inverse problems is linked to forward problem parameter tuning.

Conclusions:

  • PINNs are a viable tool for tackling complex nonlinear multiphysics challenges.
  • Careful consideration of training parameters and data quality is essential for accurate PINN applications.
  • The study provides insights into optimizing PINN performance for both forward and inverse modeling in these domains.