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

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.