Stochastic analysis of heterogeneous porous material with modified neural architecture search (NAS) based physics-informed neural networks using transfer learning

Abstract

In this work, a modified neural architecture search method (NAS) based physics-informed deep learning model is presented for stochastic analysis in heterogeneous porous material. Monte Carlo method based on a randomized spectral representation is first employed to construct a stochastic model for simulation of flow through porous media. To solve the governing equations for stochastic groundwater flow problem, we build a modified NAS model based on physics-informed neural networks (PINNs) with transfer learning in this paper that will be able to fit different partial differential equations (PDEs) with less calculation. The performance estimation strategies adopted is constructed from an error estimation model using the method of manufactured solutions. A sensitivity analysis is performed to obtain the prior knowledge of the PINNs model and narrow down the range of parameters for search space and use hyper-parameter optimization algorithms to further determine the values of the parameters. Further the NAS based PINNs model also saves the weights and biases of the most favorable architectures, then used in the fine-tuning process. It is found that the log-conductivity field using Gaussian correlation function will perform much better than exponential correlation case, which is more fitted to the PINNs model and the modified neural architecture search based PINNs model shows a great potential in approximating solutions to PDEs. Moreover, a three dimensional stochastic flow model is built to provide a benchmark to the simulation of groundwater flow in highly heterogeneous aquifers. The NAS model based deep collocation method is verified to be effective and accurate through numerical examples in different dimensions using different manufactured solutions.

References in corpus (7)

• Practical Bayesian Optimization of Machine Learning Algorithms
• Neural Architecture Search with Reinforcement Learning
• An Energy Approach to the Solution of Partial Differential Equations in Computational Mechanics via Machine Learning: Concepts, Implementation and Applications
• Hidden Physics Models: Machine Learning of Nonlinear Partial Differential Equations
• A Deep Collocation Method for the Bending Analysis of Kirchhoff Plate
• Non-stochastic Best Arm Identification and Hyperparameter Optimization
• Benchmark for numerical solutions of flow in heterogeneous groundwater formations

Cited by in corpus (5)

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• BINN: A deep learning approach for computational mechanics problems based on boundary integral equations
• A deep learning method for multi-material diffusion problems based on physics-informed neural networks
• Discovering Physics-Informed Neural Networks Model for Solving Partial Differential Equations through Evolutionary Computation