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In this work, a modified neural architecture search method (NAS) basedphysics-informed deep learning model is presented for stochastic analysis inheterogeneous porous material. Monte Carlo method based on a randomizedspectral representation is first employed to construct a stochastic model forsimulation of flow through porous media. To solve the governing equations forstochastic groundwater flow problem, we build a modified NAS model based onphysics-informed neural networks (PINNs) with transfer learning in this paperthat will be able to fit different partial differential equations (PDEs) withless calculation. The performance estimation strategies adopted is constructedfrom an error estimation model using the method of manufactured solutions. Asensitivity analysis is performed to obtain the prior knowledge of the PINNsmodel and narrow down the range of parameters for search space and usehyper-parameter optimization algorithms to further determine the values of theparameters. Further the NAS based PINNs model also saves the weights and biasesof the most favorable architectures, then used in the fine-tuning process. Itis found that the log-conductivity field using Gaussian correlation functionwill perform much better than exponential correlation case, which is morefitted to the PINNs model and the modified neural architecture search basedPINNs model shows a great potential in approximating solutions to PDEs.Moreover, a three dimensional stochastic flow model is built to provide abenchmark to the simulation of groundwater flow in highly heterogeneousaquifers. The NAS model based deep collocation method is verified to beeffective and accurate through numerical examples in different dimensions usingdifferent manufactured solutions.

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