TY  - JOUR
A1  - Rabczuk, Timon
A1  - Guo, Hongwei
A1  - Zhuang, Xiaoying
A1  - Chen, Pengwan
A1  - Alajlan, Naif
T1  - Stochastic deep collocation method based on neural architecture search and transfer learning for heterogeneous porous media
JF  - Engineering with Computers
N2  - We present a stochastic deep collocation method (DCM) based on neural architecture search (NAS) and transfer learning for heterogeneous porous media. We first carry out a sensitivity analysis to determine the key hyper-parameters of the network to reduce the search space and subsequently employ hyper-parameter optimization to finally obtain the parameter values. The presented NAS based DCM also saves the weights and biases of the most favorable architectures, which is then used in the fine-tuning process. We also employ transfer learning techniques to drastically reduce the computational cost. The presented DCM is then applied to the stochastic analysis of heterogeneous porous material. Therefore, a three dimensional stochastic flow model is built providing a benchmark to the simulation of groundwater flow in highly heterogeneous aquifers. The performance of the presented NAS based DCM is verified in different dimensions using the method of manufactured solutions. We show that it significantly outperforms finite difference methods in both accuracy and computational cost.
KW  - Maschinelles Lernen
KW  - Neuronales Lernen
KW  - Fehlerabschätzung
KW  - deep learning
KW  - neural architecture search
KW  - randomized spectral representation
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20220209-45835
UR  - https://link.springer.com/article/10.1007/s00366-021-01586-2
VL  - 2022
SP  - 1
EP  - 26
PB  - Springer
CY  - London
ER  - 
TY  - JOUR
A1  - Guo, Hongwei
A1  - Zhuang, Xiaoying
A1  - Chen, Pengwan
A1  - Alajlan, Naif
A1  - Rabczuk, Timon
T1  - Analysis of three-dimensional potential problems in non-homogeneous media with physics-informed deep collocation method using material transfer learning and sensitivity analysis
JF  - Engineering with Computers
N2  - In this work, we present a deep collocation method (DCM) for three-dimensional potential problems in non-homogeneous media. This approach utilizes a physics-informed neural network with material transfer learning reducing the solution of the non-homogeneous partial differential equations to an optimization problem. We tested different configurations of the physics-informed neural network including smooth activation functions, sampling methods for collocation points generation and combined optimizers. A material transfer learning technique is utilized for non-homogeneous media with different material gradations and parameters, which enhance the generality and robustness of the proposed method. In order to identify the most influential parameters of the network configuration, we carried out a global sensitivity analysis. Finally, we provide a convergence proof of our DCM. The approach is validated through several benchmark problems, also testing different material variations.
KW  - Deep learning
KW  - Kollokationsmethode
KW  - Collocation method
KW  - Potential problem
KW  - Activation function
KW  - Transfer learning
Y1  - 2022
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20220811-46764
UR  - https://link.springer.com/article/10.1007/s00366-022-01633-6
VL  - 2022
SP  - 1
EP  - 22
ER  -