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  - Amani, Jafar
A1  - Saboor Bagherzadeh, Amir
A1  - Rabczuk, Timon
T1  - Error estimate and adaptive refinement in mixed discrete least squares meshless method
JF  - Mathematical Problems in Engineering
N2  - The node moving and multistage node enrichment adaptive refinement procedures are extended in mixed discrete least squares meshless (MDLSM) method for efficient analysis of elasticity problems. In the formulation of MDLSM method, mixed formulation is accepted to avoid second-order differentiation of shape functions and to obtain displacements and stresses simultaneously. In the refinement procedures, a robust error estimator based on the value of the least square residuals functional of the governing differential equations and its boundaries at nodal points is used which is inherently available from the MDLSM formulation and can efficiently identify the zones with higher numerical errors. The results are compared with the refinement procedures in the irreducible formulation of discrete least squares meshless (DLSM) method and show the accuracy and efficiency of the proposed procedures. Also, the comparison of the error norms and convergence rate show the fidelity of the proposed adaptive refinement procedures in the MDLSM method.
KW  - Elastizität
KW  - Fehlerabschätzung
KW  - MDLSM method
Y1  - 2014
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20170413-31181
ER  -