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 - Chakraborty, Ayan A1 - Anitescu, Cosmin A1 - Zhuang, Xiaoying A1 - Rabczuk, Timon T1 - Domain adaptation based transfer learning approach for solving PDEs on complex geometries JF - Engineering with Computers N2 - In machine learning, if the training data is independently and identically distributed as the test data then a trained model can make an accurate predictions for new samples of data. Conventional machine learning has a strong dependence on massive amounts of training data which are domain specific to understand their latent patterns. In contrast, Domain adaptation and Transfer learning methods are sub-fields within machine learning that are concerned with solving the inescapable problem of insufficient training data by relaxing the domain dependence hypothesis. In this contribution, this issue has been addressed and by making a novel combination of both the methods we develop a computationally efficient and practical algorithm to solve boundary value problems based on nonlinear partial differential equations. We adopt a meshfree analysis framework to integrate the prevailing geometric modelling techniques based on NURBS and present an enhanced deep collocation approach that also plays an important role in the accuracy of solutions. We start with a brief introduction on how these methods expand upon this framework. We observe an excellent agreement between these methods and have shown that how fine-tuning a pre-trained network to a specialized domain may lead to an outstanding performance compare to the existing ones. As proof of concept, we illustrate the performance of our proposed model on several benchmark problems. KW - Maschinelles Lernen KW - NURBS KW - Transfer learning KW - Domain Adaptation KW - NURBS geometry KW - Navier–Stokes equations Y1 - 2022 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20220811-46776 UR - https://link.springer.com/article/10.1007/s00366-022-01661-2 VL - 2022 SP - 1 EP - 20 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 -