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 - TY - JOUR A1 - Ren, Huilong A1 - Zhuang, Xiaoying A1 - Oterkus, Erkan A1 - Zhu, Hehua A1 - Rabczuk, Timon T1 - Nonlocal strong forms of thin plate, gradient elasticity, magneto-electro-elasticity and phase-field fracture by nonlocal operator method JF - Engineering with Computers N2 - The derivation of nonlocal strong forms for many physical problems remains cumbersome in traditional methods. In this paper, we apply the variational principle/weighted residual method based on nonlocal operator method for the derivation of nonlocal forms for elasticity, thin plate, gradient elasticity, electro-magneto-elasticity and phase-field fracture method. The nonlocal governing equations are expressed as an integral form on support and dual-support. The first example shows that the nonlocal elasticity has the same form as dual-horizon non-ordinary state-based peridynamics. The derivation is simple and general and it can convert efficiently many local physical models into their corresponding nonlocal forms. In addition, a criterion based on the instability of the nonlocal gradient is proposed for the fracture modelling in linear elasticity. Several numerical examples are presented to validate nonlocal elasticity and the nonlocal thin plate. KW - Bruchmechanik KW - Elastizität KW - Peridynamik KW - energy form KW - weak form KW - peridynamics KW - variational principle KW - explicit time integration Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20211207-45388 UR - https://link.springer.com/article/10.1007/s00366-021-01502-8 VL - 2021 SP - 1 EP - 22 ER - TY - JOUR A1 - Noori, Hamidreza A1 - Mortazavi, Bohayra A1 - Keshtkari, Leila A1 - Zhuang, Xiaoying A1 - Rabczuk, Timon T1 - Nanopore creation in MoS2 and graphene monolayers by nanoparticles impact: a reactive molecular dynamics study JF - Applied Physics A N2 - In this work, extensive reactive molecular dynamics simulations are conducted to analyze the nanopore creation by nano-particles impact over single-layer molybdenum disulfide (MoS2) with 1T and 2H phases. We also compare the results with graphene monolayer. In our simulations, nanosheets are exposed to a spherical rigid carbon projectile with high initial velocities ranging from 2 to 23 km/s. Results for three different structures are compared to examine the most critical factors in the perforation and resistance force during the impact. To analyze the perforation and impact resistance, kinetic energy and displacement time history of the projectile as well as perforation resistance force of the projectile are investigated. Interestingly, although the elasticity module and tensile strength of the graphene are by almost five times higher than those of MoS2, the results demonstrate that 1T and 2H-MoS2 phases are more resistive to the impact loading and perforation than graphene. For the MoS2nanosheets, we realize that the 2H phase is more resistant to impact loading than the 1T counterpart. Our reactive molecular dynamics results highlight that in addition to the strength and toughness, atomic structure is another crucial factor that can contribute substantially to impact resistance of 2D materials. The obtained results can be useful to guide the experimental setups for the nanopore creation in MoS2or other 2D lattices. KW - Nanomechanik KW - Molekülstruktur KW - Nanoporöser Stoff KW - MoS2 KW - molecular dynamics KW - Nanopore KW - Graphene Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:gbv:wim2-20210804-44756 UR - https://link.springer.com/article/10.1007/s00339-021-04693-5 VL - 2021 IS - volume 127, article 541 SP - 1 EP - 13 PB - Springer CY - Heidelberg ER - TY - JOUR A1 - Vu-Bac, N. A1 - Lahmer, Tom A1 - Zhuang, Xiaoying A1 - Nguyen-Thoi, T. A1 - Rabczuk, Timon T1 - A software framework for probabilistic sensitivity analysis for computationally expensive models JF - Advances in Engineering Software N2 - A software framework for probabilistic sensitivity analysis for computationally expensive models KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2016 SP - 19 EP - 31 ER - TY - JOUR A1 - Nanthakumar, S.S. A1 - Lahmer, Tom A1 - Zhuang, Xiaoying A1 - Park, Harold S. A1 - Rabczuk, Timon T1 - Topology optimization of piezoelectric nanostructures JF - Journal of the Mechanics and Physics of Solids N2 - Topology optimization of piezoelectric nanostructures KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2016 SP - 316 EP - 335 ER - TY - JOUR A1 - Nanthakumar, S.S. A1 - Lahmer, Tom A1 - Zhuang, Xiaoying A1 - Zi, Goangseup A1 - Rabczuk, Timon T1 - Detection of material interfaces using a regularized level set method in piezoelectric structures JF - Inverse Problems in Science and Engineering N2 - Detection of material interfaces using a regularized level set method in piezoelectric structures KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2016 SP - 153 EP - 176 ER - TY - JOUR A1 - Ghasemi, Hamid A1 - Brighenti, Roberto A1 - Zhuang, Xiaoying A1 - Muthu, Jacob A1 - Rabczuk, Timon T1 - Optimum fiber content and distribution in fiber-reinforced solids using a reliability and NURBS based sequential optimization approach JF - Structural and Multidisciplinary Optimization N2 - Optimum _ber content and distribution in _ber-reinforced solids using a reliability and NURBS based sequential optimization approach KW - Angewandte Mathematik KW - Strukturmechanik Y1 - 2015 SP - 99 EP - 112 ER - TY - JOUR A1 - Vu-Bac, N. A1 - Silani, Mohammad A1 - Lahmer, Tom A1 - Zhuang, Xiaoying A1 - Rabczuk, Timon T1 - A unified framework for stochastic predictions of Young's modulus of clay/epoxy nanocomposites (PCNs) JF - Computational Materials Science N2 - A unified framework for stochastic predictions of Young's modulus of clay/epoxy nanocomposites (PCNs) KW - Angewandte Mathematik KW - Stochastik KW - Strukturmechanik Y1 - 2015 SP - 520 EP - 535 ER -