The Experts below are selected from a list of 24795 Experts worldwide ranked by ideXlab platform
George Em Karniadakis - One of the best experts on this subject based on the ideXlab platform.
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operator learning for predicting multiscale bubble growth dynamics
Journal of Chemical Physics, 2021Co-Authors: Chensen Lin, Shengze Cai, Martin R Maxey, George Em KarniadakisAbstract:Simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs). Herein, we develop a framework based on operator regression, the so-called deep operator network (DeepONet), with the long-term objective to simplify multiscale modeling by avoiding the fragile and time-consuming "hand-shaking" interface algorithms for stitching together heterogeneous descriptions of multiscale phenomena. To this end, as a first step, we investigate if a DeepONet can learn the dynamics of different scale regimes, one at the deterministic Macroscale and the other at the stochastic microscale regime with inherent thermal fluctuations. Specifically, we test the effectiveness and accuracy of the DeepONet in predicting multirate bubble growth dynamics, which is described by a Rayleigh-Plesset (R-P) equation at the Macroscale and modeled as a stochastic nucleation and cavitation process at the microscale by dissipative particle dynamics (DPD). First, we generate data using the R-P equation for multirate bubble growth dynamics caused by randomly time-varying liquid pressures drawn from Gaussian random fields (GRFs). Our results show that properly trained DeepONets can accurately predict the Macroscale bubble growth dynamics and can outperform long short-term memory networks. We also demonstrate that the DeepONet can extrapolate accurately outside the input distribution using only very few new measurements. Subsequently, we train the DeepONet with DPD data corresponding to stochastic bubble growth dynamics. Although the DPD data are noisy and we only collect sparse data points on the trajectories, the trained DeepONet model is able to predict accurately the mean bubble dynamics for time-varying GRF pressures. Taken together, our findings demonstrate that DeepONets can be employed to unify the Macroscale and microscale models of the multirate bubble growth problem, hence providing new insight into the role of operator regression via DNNs in tackling realistic multiscale problems and in simplifying modeling with heterogeneous descriptions.
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Operator learning for predicting multiscale bubble growth dynamics
'AIP Publishing', 2020Co-Authors: Lin Chensen, Li Zhen, Cai Shengze, Maxey Martin, George Em KarniadakisAbstract:Simulating and predicting multiscale problems that couple multiple physics and dynamics across many orders of spatiotemporal scales is a great challenge that has not been investigated systematically by deep neural networks (DNNs). Herein, we develop a framework based on operator regression, the so-called deep operator network (DeepONet), with the long term objective to simplify multiscale modeling by avoiding the fragile and time-consuming "hand-shaking" interface algorithms for stitching together heterogeneous descriptions of multiscale phenomena. To this end, as a first step, we investigate if a DeepONet can learn the dynamics of different scale regimes, one at the deterministic Macroscale and the other at the stochastic microscale regime with inherent thermal fluctuations. Specifically, we test the effectiveness and accuracy of DeepONet in predicting multirate bubble growth dynamics, which is described by a Rayleigh-Plesset (R-P) equation at the Macroscale and modeled as a stochastic nucleation and cavitation process at the microscale by dissipative particle dynamics (DPD). Taken together, our findings demonstrate that DeepONets can be employed to unify the Macroscale and microscale models of the multirate bubble growth problem, hence providing new insight into the role of operator regression via DNNs in tackling realistic multiscale problems and in simplifying modeling with heterogeneous descriptions
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Active- and transfer-learning applied to microscale-Macroscale coupling to simulate viscoelastic flows
2020Co-Authors: Zhao Lifei, Li Zhen, Wang Zhicheng, Caswell Bruce, Ouyang Jie, George Em KarniadakisAbstract:Active- and transfer-learning are applied to polymer flows for the multiscale discovery of effective constitutive approximations required in viscoelastic flow simulation. The result is macroscopic rheology directly connected to a microstructural model. Micro and Macroscale simulations are adaptively coupled by means of Gaussian process regression to run the expensive microscale computations only as necessary. This active-learning guided multiscale method can automatically detect the inaccuracy of the learned constitutive closure and initiate simulations at new sampling points informed by proper acquisition functions, leading to an autonomic microscale-Macroscale coupled system. Also, we develop a new dissipative particle dynamics model with the range of interaction cutoff between particles allowed to vary with the local strain-rate invariant, which is able to capture both the shear-thinning viscosity and the normal stress difference functions consistent with rheological experiments for aqueous polyacrylamide solutions. Our numerical experiments demonstrate the effectiveness of using active- and transfer-learning schemes to on-the-fly couple a spectral element solver and a mesoscopic particle-based simulator, and verify that the microscale-Macroscale coupled model with effective constitutive closure learned from microscopic dynamics can outperform empirical constitutive models compared to experimental observations. The effective closure learned in a channel simulation is then transferred directly to the flow past a circular cylinder, where the results show that only two additional microscopic simulations are required to achieve a satisfactory constitutive model to once again close the continuum equations. This new paradigm of active- and transfer-learning for multiscale modeling is readily applicable to other microscale-Macroscale coupled simulations of complex fluids and other materials.Comment: 26 pages, 16 figure
Rui Yang - One of the best experts on this subject based on the ideXlab platform.
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retracted micro macro mechanical model and material removal mechanism of machining carbon fiber reinforced polymer
International Journal of Machine Tools & Manufacture, 2016Co-Authors: Youliang Su, Rui YangAbstract:Abstract The present paper studies the material removal mechanism of machining carbon fiber reinforced polymer (CFRP) by a micro-mechanical model, and proposes prediction models of cutting forces from the microscale to the Macroscale. At the microscale, the micro-mechanical model for cutting a fiber in orthogonal cutting CFRP is established via the elastic foundation beam theory with explicit description of the carbon fiber and the matrix. The deflection and failure of the fiber constrained by the surrounding composite are analyzed under the cutting effects by the tool edge. In addition, the fiber failure under the pressing of the flank face is analyzed based on the undulating fiber theory. Analytical expressions are established at the microscale for evaluating the force for cutting a single fiber and the compression force for a single fiber from the flank face. At the Macroscale, the chip length is determined by analyzing the characteristics of the cutting force signals of orthogonal cutting experiments. The characteristic chip length is used for establishing the trans-scale prediction model of cutting forces from the microscale to the Macroscale. The total cutting and thrust forces at the Macroscale during the formation of a chip are predicted based on the micro-mechanical results and the characteristic chip length, which agree well with the experimental results for orthogonal cutting of CFRP. Furthermore, the fiber failure modes and the debonding between the fiber and the matrix under different supporting conditions are discussed by the micro-mechanical model, by which subsurface damages are recognized.
Joanne T Fredrich - One of the best experts on this subject based on the ideXlab platform.
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calculating the effective permeability of sandstone with multiscale lattice boltzmann finite element simulations
Acta Geotechnica, 2006Co-Authors: Joshua A White, Ronaldo I Borja, Joanne T FredrichAbstract:The lattice Boltzmann (LB) method is an efficient technique for simulating fluid flow through individual pores of complex porous media. The ease with which the LB method handles complex boundary conditions, combined with the algorithm’s inherent parallelism, makes it an elegant approach to solving flow problems at the sub-continuum scale. However, the realities of current computational resources can limit the size and resolution of these simulations. A major research focus is developing methodologies for upscaling microscale techniques for use in Macroscale problems of engineering interest. In this paper, we propose a hybrid, multiscale framework for simulating diffusion through porous media. We use the finite element (FE) method to solve the continuum boundary-value problem at the Macroscale. Each finite element is treated as a sub-cell and assigned permeabilities calculated from subcontinuum simulations using the LB method. This framework allows us to efficiently find a Macroscale solution while still maintaining information about microscale heterogeneities. As input to these simulations, we use synchrotron-computed 3D microtomographic images of a sandstone, with sample resolution of 3.34 μm. We discuss the predictive ability of these simulations, as well as implementation issues. We also quantify the lower limit of the continuum (Darcy) scale, as well as identify the optimal representative elementary volume for the hybrid LB–FE simulations.
E Weinan - One of the best experts on this subject based on the ideXlab platform.
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machine learning based non newtonian fluid model with molecular fidelity
Physical Review E, 2020Co-Authors: Huan Lei, E WeinanAbstract:We introduce a machine-learning-based framework for constructing continuum a non-Newtonian fluid dynamics model directly from a microscale description. Dumbbell polymer solutions are used as examples to demonstrate the essential ideas. To faithfully retain molecular fidelity, we establish a micro-macro correspondence via a set of encoders for the microscale polymer configurations and their Macroscale counterparts, a set of nonlinear conformation tensors. The dynamics of these conformation tensors can be derived from the microscale model, and the relevant terms can be parametrized using machine learning. The final model, named the deep non-Newtonian model (DeePN^{2}), takes the form of conventional non-Newtonian fluid dynamics models, with a generalized form of the objective tensor derivative that retains the microscale interpretations. Both the formulation of the dynamic equation and the neural network representation rigorously preserve the rotational invariance, which ensures the admissibility of the constructed model. Numerical results demonstrate the accuracy of DeePN^{2} where models based on empirical closures show limitations.
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the local microscale problem in the multiscale modeling of strongly heterogeneous media effects of boundary conditions and cell size
Journal of Computational Physics, 2007Co-Authors: Xingye Yue, E WeinanAbstract:Many multiscale methods are based on the idea of extracting macroscopic behavior of solutions by solving an array of microscale models over small domains. A key ingredient in such multiscale methods is the boundary condition and the size of the computational domain over which the microscale problems are solved. This problem is systematically investigated in the present paper in the context of modeling strongly heterogeneous media. Three different boundary conditions are considered: the periodic boundary condition, Dirichlet boundary condition, and the Neumann boundary condition. Each is applied to several benchmark problems: the random checker-board problem, periodic problem with isotropic Macroscale behavior, periodic problem with anisotropic Macroscale behavior and periodic laminated media. In each case, convergence studies are conducted as the domain size for the microscale problem is changed. Convergence rates as well as the size of fluctuations in the computed effective coefficients are compared for the different formulations. In addition, we will discuss a mixed Dirichlet-Neumann boundary condition that is often used in porous medium modeling. We explain why that leads to unsatisfactory results and how it can be corrected. Also discussed are the different averaging methods used in extracting the effective coefficients.
Kochmann, Dennis M. - One of the best experts on this subject based on the ideXlab platform.
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Data-driven topology optimization of spinodoid metamaterials with seamlessly tunable anisotropy
'Elsevier BV', 2021Co-Authors: Li Zheng, Kumar S., Kochmann, Dennis M.Abstract:We present a two-scale topology optimization framework for the design of macroscopic bodies with an optimized elastic response, which is achieved by means of a spatially-variant cellular architecture on the microscale. The chosen spinodoid topology for the cellular network on the microscale (which is inspired by natural microstructures forming during spinodal decomposition) admits a seamless spatial grading as well as tunable elastic anisotropy, and it is parametrized by a small set of design parameters associated with the underlying Gaussian random field. The Macroscale boundary value problem is discretized by finite elements, which in addition to the displacement field continuously interpolate the microscale design parameters. By assuming a separation of scales, the local constitutive behavior on the Macroscale is identified as the homogenized elastic response of the microstructure based on the local design parameters. As a departure from classical FE2-type approaches, we replace the costly microscale homogenization by a data-driven surrogate model, using deep neural networks, which accurately and efficiently maps design parameters onto the effective elasticity tensor. The model is trained on homogenized stiffness data obtained from numerical homogenization by finite elements. As an added benefit, the machine learning setup admits automatic differentiation, so that sensitivities (required for the optimization problem) can be computed exactly and without the need for numerical derivatives – a strategy that holds promise far beyond the elastic stiffness. Therefore, this framework presents a new opportunity for multiscale topology optimization based on data-driven surrogate models.Team Sid Kuma
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Data-driven topology optimization of spinodoid metamaterials with seamlessly tunable anisotropy
'Elsevier BV', 2021Co-Authors: Li Zheng, Kumar Siddhant, Kochmann, Dennis M.Abstract:We present a two-scale topology optimization framework for the design of macroscopic bodies with an optimized elastic response, which is achieved by means of a spatially-variant cellular architecture on the microscale. The chosen spinodoid topology for the cellular network on the microscale (which is inspired by natural microstructures forming during spinodal decomposition) admits a seamless spatial grading as well as tunable elastic anisotropy, and it is parametrized by a small set of design parameters associated with the underlying Gaussian random field. The Macroscale boundary value problem is discretized by finite elements, which in addition to the displacement field continuously interpolate the microscale design parameters. By assuming a separation of scales, the local constitutive behavior on the Macroscale is identified as the homogenized elastic response of the microstructure based on the local design parameters. As a departure from classical FE2 -type approaches, we replace the costly microscale homogenization by a data-driven surrogate model, using deep neural networks, which accurately and efficiently maps design parameters onto the effective elasticity tensor. The model is trained on homogenized stiffness data obtained from numerical homogenization by finite elements. As an added benefit, the machine learning setup admits automatic differentiation, so that sensitivities (required for the optimization problem) can be computed exactly and without the need for numerical derivatives – a strategy that holds promise far beyond the elastic stiffness. Therefore, this framework presents a new opportunity for multiscale topology optimization based on data-driven surrogate models.ISSN:0045-7825ISSN:1879-213
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Data-driven topology optimization of spinodoid metamaterials with seamlessly tunable anisotropy
2020Co-Authors: Li Zheng, Kumar Siddhant, Kochmann, Dennis M.Abstract:We present a two-scale topology optimization framework for the design of macroscopic bodies with an optimized elastic response, which is achieved by means of a spatially-variant cellular architecture on the microscale. The chosen spinodoid topology for the cellular network on the microscale (which is inspired by natural microstructures forming during spinodal decomposition) admits a seamless spatial grading as well as tunable elastic anisotropy, and it is parametrized by a small set of design parameters associated with the underlying Gaussian random field. The Macroscale boundary value problem is discretized by finite elements, which in addition to the displacement field continuously interpolate the microscale design parameters. By assuming a separation of scales, the local constitutive behavior on the Macroscale is identified as the homogenized elastic response of the microstructure based on the local design parameters. As a departure from classical FE$^2$-type approaches, we replace the costly microscale homogenization by a data-driven surrogate model, using deep neural networks, which accurately and efficiently maps design parameters onto the effective elasticity tensor. The model is trained on homogenized stiffness data obtained from numerical homogenization by finite elements. As an added benefit, the machine learning setup admits automatic differentiation, so that sensitivities (required for the optimization problem) can be computed exactly and without the need for numerical derivatives - a strategy that holds promise far beyond the elastic stiffness. Therefore, this framework presents a new opportunity for multiscale topology optimization based on data-driven surrogate models.Comment: 26 pages, 16 figure
