arXiv subjects

Timon Rabczuk

Publications and source records attributed to Timon Rabczuk.

At least 73 records · Page 4Linked to original sources

arXiv2022

Analysis of three dimensional potential problems in non-homogeneous media with physics-informed deep collocation method using material transfer learning and sensitivity analysis

In this work, we present a deep collocation method for three dimensional potential problems in nonhomogeneous media. This approach utilizes a physics informed neural network with material transfer learning reducing the solution of the nonhomogeneous partial differential equations to an optimization problem. We tested different cofigurations 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 utilised for nonhomogeneous 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.

cs.LG↗

arXiv2022

Mechanical, optical, and thermoelectric properties of semiconducting ZnIn2X4 (X= S, Se, Te) monolayers

Mechanical stability of the ZnIn2X4 monolayers. The ZnIn2S4 and ZnIn2Se4 are semiconductors with direct band gaps of 3.94 and 2.77 eV, respectively whereas the ZnIn2Te4 shows an indirect band gap of 1.84 eV at the G0W0 level. The optical properties achieved from the solution of the Bethe-Salpeter equation predict the exciton binding energy of the ZnIn2S4, ZnIn2Se4, and ZnIn2Te4 monolayers to be 0.51, 0.41, and 0.34 eV, respectively, suggesting the high stability of the excitonic states against thermal dissociation. Using the iterative solutions of the Boltzmann transport equation accelerated by machine learning interatomic potentials, the room-temperature lattice thermal conductivity of the ZnIn2S4, ZnIn2Se4, and ZnIn2Te4 monolayers is predicted to be remarkably low as 5.8, 2.0, and 0.4 W/mK, respectively. Due to the low lattice thermal conductivity, high thermopower, and large figure of merit, we propose the ZnIn2Se4 and ZnIn2Te4 monolayers as promising candidates for thermoelectric energy conversion systems. This study provides an extensive vision concerning the intrinsic physical properties of the ZnIn2X4 nanosheets and highlights their characteristics for energy conversion and optoelectronics applications.

cond-mat.mtrl-sci↗

arXiv2021

Multigoal-oriented dual-weighted-residual error estimation using deep neural networks

Deep learning has shown successful application in visual recognition and certain artificial intelligence tasks. Deep learning is also considered as a powerful tool with high flexibility to approximate functions. In the present work, functions with desired properties are devised to approximate the solutions of PDEs. Our approach is based on a posteriori error estimation in which the adjoint problem is solved for the error localization to formulate an error estimator within the framework of neural network. An efficient and easy to implement algorithm is developed to obtain a posteriori error estimate for multiple goal functionals by employing the dual-weighted residual approach, which is followed by the computation of both primal and adjoint solutions using the neural network. The present study shows that such a data-driven model based learning has superior approximation of quantities of interest even with relatively less training data. The novel algorithmic developments are substantiated with numerical test examples. The advantages of using deep neural network over the shallow neural network are demonstrated and the convergence enhancing techniques are also presented

cs.LG↗

arXiv2021

A robust monolithic solver for phase-field fracture integrated with fracture energy based arc-length method and under-relaxation

The phase-field fracture free-energy functional is non-convex with respect to the displacement and the phase field. This results in a poor performance of the conventional monolithic solvers like the Newton-Raphson method. In order to circumvent this issue, researchers opt for the alternate minimization (staggered) solvers. Staggered solvers are robust for the phase-field based fracture simulations as the displacement and the phase-field sub-problems are convex in nature. Nevertheless, the staggered solver requires very large number of iterations (of the order of thousands) to converge. In this work, a robust monolithic solver is presented for the phase-field fracture problem. The solver adopts a fracture energy-based arc-length method and an adaptive under-relaxation scheme. The arc-length method enables the simulation to overcome critical points (snap-back, snap-through instabilities) during the loading of a specimen. The use of an under-relaxation scheme stabilizes the solver by preventing the divergence due to an ill-behaving stiffness matrix. The efficiency of the proposed solver is further amplified with an adaptive mesh refinement scheme based on PHT-splines within the framework of isogeometric analysis. The numerical examples presented in the manuscript demonstrates the efficacy of the solver. All the codes and data-sets accompanying this work will be made available on GitHub (https://github.com/rbharali/IGAFrac).

math.NA↗

arXiv2021

Resistance-Time Co-Modulated PointNet for Temporal Super-Resolution Simulation of Blood Vessel Flows

In this paper, a novel deep learning framework is proposed for temporal super-resolution simulation of blood vessel flows, in which a high-temporal-resolution time-varying blood vessel flow simulation is generated from a low-temporal-resolution flow simulation result. In our framework, point-cloud is used to represent the complex blood vessel model, resistance-time aided PointNet model is proposed for extracting the time-space features of the time-varying flow field, and finally we can reconstruct the high-accuracy and high-resolution flow field through the Decoder module. In particular, the amplitude loss and the orientation loss of the velocity are proposed from the vector characteristics of the velocity. And the combination of these two metrics constitutes the final loss function for network training. Several examples are given to illustrate the effective and efficiency of the proposed framework for temporal super-resolution simulation of blood vessel flows.

eess.IV↗

arXiv2021

Inverse design of reconfigurable piezoelectric topological phononic plates

We present a methodology to perform inverse analysis on reconfigurable topological insulators for flexural waves in plate-like structures. First the unit cell topology of a phononic plate is designed, which offers two-fold degeneracy in the band structure by topology optimization. In the second step, piezoelectric patches bonded over the substrate plate are connected to an external circuit and used appropriately to break space inversion symmetry. The space inversion symmetry breaking opens a topological band gap by mimicking quantum valley Hall effect. Numerical simulations demonstrate that the topologically protected edge state exhibits wave propagation without backscattering and is immune to disorders. Predominantly, the proposed idea enables real-time reconfigurability of the topological interfaces in waveguide applications.

cond-mat.mes-hall↗

arXiv2021

Exploring thermal expansion of carbon-based nanosheets by machine-learning interatomic potentials

Examination of thermal expansion of two-dimensional (2D) nanomaterials is a challenging theoretical task with either ab-initio or classical molecular dynamics simulations. In this regard, while ab-initio molecular dynamics (AIMD) simulations offer extremely accurate predictions, but they are excessively demanding from computational point of view. On the other side, classical molecular dynamics simulations can be conducted with affordable computational costs, but without predictive accuracy needed to study novel materials and compositions. Herein, we explore the thermal expansion of several carbon-based nanosheets on the basis of machine-learning interatomic potentials (MLIPs). We show that passively trained MLIPs over inexpensive AIMD trajectories enable the examination of thermal expansion of complex nanomembranes over wide range of temperatures. Passively fitted MLIPs could also with outstanding accuracy reproduce the phonon dispersion relations predicted by density functional theory calculations. Our results highlight that the devised methodology on the basis of passively trained MLIPs is computationally efficient and versatile to accurately examine the thermal expansion of complex and novel materials and compositions using the molecular dynamics simulations.

cond-mat.mtrl-sci↗

arXiv2021

Outstandingly high thermal conductivity, elastic modulus, carrier mobility and piezoelectricity in two-dimensional semiconducting CrC2N4: A first-principles study

Experimental realization of single-layer MoSi2N4 is among the latest groundbreaking advances in the field of two-dimensional (2D) materials. Inspired by this accomplishment, herein we conduct first-principles calculations to explore the stability of MC2N4 (M= Cr, Mo, W, V, Nb, Ta, Ti, Zr, Hf) monolayers. Acquired results confirm the desirable thermal, dynamical and mechanical stability of MC2N4 (M= Cr, Mo, W, V) nanosheets. Interestingly, CrC2N4, MoC2N4 and WC2N4 monolayers are found to be semiconductors with band gaps of 2.32, 2.76 and 2.86 eV, respectively, using the HSE06 functional, whereas VC2N4 lattice shows a metallic nature. The direct gap semiconducting nature of CrC2N4 monolayer results in excellent absorption of visible light. The elastic modulus and tensile strength of CrC2N4 nanosheet are predicted to be remarkably high, 676 and 54.8 GPa, respectively. On the basis of iterative solutions of the Boltzmann transport equation, the room temperature lattice thermal conductivity of CrC2N4 monolayer is predicted to be 350 W/mK, among the highest in 2D semiconductors. CrC2N4 and WC2N4 lattices are also found to exhibit outstandingly high piezoelectric coefficients. This study introduces CrC2N4 nanosheet as a novel 2D semiconductor with outstandingly high mechanical strength, thermal conductivity, carrier mobility and piezoelectric coefficient.

cond-mat.mtrl-sci↗

arXiv2021

High tensile strength and thermal conductivity in BeO monolayer: A first-principles study

In a latest experimental advance, graphene-like and insulating BeO monolayer was successfully grown over silver surface by molecular beam epitaxy (ACS Nano 15(2021), 2497). Inspired by this accomplishment, in this work we conduct first-principles based simulations to explore the electronic, mechanical properties and thermal conductivity of graphene-like BeO, MgO and CaO monolayers. The considered nanosheets are found to show desirable thermal and dynamical stability. BeO monolayer is found to show remarkably high elastic modulus and tensile strength of 408 and 53.3 GPa, respectively. The electronic band gap of BeO, MgO and CaO monolayers are predicted to be 6.72, 4.79, and 3.80 eV, respectively, using the HSE06 functional. On the basis of iterative solutions of the Boltzmann transport equation, the room temperature lattice thermal conductivity of BeO, MgO and CaO monolayers are predicted to be 385, 64 and 15 W/mK, respectively. Our results reveal substantial decline in the electronic band gap, mechanical strength and thermal conductivity by increasing the weight of metal atoms. This work highlights outstandingly high thermal conductivity, carrier mobility and mechanical strength of insulating BeO nanosheets and suggest them as promising candidates to design strong and insulating components with high thermal conductivities.

cond-mat.mtrl-sci↗

arXiv2021

Machine learning assisted multiscale modeling of composite phase change materials for Li-ion batteries thermal management

In this work, we develop a combined convolutional neural networks (CNNs) and finite element method (FEM) to examine the effective thermal properties of composite phase change materials (CPCMs) consisting of paraffin and copper foam. In this approach, first the CPCM microstructures are modeled using FEM and next the image dataset with corresponding thermal properties is created. The image dataset is subsequently used to train and test the CNN performance, which is then compared with the performance of a popular network architecture for image classification tasks. The predicted thermal properties are employed to define the properties of the CPCM material of a battery pack. The heat generation and electrochemical response of a Li-ion cell during the charging/discharging is simulated by applying Newman battery model. Thermal management is achieved by the latent heat of paraffin, with copper foam for enhancing the thermal conductivity. The multiscale model is finally developed using FEM to investigate the effectiveness of the thermal management of the battery pack. In these models the thermal properties estimated by the FEM and the CNN are employed to define the CPCM materials properties of a battery pack. Our results confirm that the model developed on the basis of a CNN can evaluate the effectiveness of the battery packs thermal management system with an excellent accuracy in comparison with the original FEM models.

physics.comp-ph↗

arXiv2021

Nonlocal strong forms of thin plate, gradient elasticity, magneto-electro-elasticity and phase field fracture by nonlocal operator method

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 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 .

math.NA↗

arXiv2021

A Deep Collocation Method for the Bending Analysis of Kirchhoff Plate

In this paper, a deep collocation method (DCM) for thin plate bending problems is proposed. This method takes advantage of computational graphs and backpropagation algorithms involved in deep learning. Besides, the proposed DCM is based on a feedforward deep neural network (DNN) and differs from most previous applications of deep learning for mechanical problems. First, batches of randomly distributed collocation points are initially generated inside the domain and along the boundaries. A loss function is built with the aim that the governing partial differential equations (PDEs) of Kirchhoff plate bending problems, and the boundary/initial conditions are minimised at those collocation points. A combination of optimizers is adopted in the backpropagation process to minimize the loss function so as to obtain the optimal hyperparameters. In Kirchhoff plate bending problems, the C1 continuity requirement poses significant difficulties in traditional mesh-based methods. This can be solved by the proposed DCM, which uses a deep neural network to approximate the continuous transversal deflection, and is proved to be suitable to the bending analysis of Kirchhoff plate of various geometries.

math.NA↗

arXiv2020

Exceptional piezoelectricity, high thermal conductivity and stiffness and promising photocatalysis in two-dimensional MoSi2N4 family confirmed by first-principles

Chemical vapor deposition has been most recently employed to fabricate centimeter-scale high-quality single-layer MoSi2N4 (Science; 2020;369; 670). Motivated by this exciting experimental advance, herein we conduct extensive first-principles based simulations to explore the stability, mechanical properties, lattice thermal conductivity, piezoelectric and flexoelectric response, and photocatalytic and electronic features of MA2Z4 (M = Cr, Mo, W; A = Si, Ge; Z = N, P) monolayers. The considered nanosheets are found to exhibit dynamical stability and remarkably high mechanical properties. Moreover, they show diverse electronic properties from antiferromagnetic metal to half metal and to semiconductors with band gaps ranging from 0.31 to 2.57 eV. Among the studied nanosheets, the MoSi2N4 and WSi2N4 monolayers yield appropriate band edge positions, high electron and hole mobilities, and strong visible light absorption, highly promising for applications in optoelectronics and photocatalytic water splitting. The MoSi2N4 and WSi2N4 monolayers are also predicted to show outstandingly high lattice thermal conductivity of 440 and 500 W/mK, respectively. For the first time we show that machine learning interatomic potentials trained over small supercells can be employed to examine the flexoelectric and piezoelectric properties of complex structures. As the most exciting finding, WSi2N4, CrSi2N4 and MoSi2N4 are found to exhibit the highest piezoelectric coefficients, outperforming all other-known 2D materials. Our results highlight that MA2Z4 nanosheets not only undoubtedly outperform the transition metal dichalcogenides family but also can compete with graphene for applications in nanoelectronics, optoelectronic, energy storage/conversion and thermal management systems.

cond-mat.mtrl-sci↗

arXiv2020

A 55-line code for large-scale parallel topology optimization in 2D and 3D

This paper presents a 55-line code written in python for 2D and 3D topology optimization (TO) based on the open-source finite element computing software (FEniCS), equipped with various finite element tools and solvers. PETSc is used as the linear algebra back-end, which results in significantly less computational time than standard python libraries. The code is designed based on the popular solid isotropic material with penalization (SIMP) methodology. Extensions to multiple load cases, different boundary conditions, and incorporation of passive elements are also presented. Thus, this implementation is the most compact implementation of SIMP based topology optimization for 3D as well as 2D problems. Utilizing the concept of Euclidean distance matrix to vectorize the computation of the weight matrix for the filter, we have achieved a substantial reduction in the computational time and have also made it possible for the code to work with complex ground structure configurations. We have also presented the code's extension to large-scale topology optimization problems with support for parallel computations on complex structural configuration, which could help students and researchers explore novel insights into the TO problem with dense meshes. Appendix-A contains the complete code, and the website: \url{https://github.com/iitrabhi/topo-fenics} also contains the complete code.

cs.MS↗

arXiv2020

Stochastic analysis of heterogeneous porous material with modified neural architecture search (NAS) based physics-informed neural networks using transfer learning

In this work, a modified neural architecture search method (NAS) based physics-informed deep learning model is presented for stochastic analysis in heterogeneous porous material. Monte Carlo method based on a randomized spectral representation is first employed to construct a stochastic model for simulation of flow through porous media. To solve the governing equations for stochastic groundwater flow problem, we build a modified NAS model based on physics-informed neural networks (PINNs) with transfer learning in this paper that will be able to fit different partial differential equations (PDEs) with less calculation. The performance estimation strategies adopted is constructed from an error estimation model using the method of manufactured solutions. A sensitivity analysis is performed to obtain the prior knowledge of the PINNs model and narrow down the range of parameters for search space and use hyper-parameter optimization algorithms to further determine the values of the parameters. Further the NAS based PINNs model also saves the weights and biases of the most favorable architectures, then used in the fine-tuning process. It is found that the log-conductivity field using Gaussian correlation function will perform much better than exponential correlation case, which is more fitted to the PINNs model and the modified neural architecture search based PINNs model shows a great potential in approximating solutions to PDEs. Moreover, a three dimensional stochastic flow model is built to provide a benchmark to the simulation of groundwater flow in highly heterogeneous aquifers. The NAS model based deep collocation method is verified to be effective and accurate through numerical examples in different dimensions using different manufactured solutions.

cs.LG↗

arXiv2020

Laser Exfoliation of Graphene from Graphite

Synthesis of graphene with reduced use of chemical reagents is essential for manufacturing scale-up and to control its structure and properties. In this paper, we report on a novel chemical-free mechanism of graphene exfoliation from graphite using laser impulse. Our experimental setup consists of a graphite slab irradiated with an Nd:YAG laser of wavelength 532 nm and 10 ns pulse width. The results show the formation of graphene layers with conformational morphology from electron microscopy and Raman spectra. Based on the experimental results, we develop a simulation set up within the framework of the molecular dynamics that supplies the laser-induced electromagnetic energies to atoms in the graphite slab. We investigate the influence of different laser fluence on the exfoliation process of graphene. The variations in inter-layer interaction energy and inter-layer distance are the confirmative measures for the possible graphene layer formation. The simulation results confirm the exfoliation of a single layer graphene sheet for the laser power ranging from 100x10^(-14) to 2000x10^(-14) J/nm2. With an increase of laser fluence from 2000x10^(-14) to 4000x10^(-14) J/nm2, there is an increase in the graphene yield via the layer-after-layer exfoliation. The bridging bond dynamics between the successive graphene layers govern the possibility of second-layer exfoliation. The experimental and simulation observations are useful and promising for producing chemical-free graphene on a large scale for industrial and commercial applications.

physics.app-ph↗

arXiv2020

Integrated intelligent Jaya Runge-Kutta method for solving Falkner-Skan equations for Various Wedge Angles

In this work, the hybrid intelligent computing method, which combines efficient Jaya algorithm with classical Runge-Kutta method is applied to solve the Falkner-Skan equations with various wedge angles, which is the fundamental equation for a variety of computational fluid mechanical problems. With some coordinate transformation, the Falkner-Skan boundary layer problem is then converted into a free boundary problem defined on a finite interval. Then using higher order reduction strategies, the whole problem can be boiled down to a solving of coupled differential equations with prescribed initial and boundary conditions. The hybrid Jaya Runge-Kutta method is found to yield stable and accurate results and able to extract those unknown parameters. The sensitivity of classical shooting method to the guess of initial values can be easily overcome by an integrated robust optimization method. In addition, the Jaya algorithm, without the need for tuning the algorithm-specific parameters, is proved to be effective and stable for minimizing the fitness function in application. By comparing the solutions using the Jaya method with PSO (particle swarm optimization), Genetic algorithm (GA), Hyperband, and the classical analytical methods, the hybrid Jaya Runge-Kutta method yields more stable and accurate results, which shows great potential for solving more complicated multi-field and multiphase flow problems.

math.NA↗

arXiv2020

Deep Autoencoder based Energy Method for the Bending, Vibration, and Buckling Analysis of Kirchhoff Plates

In this paper, we present a deep autoencoder based energy method (DAEM) for the bending, vibration and buckling analysis of Kirchhoff plates. The DAEM exploits the higher order continuity of the DAEM and integrates a deep autoencoder and the minimum total potential principle in one framework yielding an unsupervised feature learning method. The DAEM is a specific type of feedforward deep neural network (DNN) and can also serve as function approximator. With robust feature extraction capacity, the DAEM can more efficiently identify patterns behind the whole energy system, such as the field variables, natural frequency and critical buckling load factor studied in this paper. The objective function is to minimize the total potential energy. The DAEM performs unsupervised learning based on random generated points inside the physical domain so that the total potential energy is minimized at all points. For vibration and buckling analysis, the loss function is constructed based on Rayleigh's principle and the fundamental frequency and the critical buckling load is extracted. A scaled hyperbolic tangent activation function for the underlying mechanical model is presented which meets the continuity requirement and alleviates the gradient vanishing/explosive problems under bending analysis. The DAEM can be easily implemented and we employed the Pytorch library and the LBFGS optimizer. A comprehensive study of the DAEM configuration is performed for several numerical examples with various geometries, load conditions, and boundary conditions.

cs.LG↗