The non-equilibrium gas dynamics is described by the Boltzmann equation, which can be solved numerically through the deterministic and stochastic methods. Due to the complicated collision term of the Boltzmann equation, many kinetic relaxation models have been proposed and used in the past seventy years for the study of rarefied flow. In order to develop a multiscale method for the rarefied and continuum flow simulation, by adopting the integral solution of the kinetic model equation a DVM-type unified gas-kinetic scheme (UGKS) has been constructed. The UGKS models the gas dynamics on the cell size and time step scales while the accumulating effect from particle transport and collision has been taken into account within a time step. Under the UGKS framework, a unified gas-kinetic wave-particle (UGKWP) method has been further developed for non-equilibrium flow simulation, where the time evolution of gas distribution function is composed of analytical wave and individual particle. In the highly rarefied regime, particle transport and collision will play a dominant role. Due to the single relaxation time model for particle collision, there is a noticeable discrepancy between the UGKWP solution and the full Boltzmann or DSMC result, especially in the high Mach and Knudsen number cases. In this paper, besides the kinetic relaxation model, a modification of particle collision time according to the particle velocity will be implemented in UGKWP. As a result, the new model greatly improves the performance of UGKWP in the capturing of non-equilibrium flow. There is a perfect match between UGKWP and DSMC or Boltzmann solution in the highly rarefied regime. In the near continuum and continuum flow regime, the UGKWP will gradually get back to the macroscopic variables based Navier-Stokes flow solver at small cell Knudsen number.
{"title":"Modeling and computation for non-equilibrium gas dynamics: Beyond single relaxation time kinetic models","authors":"Xiaocong Xu, Yipei Chen, K. Xu","doi":"10.1063/5.0036203","DOIUrl":"https://doi.org/10.1063/5.0036203","url":null,"abstract":"The non-equilibrium gas dynamics is described by the Boltzmann equation, which can be solved numerically through the deterministic and stochastic methods. Due to the complicated collision term of the Boltzmann equation, many kinetic relaxation models have been proposed and used in the past seventy years for the study of rarefied flow. In order to develop a multiscale method for the rarefied and continuum flow simulation, by adopting the integral solution of the kinetic model equation a DVM-type unified gas-kinetic scheme (UGKS) has been constructed. The UGKS models the gas dynamics on the cell size and time step scales while the accumulating effect from particle transport and collision has been taken into account within a time step. Under the UGKS framework, a unified gas-kinetic wave-particle (UGKWP) method has been further developed for non-equilibrium flow simulation, where the time evolution of gas distribution function is composed of analytical wave and individual particle. In the highly rarefied regime, particle transport and collision will play a dominant role. Due to the single relaxation time model for particle collision, there is a noticeable discrepancy between the UGKWP solution and the full Boltzmann or DSMC result, especially in the high Mach and Knudsen number cases. In this paper, besides the kinetic relaxation model, a modification of particle collision time according to the particle velocity will be implemented in UGKWP. As a result, the new model greatly improves the performance of UGKWP in the capturing of non-equilibrium flow. There is a perfect match between UGKWP and DSMC or Boltzmann solution in the highly rarefied regime. In the near continuum and continuum flow regime, the UGKWP will gradually get back to the macroscopic variables based Navier-Stokes flow solver at small cell Knudsen number.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-10-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79153725","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present a computational method to directly calculate and visualize the directional components of the Coulomb, radiation, and total electromagnetic fields, as well as the scalar and vector potentials, generated from moving point charges in arbitrary motion with varying speeds. We explicitly calculate the retarded time of the point charge along a discretized grid which is then used to determine the fields and potentials. Our computational approach, implemented in Python, provides an intuitive understanding of the electromagnetic waves generated from moving point charges and can be used in conjunction with grid-based numerical modeling methods to solve real-world computational electromagnetics problems. The method can also be used to help students visualize problems related to moving potentials, which are often only treated analytically for very simple problems, and can be used to compute electromagnetic sources for non-trivial electron beams with other approaches in computational electromagnetics.
{"title":"Space-time computation and visualization of the electromagnetic fields and potentials generated by moving point charges","authors":"M. Filipovich, S. Hughes","doi":"10.1119/10.0003207","DOIUrl":"https://doi.org/10.1119/10.0003207","url":null,"abstract":"We present a computational method to directly calculate and visualize the directional components of the Coulomb, radiation, and total electromagnetic fields, as well as the scalar and vector potentials, generated from moving point charges in arbitrary motion with varying speeds. We explicitly calculate the retarded time of the point charge along a discretized grid which is then used to determine the fields and potentials. Our computational approach, implemented in Python, provides an intuitive understanding of the electromagnetic waves generated from moving point charges and can be used in conjunction with grid-based numerical modeling methods to solve real-world computational electromagnetics problems. The method can also be used to help students visualize problems related to moving potentials, which are often only treated analytically for very simple problems, and can be used to compute electromagnetic sources for non-trivial electron beams with other approaches in computational electromagnetics.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91453271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-09-28DOI: 10.1103/PhysRevB.103.214102
Amir Hajibabaei, C. Myung, Kwang Soo Kim
For machine learning of interatomic potentials the sparse Gaussian process regression formalism is introduced with a data-efficient adaptive sampling algorithm. This is applied for dozens of solid electrolytes. As a showcase, experimental melting and glass-crystallization temperatures are reproduced for Li7P3S11 and an unchartered infelicitous phase is revealed with much lower Li diffusivity which should be circumvented. By hierarchical combinations of the expert models universal potentials are generated, which pave the way for modeling large-scale complexity by a combinatorial approach.
{"title":"Sparse Gaussian process potentials: Application to lithium diffusivity in superionic conducting solid electrolytes","authors":"Amir Hajibabaei, C. Myung, Kwang Soo Kim","doi":"10.1103/PhysRevB.103.214102","DOIUrl":"https://doi.org/10.1103/PhysRevB.103.214102","url":null,"abstract":"For machine learning of interatomic potentials the sparse Gaussian process regression formalism is introduced with a data-efficient adaptive sampling algorithm. This is applied for dozens of solid electrolytes. As a showcase, experimental melting and glass-crystallization temperatures are reproduced for Li7P3S11 and an unchartered infelicitous phase is revealed with much lower Li diffusivity which should be circumvented. By hierarchical combinations of the expert models universal potentials are generated, which pave the way for modeling large-scale complexity by a combinatorial approach.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74780541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yu-Hua Yao, Q. Zeng, Ke-Ming Chen, D. Kang, Yong Hou, Q. Ma, Jiayu Dai
The dynamic electron-ion collisions play an important role in determining the static and transport properties of warm dense matter (WDM). Electron force field (eFF) method is applied to study the ionic transport properties of warm dense hydrogen. Compared with the results from quantum molecular dynamics and orbital-free molecular dynamics, the ionic diffusions are largely reduced by involving the dynamic collisions of electrons and ions. This physics is verfied by the quantum Langevin molecular dynamics simulations, which includes electron-ion collisions induced friction into the dynamic equation of ions. Based on these new results, we proposed a model including the correction of collisions induced friction (CIF) of ionic diffusion. The CIF model has been verified to be valid at a wide range of density and temperature. We also compare the results with the one component plasma (OCP), Yukawa OCP (YOCP) and Effective OCP (EOCP) models, showing the significant effect of non-adibatic dynamics.
{"title":"Reduced ionic diffusion by the dynamic electron–ion collisions in warm dense hydrogen","authors":"Yu-Hua Yao, Q. Zeng, Ke-Ming Chen, D. Kang, Yong Hou, Q. Ma, Jiayu Dai","doi":"10.1063/5.0028925","DOIUrl":"https://doi.org/10.1063/5.0028925","url":null,"abstract":"The dynamic electron-ion collisions play an important role in determining the static and transport properties of warm dense matter (WDM). Electron force field (eFF) method is applied to study the ionic transport properties of warm dense hydrogen. Compared with the results from quantum molecular dynamics and orbital-free molecular dynamics, the ionic diffusions are largely reduced by involving the dynamic collisions of electrons and ions. This physics is verfied by the quantum Langevin molecular dynamics simulations, which includes electron-ion collisions induced friction into the dynamic equation of ions. Based on these new results, we proposed a model including the correction of collisions induced friction (CIF) of ionic diffusion. The CIF model has been verified to be valid at a wide range of density and temperature. We also compare the results with the one component plasma (OCP), Yukawa OCP (YOCP) and Effective OCP (EOCP) models, showing the significant effect of non-adibatic dynamics.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90568867","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Hep Software Foundation Thea Aarrestad, S. Amoroso, M. Atkinson, J. Bendavid, T. Boccali, A. Bocci, Andy Buckley, M. Cacciari, P. Calafiura, P. Canal, F. Carminati, T. Childers, V. Ciulli, G. Corti, D. Costanzo, J. G. Dezoort, C. Doglioni, Javier Mauricio Duarte, A. Dziurda, P. Elmer, M. Elsing, V. Elvira, G. Eulisse, J. Menendez, C. Fitzpatrick, R. Frederix, S. Frixione, K. Genser, A. Gheata, F. Giuli, V. Gligorov, Hadrien Grasland, H. Gray, L. Gray, A. Grohsjean, C. Gutschow, S. Hageboeck, P. Harris, B. Hegner, L. Heinrich, B. Holzman, W. Hopkins, S. Hsu, S. Hoche, P. Ilten, V. Ivantchenko, Chris Jones, M. Jouvin, T. J. Khoo, I. Kisel, K. Knoepfel, D. Konstantinov, A. Krasznahorkay, F. Krauss, B. Krikler, D. Lange, P. Laycock, Qiang Li, K. Lieret, Miaoyuan Liu, V. Loncar, L. Lonnblad, F. Maltoni, M. Mangano, Z. Marshall, P. Mato, O. Mattelaer, J. Mcfayden, S. Meehan, A. S. Mete, B. Morgan, S. Mrenna, S. Muralidharan, B. Nachman, M. Neubauer, T. Neumann, J. Ngadiuba, I. Ojalvo, K. Pedro, M. Perini, D. Pi
Common and community software packages, such as ROOT, Geant4 and event generators have been a key part of the LHC's success so far and continued development and optimisation will be critical in the future. The challenges are driven by an ambitious physics programme, notably the LHC accelerator upgrade to high-luminosity, HL-LHC, and the corresponding detector upgrades of ATLAS and CMS. In this document we address the issues for software that is used in multiple experiments (usually even more widely than ATLAS and CMS) and maintained by teams of developers who are either not linked to a particular experiment or who contribute to common software within the context of their experiment activity. We also give space to general considerations for future software and projects that tackle upcoming challenges, no matter who writes it, which is an area where community convergence on best practice is extremely useful.
{"title":"HL-LHC Computing Review: Common Tools and Community Software","authors":"Hep Software Foundation Thea Aarrestad, S. Amoroso, M. Atkinson, J. Bendavid, T. Boccali, A. Bocci, Andy Buckley, M. Cacciari, P. Calafiura, P. Canal, F. Carminati, T. Childers, V. Ciulli, G. Corti, D. Costanzo, J. G. Dezoort, C. Doglioni, Javier Mauricio Duarte, A. Dziurda, P. Elmer, M. Elsing, V. Elvira, G. Eulisse, J. Menendez, C. Fitzpatrick, R. Frederix, S. Frixione, K. Genser, A. Gheata, F. Giuli, V. Gligorov, Hadrien Grasland, H. Gray, L. Gray, A. Grohsjean, C. Gutschow, S. Hageboeck, P. Harris, B. Hegner, L. Heinrich, B. Holzman, W. Hopkins, S. Hsu, S. Hoche, P. Ilten, V. Ivantchenko, Chris Jones, M. Jouvin, T. J. Khoo, I. Kisel, K. Knoepfel, D. Konstantinov, A. Krasznahorkay, F. Krauss, B. Krikler, D. Lange, P. Laycock, Qiang Li, K. Lieret, Miaoyuan Liu, V. Loncar, L. Lonnblad, F. Maltoni, M. Mangano, Z. Marshall, P. Mato, O. Mattelaer, J. Mcfayden, S. Meehan, A. S. Mete, B. Morgan, S. Mrenna, S. Muralidharan, B. Nachman, M. Neubauer, T. Neumann, J. Ngadiuba, I. Ojalvo, K. Pedro, M. Perini, D. Pi","doi":"10.5281/zenodo.4009114","DOIUrl":"https://doi.org/10.5281/zenodo.4009114","url":null,"abstract":"Common and community software packages, such as ROOT, Geant4 and event generators have been a key part of the LHC's success so far and continued development and optimisation will be critical in the future. The challenges are driven by an ambitious physics programme, notably the LHC accelerator upgrade to high-luminosity, HL-LHC, and the corresponding detector upgrades of ATLAS and CMS. In this document we address the issues for software that is used in multiple experiments (usually even more widely than ATLAS and CMS) and maintained by teams of developers who are either not linked to a particular experiment or who contribute to common software within the context of their experiment activity. We also give space to general considerations for future software and projects that tackle upcoming challenges, no matter who writes it, which is an area where community convergence on best practice is extremely useful.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87515500","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In density functional high temperature simulations (from tens of eV to keV) the total number of Kohn-Sham orbitals is a critical quantity to get sound results. The occupation of the highest orbital in energy is here derived from the properties of the homogeneous electron gas, which gives a prescription on the total number of orbitals to reach a given level of occupation. Very low levels of occupation (10-5 to 10-6) must be considered to get convergence with Kohn-Sham orbitals, making high temperature simulations unreachable beyond a few tens of eV. After testing these predictions against ABINIT oftware package results, we test the implementation of the Extended method of Zhang et al. [PoP 23 042707, 2016] in the ABINIT package to adress very high temperatures by bypassing these strong orbital constraint.
{"title":"Requirements for very high temperature Kohn–Sham DFT simulations and how to bypass them","authors":"A. Blanchet, M. Torrent, J. Clérouin","doi":"10.1063/5.0016538","DOIUrl":"https://doi.org/10.1063/5.0016538","url":null,"abstract":"In density functional high temperature simulations (from tens of eV to keV) the total number of Kohn-Sham orbitals is a critical quantity to get sound results. The occupation of the highest orbital in energy is here derived from the properties of the homogeneous electron gas, which gives a prescription on the total number of orbitals to reach a given level of occupation. Very low levels of occupation (10-5 to 10-6) must be considered to get convergence with Kohn-Sham orbitals, making high temperature simulations unreachable beyond a few tens of eV. After testing these predictions against ABINIT oftware package results, we test the implementation of the Extended method of Zhang et al. [PoP 23 042707, 2016] in the ABINIT package to adress very high temperatures by bypassing these strong orbital constraint.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83731417","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present a novel adaptive machine-learning based approach for reconstructing three-dimensional (3D) crystals from coherent diffraction imaging (CDI). We represent the crystals using spherical harmonics (SH) and generate corresponding synthetic diffraction patterns. We utilize 3D convolutional neural networks (CNN) to learn a mapping between 3D diffraction volumes and the SH which describe the boundary of the physical volumes from which they were generated. We use the 3D CNN-predicted SH coefficients as the initial guesses which are then fine tuned using adaptive model independent feedback for improved accuracy.
{"title":"Adaptive 3D convolutional neural network-based reconstruction method for 3D coherent diffraction imaging","authors":"A. Scheinker, R. Pokharel","doi":"10.1063/5.0014725","DOIUrl":"https://doi.org/10.1063/5.0014725","url":null,"abstract":"We present a novel adaptive machine-learning based approach for reconstructing three-dimensional (3D) crystals from coherent diffraction imaging (CDI). We represent the crystals using spherical harmonics (SH) and generate corresponding synthetic diffraction patterns. We utilize 3D convolutional neural networks (CNN) to learn a mapping between 3D diffraction volumes and the SH which describe the boundary of the physical volumes from which they were generated. We use the 3D CNN-predicted SH coefficients as the initial guesses which are then fine tuned using adaptive model independent feedback for improved accuracy.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81576181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-08-17DOI: 10.1103/physrevb.102.174105
K. Toyoura, Kansei Kanayama
An efficient machine-learning-based method combined with a conventional local optimization technique has been proposed for exploring local energy minima of interstitial species in a crystal. In the proposed method, an effective initial point for local optimization is sampled at each iteration from a given feasible set in the search space. The effective initial point is here defined as the grid point that most likely converges to a new local energy minimum by local optimization and/or is located in the vicinity of the boundaries between energy basins. Specifically, every grid point in the feasible set is classified by the predicted label indicating the local energy minimum that the grid point converges to. The classifier is created and updated at every iteration using the already-known information on the local optimizations at the earlier iterations, which is based on the support vector machine (SVM). The SVM classifier uses our original kernel function designed as reflecting the symmetries of both host crystal and interstitial species. The most distant unobserved point on the classification boundaries from the observed points is sampled as the next initial point for local optimization. The proposed method is applied to three model cases, i.e., the six-hump camelback function, a proton in strontium zirconate with the orthorhombic perovskite structure, and a water molecule in lanthanum sulfate with the monoclinic structure, to demonstrate the high performance of the proposed method.
{"title":"Machine-learning-based sampling method for exploring local energy minima of interstitial species in a crystal","authors":"K. Toyoura, Kansei Kanayama","doi":"10.1103/physrevb.102.174105","DOIUrl":"https://doi.org/10.1103/physrevb.102.174105","url":null,"abstract":"An efficient machine-learning-based method combined with a conventional local optimization technique has been proposed for exploring local energy minima of interstitial species in a crystal. In the proposed method, an effective initial point for local optimization is sampled at each iteration from a given feasible set in the search space. The effective initial point is here defined as the grid point that most likely converges to a new local energy minimum by local optimization and/or is located in the vicinity of the boundaries between energy basins. Specifically, every grid point in the feasible set is classified by the predicted label indicating the local energy minimum that the grid point converges to. The classifier is created and updated at every iteration using the already-known information on the local optimizations at the earlier iterations, which is based on the support vector machine (SVM). The SVM classifier uses our original kernel function designed as reflecting the symmetries of both host crystal and interstitial species. The most distant unobserved point on the classification boundaries from the observed points is sampled as the next initial point for local optimization. The proposed method is applied to three model cases, i.e., the six-hump camelback function, a proton in strontium zirconate with the orthorhombic perovskite structure, and a water molecule in lanthanum sulfate with the monoclinic structure, to demonstrate the high performance of the proposed method.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80335369","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-21DOI: 10.1103/PhysRevResearch.2.033107
Naoki Seryo, Takeshi Sato, J. J. Molina, T. Taniguchi
We develop a learning strategy to infer the constitutive relation for the stress of polymeric flows with memory. We make no assumptions regarding the functional form of the constitutive relations, except that they should be expressible in differential form as a function of the local stress- and strain-rate tensors. In particular, we use a Gaussian Process regression to infer the constitutive relations from stress trajectories generated from small-scale (fixed strain-rate) microscopic polymer simulations. For simplicity, a Hookean dumbbell representation is used as a microscopic model, but the method itself can be generalized to incorporate more realistic descriptions. The learned constitutive relation is then used to perform macroscopic flow simulations, allowing us to update the stress distribution in the fluid in a manner that accounts for the microscopic polymer dynamics. The results using the learned constitutive relation are in excellent agreement with full Multi-Scale Simulations, which directly couple micro/macro degrees of freedom, as well as the exact analytical solution given by the Maxwell constitutive relation. We are able to fully capture the history dependence of the flow, as well as the elastic effects in the fluid. We expect the proposed learning/simulation approach to be used not only to study the dynamics of entangled polymer flows, but also for the complex dynamics of other Soft Matter systems, which possess a similar hierarchy of length- and time-scales.
{"title":"Learning the constitutive relation of polymeric flows with memory","authors":"Naoki Seryo, Takeshi Sato, J. J. Molina, T. Taniguchi","doi":"10.1103/PhysRevResearch.2.033107","DOIUrl":"https://doi.org/10.1103/PhysRevResearch.2.033107","url":null,"abstract":"We develop a learning strategy to infer the constitutive relation for the stress of polymeric flows with memory. We make no assumptions regarding the functional form of the constitutive relations, except that they should be expressible in differential form as a function of the local stress- and strain-rate tensors. In particular, we use a Gaussian Process regression to infer the constitutive relations from stress trajectories generated from small-scale (fixed strain-rate) microscopic polymer simulations. For simplicity, a Hookean dumbbell representation is used as a microscopic model, but the method itself can be generalized to incorporate more realistic descriptions. The learned constitutive relation is then used to perform macroscopic flow simulations, allowing us to update the stress distribution in the fluid in a manner that accounts for the microscopic polymer dynamics. The results using the learned constitutive relation are in excellent agreement with full Multi-Scale Simulations, which directly couple micro/macro degrees of freedom, as well as the exact analytical solution given by the Maxwell constitutive relation. We are able to fully capture the history dependence of the flow, as well as the elastic effects in the fluid. We expect the proposed learning/simulation approach to be used not only to study the dynamics of entangled polymer flows, but also for the complex dynamics of other Soft Matter systems, which possess a similar hierarchy of length- and time-scales.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83552570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2020-07-20DOI: 10.1615/JMACHLEARNMODELCOMPUT.2021037052
G. Dong, K. Felker, Alexey Svyatkovskiy, W. Tang, J. Kates-Harbeck
We have trained a fully convolutional spatio-temporal model for fast and accurate representation learning in the challenging exemplar application area of fusion energy plasma science. The onset of major disruptions is a critically important fusion energy science (FES) issue that must be resolved for advanced tokamak. While a variety of statistical methods have been used to address the problem of tokamak disruption prediction and control, recent approaches based on deep learning have proven particularly compelling. In the present paper, we introduce further improvements to the fusion recurrent neural network (FRNN) software suite. Up to now, FRNN was based on the long short-term memory (LSTM) variant of recurrent neural networks to leverage the temporal information in the data. Here, we implement and apply the temporal convolutional neural network (TCN) architecture to the time-dependent input signals, thus rendering the FRNN architecture fully convolutional. This allows highly optimized convolution operations to carry the majority of the computational load of training, thus enabling a reduction in training time, and the effective use of high performance computing (HPC) resources for hyperparameter tuning. At the same time, the TCN based architecture achieves equal or better predictive performance when compared with the LSTM architecture for a large, representative fusion database. Across data-rich scientific disciplines, these results have implications for the resource-effective training of general spatio-temporal feature extractors based on deep learning. Moreover, this challenging exemplar case study illustrates the advantages of a predictive platform with flexible architecture selection options capable of being readily tuned and adapted for responding to prediction needs that increasingly arise in large modern observational dataset.
{"title":"FULLY CONVOLUTIONAL SPATIO-TEMPORAL MODELS FOR REPRESENTATION LEARNING IN PLASMA SCIENCE","authors":"G. Dong, K. Felker, Alexey Svyatkovskiy, W. Tang, J. Kates-Harbeck","doi":"10.1615/JMACHLEARNMODELCOMPUT.2021037052","DOIUrl":"https://doi.org/10.1615/JMACHLEARNMODELCOMPUT.2021037052","url":null,"abstract":"We have trained a fully convolutional spatio-temporal model for fast and accurate representation learning in the challenging exemplar application area of fusion energy plasma science. The onset of major disruptions is a critically important fusion energy science (FES) issue that must be resolved for advanced tokamak. While a variety of statistical methods have been used to address the problem of tokamak disruption prediction and control, recent approaches based on deep learning have proven particularly compelling. In the present paper, we introduce further improvements to the fusion recurrent neural network (FRNN) software suite. Up to now, FRNN was based on the long short-term memory (LSTM) variant of recurrent neural networks to leverage the temporal information in the data. Here, we implement and apply the temporal convolutional neural network (TCN) architecture to the time-dependent input signals, thus rendering the FRNN architecture fully convolutional. This allows highly optimized convolution operations to carry the majority of the computational load of training, thus enabling a reduction in training time, and the effective use of high performance computing (HPC) resources for hyperparameter tuning. At the same time, the TCN based architecture achieves equal or better predictive performance when compared with the LSTM architecture for a large, representative fusion database. Across data-rich scientific disciplines, these results have implications for the resource-effective training of general spatio-temporal feature extractors based on deep learning. Moreover, this challenging exemplar case study illustrates the advantages of a predictive platform with flexible architecture selection options capable of being readily tuned and adapted for responding to prediction needs that increasingly arise in large modern observational dataset.","PeriodicalId":8424,"journal":{"name":"arXiv: Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2020-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81810185","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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