Ryuichi Sai, Francois P. Hamon, John Mellor-Crummey, Mauricio Araya-Polo
Fast and accurate numerical simulations are crucial for designing large-scale geological carbon storage projects ensuring safe long-term CO2 containment as a climate change mitigation strategy. These simulations involve solving numerous large and complex linear systems arising from the implicit Finite Volume (FV) discretization of PDEs governing subsurface fluid flow. Compounded with highly detailed geomodels, solving linear systems is computationally and memory expensive, and accounts for the majority of the simulation time. Modern memory hierarchies are insufficient to meet the latency and bandwidth needs of large-scale numerical simulations. Therefore, exploring algorithms that can leverage alternative and balanced paradigms, such as dataflow and in-memory computing is crucial. This work introduces a matrix-free algorithm to solve FV-based linear systems using a dataflow architecture to significantly minimize memory latency and bandwidth bottlenecks. Our implementation achieves two orders of magnitude speedup compared to a GPGPU-based reference implementation, and up to 1.2 PFlops on a single dataflow device.
{"title":"Matrix-Free Finite Volume Kernels on a Dataflow Architecture","authors":"Ryuichi Sai, Francois P. Hamon, John Mellor-Crummey, Mauricio Araya-Polo","doi":"arxiv-2408.03452","DOIUrl":"https://doi.org/arxiv-2408.03452","url":null,"abstract":"Fast and accurate numerical simulations are crucial for designing large-scale\u0000geological carbon storage projects ensuring safe long-term CO2 containment as a\u0000climate change mitigation strategy. These simulations involve solving numerous\u0000large and complex linear systems arising from the implicit Finite Volume (FV)\u0000discretization of PDEs governing subsurface fluid flow. Compounded with highly\u0000detailed geomodels, solving linear systems is computationally and memory\u0000expensive, and accounts for the majority of the simulation time. Modern memory\u0000hierarchies are insufficient to meet the latency and bandwidth needs of\u0000large-scale numerical simulations. Therefore, exploring algorithms that can\u0000leverage alternative and balanced paradigms, such as dataflow and in-memory\u0000computing is crucial. This work introduces a matrix-free algorithm to solve\u0000FV-based linear systems using a dataflow architecture to significantly minimize\u0000memory latency and bandwidth bottlenecks. Our implementation achieves two\u0000orders of magnitude speedup compared to a GPGPU-based reference implementation,\u0000and up to 1.2 PFlops on a single dataflow device.","PeriodicalId":501369,"journal":{"name":"arXiv - PHYS - Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937472","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 Kolmogorov-Arnold PointNet (KA-PointNet) as a novel supervised deep learning framework for the prediction of incompressible steady-state fluid flow fields in irregular domains, where the predicted fields are a function of the geometry of the domains. In KA-PointNet, we implement shared Kolmogorov-Arnold Networks (KANs) in the segmentation branch of the PointNet architecture. We utilize Jacobi polynomials to construct shared KANs. As a benchmark test case, we consider incompressible laminar steady-state flow over a cylinder, where the geometry of its cross-section varies over the data set. We investigate the performance of Jacobi polynomials with different degrees as well as special cases of Jacobi polynomials such as Legendre polynomials, Chebyshev polynomials of the first and second kinds, and Gegenbauer polynomials, in terms of the computational cost of training and accuracy of prediction of the test set. Additionally, we compare the performance of PointNet with shared KANs (i.e., KA-PointNet) and PointNet with shared Multilayer Perceptrons (MLPs). It is observed that when the number of trainable parameters is approximately equal, PointNet with shared KANs (i.e., KA-PointNet) outperforms PointNet with shared MLPs.
{"title":"Kolmogorov-Arnold PointNet: Deep learning for prediction of fluid fields on irregular geometries","authors":"Ali Kashefi","doi":"arxiv-2408.02950","DOIUrl":"https://doi.org/arxiv-2408.02950","url":null,"abstract":"We present Kolmogorov-Arnold PointNet (KA-PointNet) as a novel supervised\u0000deep learning framework for the prediction of incompressible steady-state fluid\u0000flow fields in irregular domains, where the predicted fields are a function of\u0000the geometry of the domains. In KA-PointNet, we implement shared\u0000Kolmogorov-Arnold Networks (KANs) in the segmentation branch of the PointNet\u0000architecture. We utilize Jacobi polynomials to construct shared KANs. As a\u0000benchmark test case, we consider incompressible laminar steady-state flow over\u0000a cylinder, where the geometry of its cross-section varies over the data set.\u0000We investigate the performance of Jacobi polynomials with different degrees as\u0000well as special cases of Jacobi polynomials such as Legendre polynomials,\u0000Chebyshev polynomials of the first and second kinds, and Gegenbauer\u0000polynomials, in terms of the computational cost of training and accuracy of\u0000prediction of the test set. Additionally, we compare the performance of\u0000PointNet with shared KANs (i.e., KA-PointNet) and PointNet with shared\u0000Multilayer Perceptrons (MLPs). It is observed that when the number of trainable\u0000parameters is approximately equal, PointNet with shared KANs (i.e.,\u0000KA-PointNet) outperforms PointNet with shared MLPs.","PeriodicalId":501369,"journal":{"name":"arXiv - PHYS - Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937481","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}
Yangyiwei Yang, Patrick Kühn, Mozhdeh Fathidoost, Esmaeil Adabifiroozjaei, Ruiwen Xie, Eren Foya, Dominik Ohmer, Konstantin Skokov, Leopoldo Molina-Luna, Oliver Gutfleisch, Hongbin Zhang, Bai-Xiang Xu
Around 17,000 micromagnetic simulations were performed with a wide variation of geometric and magnetic parameters of different cellular nanostructures in the samarium-cobalt-based 1:7-type (SmCo-1:7) magnets. A forward prediction neural network (NN) model is trained to unveil the influence of these parameters on the coercivity of materials, along with the sensitivity analysis. Results indicate the important role of the 1:5-phase in enhancing coercivity. Moreover, an inverse design NN model is obtained to suggest the nanostructure for a queried coercivity.
对钐钴基 1:7 型（SmCo-1:7）磁体中不同细胞纳米结构的几何和磁性参数进行了约 17,000 次微磁模拟。结果表明，1:5 相在提高矫顽力方面起着重要作用。此外，还建立了一个反向设计 NN 模型，为查询矫顽力的纳米结构提供建议。
{"title":"Coercivity influence of nanostructure in SmCo-1:7 magnets: Machine learning of high-throughput micromagnetic data","authors":"Yangyiwei Yang, Patrick Kühn, Mozhdeh Fathidoost, Esmaeil Adabifiroozjaei, Ruiwen Xie, Eren Foya, Dominik Ohmer, Konstantin Skokov, Leopoldo Molina-Luna, Oliver Gutfleisch, Hongbin Zhang, Bai-Xiang Xu","doi":"arxiv-2408.03198","DOIUrl":"https://doi.org/arxiv-2408.03198","url":null,"abstract":"Around 17,000 micromagnetic simulations were performed with a wide variation\u0000of geometric and magnetic parameters of different cellular nanostructures in\u0000the samarium-cobalt-based 1:7-type (SmCo-1:7) magnets. A forward prediction\u0000neural network (NN) model is trained to unveil the influence of these\u0000parameters on the coercivity of materials, along with the sensitivity analysis.\u0000Results indicate the important role of the 1:5-phase in enhancing coercivity.\u0000Moreover, an inverse design NN model is obtained to suggest the nanostructure\u0000for a queried coercivity.","PeriodicalId":501369,"journal":{"name":"arXiv - PHYS - Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937483","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}
Adithya N Sreenivasan, C. Levi Petix, Zachary M. Sherman, Michael P. Howard
relentless is an open-source Python package that enables the optimization of objective functions computed using molecular dynamics simulations. It has a high-level, extensible interface for model parametrization; setting up, running, and analyzing simulations natively in established software packages; and gradient-based optimization. We describe the design and implementation of relentless in the context of relative entropy minimization, and we demonstrate its abilities to design pairwise interactions between particles that form targeted structures. relentless aims to streamline the development of computational materials design methodologies and promote the transparency and reproducibility of complex workflows integrating molecular dynamics simulations.
{"title":"relentless: Transparent, reproducible molecular dynamics simulations for optimization","authors":"Adithya N Sreenivasan, C. Levi Petix, Zachary M. Sherman, Michael P. Howard","doi":"arxiv-2408.03213","DOIUrl":"https://doi.org/arxiv-2408.03213","url":null,"abstract":"relentless is an open-source Python package that enables the optimization of\u0000objective functions computed using molecular dynamics simulations. It has a\u0000high-level, extensible interface for model parametrization; setting up,\u0000running, and analyzing simulations natively in established software packages;\u0000and gradient-based optimization. We describe the design and implementation of\u0000relentless in the context of relative entropy minimization, and we demonstrate\u0000its abilities to design pairwise interactions between particles that form\u0000targeted structures. relentless aims to streamline the development of\u0000computational materials design methodologies and promote the transparency and\u0000reproducibility of complex workflows integrating molecular dynamics\u0000simulations.","PeriodicalId":501369,"journal":{"name":"arXiv - PHYS - Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937477","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}
Sebastian Falkner, Alessandro Coretti, Baron Peters, Peter G. Bolhuis, Christoph Dellago
Rare event sampling algorithms are essential for understanding processes that occur infrequently on the molecular scale, yet they are important for the long-time dynamics of complex molecular systems. One of these algorithms, transition path sampling, has become a standard technique to study such rare processes since no prior knowledge on the transition region is required. Most TPS methods generate new trajectories from old trajectories by selecting a point along the old trajectory, modifying its momentum in some way, and then ``shooting'' a new trajectory by integrating forward and backward in time. In some procedures, the shooting point is selected independently for each trial move, but in others, the shooting point evolves from one path to the next so that successive shooting points are related to each other. We provide an extended detailed balance criterion for shooting methods. We affirm detailed balance for most TPS methods, but the new criteria reveals the need for amended acceptance criteria in the flexible length aimless shooting and spring shooting methods.
{"title":"Revisiting Shooting Point Monte Carlo Methods for Transition Path Sampling","authors":"Sebastian Falkner, Alessandro Coretti, Baron Peters, Peter G. Bolhuis, Christoph Dellago","doi":"arxiv-2408.03054","DOIUrl":"https://doi.org/arxiv-2408.03054","url":null,"abstract":"Rare event sampling algorithms are essential for understanding processes that\u0000occur infrequently on the molecular scale, yet they are important for the\u0000long-time dynamics of complex molecular systems. One of these algorithms,\u0000transition path sampling, has become a standard technique to study such rare\u0000processes since no prior knowledge on the transition region is required. Most\u0000TPS methods generate new trajectories from old trajectories by selecting a\u0000point along the old trajectory, modifying its momentum in some way, and then\u0000``shooting'' a new trajectory by integrating forward and backward in time. In\u0000some procedures, the shooting point is selected independently for each trial\u0000move, but in others, the shooting point evolves from one path to the next so\u0000that successive shooting points are related to each other. We provide an\u0000extended detailed balance criterion for shooting methods. We affirm detailed\u0000balance for most TPS methods, but the new criteria reveals the need for amended\u0000acceptance criteria in the flexible length aimless shooting and spring shooting\u0000methods.","PeriodicalId":501369,"journal":{"name":"arXiv - PHYS - Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937407","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}
The widely used thermal Hartree-Fock (HF) theory is generalized to include the effect of electron correlation while maintaining its quasi-independent-particle framework. An electron-correlated internal energy (or grand potential) is defined by the second-order finite-temperature many-body perturbation theory (MBPT), which then dictates the corresponding thermal orbital (quasi-particle) energies in such a way that all thermodynamic relations are obeyed. The associated density matrix is of the one-electron type, whose diagonal elements take the form of the Fermi-Dirac distribution functions, when the grand potential is minimized. The formulas for the entropy and chemical potential are unchanged from those of Fermi-Dirac or thermal HF theory. The theory thus postulates a finite-temperature extension of the second-order Dyson self-energy of one-particle many-body Green's function theory and can be viewed as a second-order, diagonal, frequency-independent, thermal inverse Dyson equation. At low temperature, the theory approaches finite-temperature MBPT of the same order, but it outperforms the latter at intermediate temperature by including additional electron-correlation effects through orbital energies. A physical meaning of these thermal orbital energies (including that of thermal HF orbital energies, which has been elusive) is proposed.
{"title":"Thermal quasi-particle theory","authors":"So Hirata","doi":"arxiv-2408.03970","DOIUrl":"https://doi.org/arxiv-2408.03970","url":null,"abstract":"The widely used thermal Hartree-Fock (HF) theory is generalized to include\u0000the effect of electron correlation while maintaining its\u0000quasi-independent-particle framework. An electron-correlated internal energy\u0000(or grand potential) is defined by the second-order finite-temperature\u0000many-body perturbation theory (MBPT), which then dictates the corresponding\u0000thermal orbital (quasi-particle) energies in such a way that all thermodynamic\u0000relations are obeyed. The associated density matrix is of the one-electron\u0000type, whose diagonal elements take the form of the Fermi-Dirac distribution\u0000functions, when the grand potential is minimized. The formulas for the entropy\u0000and chemical potential are unchanged from those of Fermi-Dirac or thermal HF\u0000theory. The theory thus postulates a finite-temperature extension of the\u0000second-order Dyson self-energy of one-particle many-body Green's function\u0000theory and can be viewed as a second-order, diagonal, frequency-independent,\u0000thermal inverse Dyson equation. At low temperature, the theory approaches\u0000finite-temperature MBPT of the same order, but it outperforms the latter at\u0000intermediate temperature by including additional electron-correlation effects\u0000through orbital energies. A physical meaning of these thermal orbital energies\u0000(including that of thermal HF orbital energies, which has been elusive) is\u0000proposed.","PeriodicalId":501369,"journal":{"name":"arXiv - PHYS - Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937402","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}
Andrij VasylenkoDepartment of Chemistry, University of Liverpool, Crown Street, United Kingdom, Dmytro AntypovDepartment of Chemistry, University of Liverpool, Crown Street, United Kingdom, Sven ScheweDepartment of Computer Science, University of Liverpool, Ashton Building, United Kingdom, Luke M. DanielsDepartment of Chemistry, University of Liverpool, Crown Street, United Kingdom, John B. ClaridgeDepartment of Chemistry, University of Liverpool, Crown Street, United Kingdom, Matthew S. DyerDepartment of Chemistry, University of Liverpool, Crown Street, United Kingdom, Matthew J. RosseinskyDepartment of Chemistry, University of Liverpool, Crown Street, United Kingdom
Computational modelling of materials using machine learning, ML, and historical data has become integral to materials research. The efficiency of computational modelling is strongly affected by the choice of the numerical representation for describing the composition, structure and chemical elements. Structure controls the properties, but often only the composition of a candidate material is available. Existing elemental descriptors lack direct access to structural insights such as the coordination geometry of an element. In this study, we introduce Local Environment-induced Atomic Features, LEAFs, which incorporate information about the statistically preferred local coordination geometry for atoms in crystal structure into descriptors for chemical elements, enabling the modelling of materials solely as compositions without requiring knowledge of their crystal structure. In the crystal structure, each atomic site can be described by similarity to common local structural motifs; by aggregating these features of similarity from the experimentally verified crystal structures of inorganic materials, LEAFs formulate a set of descriptors for chemical elements and compositions. The direct connection of LEAFs to the local coordination geometry enables the analysis of ML model property predictions, linking compositions to the underlying structure-property relationships. We demonstrate the versatility of LEAFs in structure-informed property predictions for compositions, mapping of chemical space in structural terms, and prioritising elemental substitutions. Based on the latter for predicting crystal structures of binary ionic compounds, LEAFs achieve the state-of-the-art accuracy of 86 per cent. These results suggest that the structurally informed description of chemical elements and compositions developed in this work can effectively guide synthetic efforts in discovering new materials.
{"title":"Learning Atoms from Crystal Structure","authors":"Andrij VasylenkoDepartment of Chemistry, University of Liverpool, Crown Street, United Kingdom, Dmytro AntypovDepartment of Chemistry, University of Liverpool, Crown Street, United Kingdom, Sven ScheweDepartment of Computer Science, University of Liverpool, Ashton Building, United Kingdom, Luke M. DanielsDepartment of Chemistry, University of Liverpool, Crown Street, United Kingdom, John B. ClaridgeDepartment of Chemistry, University of Liverpool, Crown Street, United Kingdom, Matthew S. DyerDepartment of Chemistry, University of Liverpool, Crown Street, United Kingdom, Matthew J. RosseinskyDepartment of Chemistry, University of Liverpool, Crown Street, United Kingdom","doi":"arxiv-2408.02292","DOIUrl":"https://doi.org/arxiv-2408.02292","url":null,"abstract":"Computational modelling of materials using machine learning, ML, and\u0000historical data has become integral to materials research. The efficiency of\u0000computational modelling is strongly affected by the choice of the numerical\u0000representation for describing the composition, structure and chemical elements.\u0000Structure controls the properties, but often only the composition of a\u0000candidate material is available. Existing elemental descriptors lack direct\u0000access to structural insights such as the coordination geometry of an element.\u0000In this study, we introduce Local Environment-induced Atomic Features, LEAFs,\u0000which incorporate information about the statistically preferred local\u0000coordination geometry for atoms in crystal structure into descriptors for\u0000chemical elements, enabling the modelling of materials solely as compositions\u0000without requiring knowledge of their crystal structure. In the crystal\u0000structure, each atomic site can be described by similarity to common local\u0000structural motifs; by aggregating these features of similarity from the\u0000experimentally verified crystal structures of inorganic materials, LEAFs\u0000formulate a set of descriptors for chemical elements and compositions. The\u0000direct connection of LEAFs to the local coordination geometry enables the\u0000analysis of ML model property predictions, linking compositions to the\u0000underlying structure-property relationships. We demonstrate the versatility of\u0000LEAFs in structure-informed property predictions for compositions, mapping of\u0000chemical space in structural terms, and prioritising elemental substitutions.\u0000Based on the latter for predicting crystal structures of binary ionic\u0000compounds, LEAFs achieve the state-of-the-art accuracy of 86 per cent. These\u0000results suggest that the structurally informed description of chemical elements\u0000and compositions developed in this work can effectively guide synthetic efforts\u0000in discovering new materials.","PeriodicalId":501369,"journal":{"name":"arXiv - PHYS - Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937484","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}
Leo Weimer, Michela Lai, Emma Ellingwood, Shawn Westerdale
De-excitation $gamma$ cascades from neutron captures form a dominant background to MeV-scale signals. The Geant4 Monte Carlo simulation toolkit is widely used to model backgrounds in nuclear and particle physics experiments. While its current modules for simulating (n, $gamma$) signals, GFNDL and G4PhotoEvaporation, are excellent for many applications, they do not reproduce known gamma-ray lines and correlations relevant at 2-15 MeV. G4CASCADE is a new data-driven Geant4 module that simulates (n, $gamma$) de-excitation pathways, with options for how to handle shortcomings in nuclear data. Benchmark comparisons to measured gamma-ray lines and level structures in the ENSDF database show significant improvements, with decreased residuals and full energy conservation. This manuscript describes the underlying calculations performed by G4CASCADE, its various usage options, and benchmark comparisons. G4CASCADE for Geant4-10 is available on GitHub at https://github.com/UCRDarkMatter/CASCADE
{"title":"G4CASCADE: A data-driven implementation of (n, $γ$) cascades in Geant4","authors":"Leo Weimer, Michela Lai, Emma Ellingwood, Shawn Westerdale","doi":"arxiv-2408.02774","DOIUrl":"https://doi.org/arxiv-2408.02774","url":null,"abstract":"De-excitation $gamma$ cascades from neutron captures form a dominant\u0000background to MeV-scale signals. The Geant4 Monte Carlo simulation toolkit is\u0000widely used to model backgrounds in nuclear and particle physics experiments.\u0000While its current modules for simulating (n, $gamma$) signals, GFNDL and\u0000G4PhotoEvaporation, are excellent for many applications, they do not reproduce\u0000known gamma-ray lines and correlations relevant at 2-15 MeV. G4CASCADE is a new\u0000data-driven Geant4 module that simulates (n, $gamma$) de-excitation pathways,\u0000with options for how to handle shortcomings in nuclear data. Benchmark\u0000comparisons to measured gamma-ray lines and level structures in the ENSDF\u0000database show significant improvements, with decreased residuals and full\u0000energy conservation. This manuscript describes the underlying calculations\u0000performed by G4CASCADE, its various usage options, and benchmark comparisons.\u0000G4CASCADE for Geant4-10 is available on GitHub at\u0000https://github.com/UCRDarkMatter/CASCADE","PeriodicalId":501369,"journal":{"name":"arXiv - PHYS - Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937480","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}
Tom Beucler, Arthur Grundner, Sara Shamekh, Peter Ukkonen, Matthew Chantry, Ryan Lagerquist
While the added value of machine learning (ML) for weather and climate applications is measurable, explaining it remains challenging, especially for large deep learning models. Inspired by climate model hierarchies, we propose that a full hierarchy of Pareto-optimal models, defined within an appropriately determined error-complexity plane, can guide model development and help understand the models' added value. We demonstrate the use of Pareto fronts in atmospheric physics through three sample applications, with hierarchies ranging from semi-empirical models with minimal tunable parameters (simplest) to deep learning algorithms (most complex). First, in cloud cover parameterization, we find that neural networks identify nonlinear relationships between cloud cover and its thermodynamic environment, and assimilate previously neglected features such as vertical gradients in relative humidity that improve the representation of low cloud cover. This added value is condensed into a ten-parameter equation that rivals the performance of deep learning models. Second, we establish a ML model hierarchy for emulating shortwave radiative transfer, distilling the importance of bidirectional vertical connectivity for accurately representing absorption and scattering, especially for multiple cloud layers. Third, we emphasize the importance of convective organization information when modeling the relationship between tropical precipitation and its surrounding environment. We discuss the added value of temporal memory when high-resolution spatial information is unavailable, with implications for precipitation parameterization. Therefore, by comparing data-driven models directly with existing schemes using Pareto optimality, we promote process understanding by hierarchically unveiling system complexity, with the hope of improving the trustworthiness of ML models in atmospheric applications.
虽然机器学习（ML）为天气和气候应用带来的附加值是可以衡量的，但解释它仍然具有挑战性，尤其是对于大型深度学习模型而言。受气候模型层次结构的启发，我们提出在适当确定的误差-复杂度平面内定义帕累托最优模型的完整层次结构，可以指导模型开发并帮助理解模型的附加值。我们通过三个示例应用展示了帕累托前沿在大气物理学中的应用，其层次结构从具有最小可调参数的半经验模型（最简单）到深度学习算法（最复杂）不等。首先，在云层参数化方面，我们发现神经网络可以识别云层与其热力学环境之间的非线性关系，并吸收以前被忽视的特征，如相对湿度的垂直梯度，从而改善低云层的表示。这一附加值被浓缩为一个十参数方程，其性能可与深度学习模型相媲美。其次，我们建立了模拟短波辐射传输的 ML 模型层次，提炼出双向垂直连通性对于准确表示吸收和散射的重要性，特别是对于多云层。第三，我们强调了对流组织信息在模拟热带降水与其周围环境关系时的重要性。我们讨论了当高分辨率空间信息不可用时，时间记忆的附加价值，以及对降水参数化的影响。因此，通过利用帕累托最优性直接比较数据驱动模型和现有方案，我们通过分层揭示系统的复杂性来促进对过程的理解，希望能提高 ML 模型在大气应用中的可信度。
{"title":"Distilling Machine Learning's Added Value: Pareto Fronts in Atmospheric Applications","authors":"Tom Beucler, Arthur Grundner, Sara Shamekh, Peter Ukkonen, Matthew Chantry, Ryan Lagerquist","doi":"arxiv-2408.02161","DOIUrl":"https://doi.org/arxiv-2408.02161","url":null,"abstract":"While the added value of machine learning (ML) for weather and climate\u0000applications is measurable, explaining it remains challenging, especially for\u0000large deep learning models. Inspired by climate model hierarchies, we propose\u0000that a full hierarchy of Pareto-optimal models, defined within an appropriately\u0000determined error-complexity plane, can guide model development and help\u0000understand the models' added value. We demonstrate the use of Pareto fronts in\u0000atmospheric physics through three sample applications, with hierarchies ranging\u0000from semi-empirical models with minimal tunable parameters (simplest) to deep\u0000learning algorithms (most complex). First, in cloud cover parameterization, we\u0000find that neural networks identify nonlinear relationships between cloud cover\u0000and its thermodynamic environment, and assimilate previously neglected features\u0000such as vertical gradients in relative humidity that improve the representation\u0000of low cloud cover. This added value is condensed into a ten-parameter equation\u0000that rivals the performance of deep learning models. Second, we establish a ML\u0000model hierarchy for emulating shortwave radiative transfer, distilling the\u0000importance of bidirectional vertical connectivity for accurately representing\u0000absorption and scattering, especially for multiple cloud layers. Third, we\u0000emphasize the importance of convective organization information when modeling\u0000the relationship between tropical precipitation and its surrounding\u0000environment. We discuss the added value of temporal memory when high-resolution\u0000spatial information is unavailable, with implications for precipitation\u0000parameterization. Therefore, by comparing data-driven models directly with\u0000existing schemes using Pareto optimality, we promote process understanding by\u0000hierarchically unveiling system complexity, with the hope of improving the\u0000trustworthiness of ML models in atmospheric applications.","PeriodicalId":501369,"journal":{"name":"arXiv - PHYS - Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937479","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}
Quasicrystals are unique materials characterized by long-range order without periodicity. They are observed in systems such as metallic alloys, soft matter, and particle simulations. Unlike periodic crystals, which are invariant under real-space symmetry operations, quasicrystals possess symmetry described by a space group in reciprocal space. In this study, we report the self-assembly of a six-fold chiral quasicrystal using molecular dynamics simulations of a two-dimensional particle system. These particles interact via the Lennard-Jones-Gauss pair potential and are subjected to a periodic substrate potential. Our findings confirm the presence of chiral symmetry through diffraction patterns and order parameters, revealing unique local motifs in both real and reciprocal space. We demonstrate that the quasicrystal's properties, including the tiling structure and symmetry and the extent of diffuse scattering, are influenced by substrate potential depth and temperature. Our results provide insights into the mechanisms of chiral quasicrystal formation and the role of external fields in tailoring quasicrystal structures.
{"title":"Computational Self-Assembly of a Six-Fold Chiral Quasicrystal","authors":"Nydia Roxana Varela-Rosales, Michael Engel","doi":"arxiv-2408.01984","DOIUrl":"https://doi.org/arxiv-2408.01984","url":null,"abstract":"Quasicrystals are unique materials characterized by long-range order without\u0000periodicity. They are observed in systems such as metallic alloys, soft matter,\u0000and particle simulations. Unlike periodic crystals, which are invariant under\u0000real-space symmetry operations, quasicrystals possess symmetry described by a\u0000space group in reciprocal space. In this study, we report the self-assembly of\u0000a six-fold chiral quasicrystal using molecular dynamics simulations of a\u0000two-dimensional particle system. These particles interact via the\u0000Lennard-Jones-Gauss pair potential and are subjected to a periodic substrate\u0000potential. Our findings confirm the presence of chiral symmetry through\u0000diffraction patterns and order parameters, revealing unique local motifs in\u0000both real and reciprocal space. We demonstrate that the quasicrystal's\u0000properties, including the tiling structure and symmetry and the extent of\u0000diffuse scattering, are influenced by substrate potential depth and\u0000temperature. Our results provide insights into the mechanisms of chiral\u0000quasicrystal formation and the role of external fields in tailoring\u0000quasicrystal structures.","PeriodicalId":501369,"journal":{"name":"arXiv - PHYS - Computational Physics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-08-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141937482","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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