Boltzmann transport equation (BTE) is an ideal tool to describe the multiscale phonon transport phenomena, which are critical to applications like microelectronics cooling. Numerically solving phonon BTE is extremely computationally challenging due to the high dimensionality of such problems, especially when mode-resolved properties are considered. In this work, we demonstrate the use of physics-informed neural networks (PINNs) to efficiently solve phonon BTE for multiscale thermal transport problems with the consideration of phonon dispersion and polarization. In particular, a PINN framework is devised to predict the phonon energy distribution by minimizing the residuals of governing equations and boundary conditions, without the need for any labeled training data. Moreover, geometric parameters, such as the characteristic length scale, are included as a part of the input to PINN, which enables learning BTE solutions in a parametric setting. The effectiveness of the present scheme is demonstrated by solving a number of phonon transport problems in different spatial dimensions (from 1D to 3D). Compared to existing numerical BTE solvers, the proposed method exhibits superiority in efficiency and accuracy, showing great promises for practical applications, such as the thermal design of electronic devices.
Multiscale method based on coupled lattice-Boltzmann and Langevin-dynamics for direct simulation of nanoscale particle/polymer suspensions in complex flows
EquiNO: A Physics-Informed Neural Operator for Multiscale Simulations
Institute for Software and Systems Engineering, Clausthal University of Technology（软件与系统工程研究所，克劳斯塔尔大学）；Institute of Applied Mechanics, Clausthal University of Technology（应用力学研究所，克劳斯塔尔大学）
A unified gas-kinetic framework from Boltzmann to Navier-Stokes scales
Huazhong University of Science and Technology（华中科技大学）；Hong Kong University of Science and Technology（香港科技大学）；Shanghai Suochen Information Technology Co., Ltd（上海速晨信息技术有限公司）
Fast-Forward Lattice Boltzmann: Learning Kinetic Behaviour with Physics-Informed Neural Operators
Centre for Computational Science, University College London, UK；Institute for Mechanics, Computational Mechanics Group, Technical University of Darmstadt, Germany；Centre for Dynamic Systems, University College London, UK；Department of Statistical Science, University College London, UK；Department of Physics, Eindhoven University of Technology, Eindhoven, Netherlands；Centre d'Enseignement et de Recherche en Environnement Atmosphérique (CEREA), \' E cole des Ponts；Computational Science Laboratory, Institute for Informatics, University of Amsterdam, the Netherlands；Centre for Advanced Research Computing, University College London, UK
Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problems
Pacific Northwest National Laboratory（太平洋西北国家实验室）；University of North Carolina, Charlotte（北卡罗来纳大学夏洛特分校）；Delft University of Technology（代尔夫特理工大学）；University of Washington, Applied Mathematics（华盛顿大学应用数学系）；Brown University, Applied Mathematics（布朗大学应用数学系）
Neural operator accelerated atomistic to continuum concurrent multiscale simulations of viscoelasticity
National Center for Computational Sciences, Oak Ridge National Laboratory（橡树岭国家实验室计算科学国家中心）；Department of Engineering, University of Cambridge（剑桥大学工程系）
Uni-Flow: a unified autoregressive-diffusion model for complex multiscale flows
Centre for Computational Science, University College London, London, UK；Department of Earth Science；Engineering, Imperial College London, London, UK；Department of Chemical Engineering, University College London, London, UK；Department of Physics, Eindhoven University of Technology, Eindhoven, Netherlands；School of Civil \& Environmental Engineering, Queensland University of Technology, Brisbane, Australia；Australian Centre for Water；Environmental Biotechnology, The University of Queensland, Brisbane, Australia；Institute for Mechanics, Computational Mechanics Group, Technical University of Darmstadt, Germany；Centre for Advanced Research Computing, University College London, London, UK
Hard-constraining Neumann boundary conditions in physics-informed neural networks via Fourier feature embeddings
Department Modeling and Artificial Intelligence（建模与人工智能系）；Fraunhofer Institute for Integrated Systems and Device Technology IISB（弗劳恩霍夫集成系统与器件技术研究所IISB）
School of Aeronautics and Astronautics, Shanghai Jiao Tong University（上海交通大学航空航天学院）；Department of Aeronautics, Imperial College London（伦敦帝国理工学院航空系）；School of Energy and Power Engineering, Xi’an Jiao Tong University（西安交通大学能源与动力工程学院）
Physics-Informed Neural Networks with Fourier Features and Attention-Driven Decoding
High Technology High School（高科技高中）；Institute for Gravitation and the Cosmos（引力与宇宙研究所）；The Pennsylvania State University（宾夕法尼亚州立大学）；Department of Physics（物理系）；Princeton University（普林斯顿大学）
