Phonon Boltzmann transport equation (BTE) is a key tool for modeling multiscale phonon transport, which is critical to the thermal management of miniaturized integrated circuits, but assumptions about the system temperatures (i.e., small temperature gradients) are usually made to ensure that it is computationally tractable. To include the effects of large temperature non-equilibrium, we demonstrate a data-free deep learning scheme, physics-informed neural network (PINN), for solving stationary, mode-resolved phonon BTE with arbitrary temperature gradients. This scheme uses the temperature-dependent phonon relaxation times and learns the solutions in parameterized spaces with both length scale and temperature gradient treated as input variables. Numerical experiments suggest that the proposed PINN can accurately predict phonon transport (from 1D to 3D) under arbitrary temperature gradients. Moreover, the proposed scheme shows great promise in simulating device-level phonon heat conduction efficiently and can be potentially used for thermal design.
In this work, a lattice Boltzmann scheme is developed for numerical solution of the phonon Boltzmann equation under Callaway's dual relaxation model in the hydrodynamic limit. Through a Chapman-Enskog expansion to the lattice Boltzmann equation with the resistive scattering term as an equivalent source term, we recover a phonon hydrodynamic equation which is reduced to the Guyer-Krumhansl heat transport equation and the Fourier's law in the limit of dominant normal scattering and dominant resistive scattering respectively. Several cases of heat transport from diffusive regime to hydrodynamic r…
Numerical prediction of multiscale heat transfer is a challenging problem due to the wide range of time and length scales involved. In this work a discrete unified gas kinetic scheme (DUGKS) is developed for heat transfer in materials with different acoustic thickness based on the phonon Boltzmann equation. With discrete phonon direction, the Boltzmann equation is discretized with a second-order finite-volume formulation, in which the time-step is fully determined by the Courant-Friedrichs-Lewy (CFL) condition. The scheme has the asymptotic preserving (AP) properties for both diffusive and bal…
almaBTE is a software package that solves the space- and time-dependent Boltzmann transport equation for phonons, using only ab-initio calculated quantities as inputs. The program can predictively tackle phonon transport in bulk crystals and alloys, thin films, superlattices, and multiscale structures with size features in the nm-$μ$m range. Among many other quantities, the program can output thermal conductances and effective thermal conductivities, space-resolved average temperature profiles, and heat-current distributions resolved in frequency and space. Its first-principles character makes…
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 …
Mesoscopic numerical simulation has become an important tool in thermal management and energy harvesting at the micro/nano scale, where the Fourier's law failed. However, it is not easy to efficiently solve the phonon Boltzmann transport equation (BTE) from ballistic to diffusive limit. In order to accelerate convergence, an implicit synthetic iterative scheme is developed for the stationary phonon BTE, in which a macroscopic moment equation is invoked and solved iteratively coupled with the typical source iteration of the kinetic equation. Different from previous numerical interpolation, the …
Phonon Boltzmann transport equation (BTE) is an important tool for studying the nanoscale thermal transport. Because phonons have a large spread in their properties, the non-gray (i.e. considering different phonon bands) phonon BTE is needed to accurately capture the nanoscale transport phenomena. However, BTE solvers generally require large computational cost. Non-gray modeling imposes significant additional complexity to the numerical simulations, which hinders the modeling of real nanoscale systems. In this work, we address this issue by a systematic investigation on the phonon band discret…
In this study, we employ physics-informed neural networks (PINNs) to solve forward and inverse problems via the Boltzmann-BGK formulation (PINN-BGK), enabling PINNs to model flows in both the continuum and rarefied regimes. In particular, the PINN-BGK is composed of three sub-networks, i.e., the first for approximating the equilibrium distribution function, the second for approximating the non-equilibrium distribution function, and the third one for encoding the Boltzmann-BGK equation as well as the corresponding boundary/initial conditions. By minimizing the residuals of the governing equatio…
The direct simulation of the dynamics of second sound in graphitic materials remains a challenging task due to lack of methodology for solving the phonon Boltzmann equation in such a stiff hydrodynamic regime. In this work, we aim to tackle this challenge by developing a multiscale numerical scheme for the transient phonon Boltzmann equation under Callaway's dual relaxation model which captures well the collective phonon kinetics. Comparing to traditional numerical methods, the present multiscale scheme is efficient, accurate and stable in all transport regimes attributed to avoiding the use o…
In this paper, a fast synthetic iterative scheme is developed to accelerate convergence for the implicit DOM based on the stationary phonon BTE. The key innovative point of the present scheme is the introduction of the macroscopic synthetic diffusion equation for the temperature, which is obtained from the zero- and first-order moment equations of the phonon BTE. The synthetic diffusion equation, which is asymptomatically preserving to the Fourier's heat conduction equation in the diffusive regime, contains a term related to the Fourier's law and a term determined by the second-order moment of…
In this article, we address lattice heat transport in single-walled carbon nanotubes (CNTs) by a quantum mechanical calculation of three-phonon scattering rates in the framework of the Boltzmann transport equation (BTE) and classical molecular dynamics (MD) simulation. Under a consistent choice of an empirical, realistic atomic interaction potential, we compare the tube length dependence of the lattice thermal conductivity (TC) at room temperature determined from an iterative solution of the BTE and from a nonequilibrium MD (NEMD) approach. Qualitatively similar trends are found in the limit o…
Callaway's dual relaxation times model, which takes into account the normal and resistive scatterings of phonon, is used to describe the heat conduction in materials like graphene. For steady-state problems, the Callaway model is usually solved by the conventional iterative scheme (CIS), which is efficient in the ballistic regime, but inefficient in the diffusive/hydrodynamic regime. In this paper, a general synthetic iterative scheme (GSIS) is proposed to expedite the convergence to steady-state solutions. First, macroscopic synthetic equations are designed to guide the evolution of equilibri…
The lattice Boltzmann method (LBM) is a numerical approach to tackle problems described by a Boltzmann type-equation, where time, space, and velocities are discretized to describe scattering and advection. Even though the LBM executes advection along a lattice direction without numerical error, its usage in the high Knudsen number regime (ballistic) has been hindered by the ray effect problem (for dimensions greater than 1D). This problem has its origin in the low number of available propagation directions on standard LBM lattices. Here, to overcome this limitation, we propose the worm-lattice…
Physics Enhanced Deep Surrogates for the Phonon Boltzmann Transport Equation
School of Computational Science and Engineering, Georgia Institute of Technology（计算科学与工程学院，佐治亚理工学院）；Institute for Soldier Nanotechnologies, Massachusetts Institute of Technology（士兵纳米技术研究所，麻省理工学院）
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
Accelerating dynamic simulations of photoexcited materials and their evolution by electron-informed machine learning
Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所凝聚态物理国家实验室）；School of Physical Sciences, University of Chinese Academy of Sciences（中国科学院大学物理科学学院）；Songshan Lake Materials Laboratory（松山湖材料实验室）
We present a general coupled electron-phonon Boltzmann transport equations (BTEs) scheme designed to capture the mutual drag of the two interacting systems. By combining density functional theory based first principles calculations of anharmonic phonon-phonon interactions with physical models of electron-phonon interactions, we apply our implementation of the coupled BTEs to calculate the thermal conductivity, mobility, Seebeck and Peltier coefficients of n-doped gallium arsenide. The measured low temperature enhancement in the Seebeck coefficient is captured using the solution of the fully co…
In this work, the heat vortexes in two-dimensional porous or ribbon structures are investigated based on the phonon Boltzmann transport equation (BTE) under the Callaway model. First, the separate thermal effects of normal (N) scattering and resistive (R) scattering are investigated with frequency-independent assumptions. And then the heat vortexes in graphene are studied as a specific example. It is found that the heat vortexes can appear in both ballistic (rare R/N scattering) and hydrodynamic (N scattering dominates) regimes but disappear in the diffusive (R scattering dominates) regime. As…
Transient heat dissipation in close-packed quasi-2D nanoline and 3D nanocuboid hotspot systems is studied based on phonon Boltzmann transport equation. It is found that, counter-intuitively, the heat dissipation efficiency is not a monotonic function of the distance between adjacent nanoscale heat sources: the heat dissipation efficiency reaches the highest value when this distance is comparable to the phonon mean free path. This is due to the competition of two thermal transport processes: quasiballistic transport when phonons escape from the nanoscale heat source and the scattering among pho…
Beijing National Lab for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences（中国科学院物理研究所北京凝聚态物理国家实验室）
Boltzmann machines are physics informed generative models with wide applications in machine learning. They can learn the probability distribution from an input dataset and generate new samples accordingly. Applying them back to physics, the Boltzmann machines are ideal recommender systems to accelerate Monte Carlo simulation of physical systems due to their flexibility and effectiveness. More intriguingly, we show that the generative sampling of the Boltzmann Machines can even discover unknown cluster Monte Carlo algorithms. The creative power comes from the latent representation of the Boltzm…
An alternative approach to efficient simulation of micro/nanoscale phonon transport
从最近提出的用于求解Boltzmann方程的基于能量的偏差公式开始[J. P. Peraud和N. G. Hadjiconstantinou，Phys.Rev.B84，2011]，与标准Monte Carlo方法相比，对于与平衡的小偏差提供了显著的计算加速，我们表明，在控制方程可以线性化的限制下，额外的计算益处是可能的。所提出的方法利用的观察，在线性化条件下（小的温度差）的个别偏差粒子的轨迹可以被解耦，从而独立地模拟，这导致一个特别简单和有效的算法，用于模拟稳态和瞬态问题，在任意三维几何形状，而不引入任何额外的近似。
