Related papers: The Vector Heat Method
In order to better understand micromechanical phenomena such as viscoelasticity and plasticity, the thermomechanical viewpoint is of prime importance but requires calorimetric measurements to be performed during a deformation process.…
This paper introduces a Bayesian inference framework for two-dimensional steady-state heat conduction, focusing on the estimation of unknown distributed heat sources in a thermally-conducting medium with uniform conductivity. The goal is to…
In this paper, we propose to compute Voronoi diagrams over mesh surfaces driven by an arbitrary geodesic distance solver, assuming that the input is a triangle mesh as well as a collection of sites $P=\{p_i\}_{i=1}^m$ on the surface. We…
We present an efficient algorithm for recent generalizations of optimal mass transport theory to matrix-valued and vector-valued densities. These generalizations lead to several applications including diffusion tensor imaging, color images…
As parallel computing trends towards the exascale, scientific data produced by high-fidelity simulations are growing increasingly massive. For instance, a simulation on a three-dimensional spatial grid with 512 points per dimension that…
Starting from the recently proposed energy-based deviational formulation for solving the Boltzmann equation [J.-P. Peraud and N. G. Hadjiconstantinou, Phys. Rev. B 84, 2011], which provides significant computational speedup compared to…
We present a novel class of methods to compute functions of matrices or their action on vectors that are suitable for parallel programming. Solving appropriate simple linear systems of equations in parallel (or computing the inverse of…
Given a submanifold $M\subset \mathbf{R}^\nu$, a curve $\gamma:I\to M$ and tangent vectors $v$ along $\gamma$, we roll the tangent space along $\gamma$. In doing so, we get an imprint/trace of $\gamma$ on the tangent space, as well as an…
A novel inline data compression method is presented for single-precision vectors in three dimensions. The primary application of the method is for accelerating computational physics calculations where the throughput is bound by memory…
In this work, we design and analyze a novel, provably conditionally stable, weakly coupled partitioned scheme to solve the conjugate heat transfer (CHT) problem. We consider a model CHT problem consisting of linear advection-diffusion and…
In this paper, we derive closed form solutions for the quasi-stationary problems of moving heat sources within the gradient theory of heat transfer. This theory can be formally deduced from the two-temperature model and it can be treated as…
We present a methodology to simulate the quantum thermodynamics of thermal machines which are built from an interacting working medium in contact with fermionic reservoirs at fixed temperature and chemical potential. Our method works at…
This paper considers the problem of embedding directed graphs in Euclidean space while retaining directional information. We model a directed graph as a finite set of observations from a diffusion on a manifold endowed with a vector field.…
We present our deep learning framework to solve and accelerate the Time-Dependent partial differential equation's solution of one and two spatial dimensions. We demonstrate DiffusionNet solver by solving the 2D transient heat conduction…
Trajectory prediction is a fundamental problem and challenge for autonomous vehicles. Early works mainly focused on designing complicated architectures for deep-learning-based prediction models in normal-illumination environments, which…
In this paper, we present an open-source, automated, and multi-faceted computational-statistical platform to obtain synthetic homogeneous isotropic turbulent flow and passive scalar transport. A parallel implementation of the well-known…
In this work we develop a numerical method for solving a type of convex graph-structured tensor optimization problems. This type of problems, which can be seen as a generalization of multi-marginal optimal transport problems with…
We propose integrating optimal transport (OT) into operator learning for partial differential equations (PDEs) on complex geometries. Classical geometric learning methods typically represent domains as meshes, graphs, or point clouds. Our…
Heat conduction in one-dimensional (1D) systems is studied based on an analytical S-matrix method, which is developed in the mesoscopic electronic transport theory and molecular dynamic (MD) simulations. It is found that heat conduction in…
Simultaneous trajectory prediction for multiple heterogeneous traffic participants is essential for the safe and efficient operation of connected automated vehicles under complex driving situations in the real world. The multi-agent…