Related papers: The Vector Heat Method
This paper aims to efficiently compute transport maps between probability distributions arising from particle representation of bio-physical problems. We develop a bidirectional DeepParticle (BDP) method to learn and generate solutions…
Traditional numerical schemes for simulating fluid flow and transport in porous media can be computationally expensive. Advances in machine learning for scientific computing have the potential to help speed up the simulation time in many…
Discrete variational methods show excellent performance in numerical simulations of different mechanical systems. In this paper, we introduce an iterative procedure for the solution of discrete variational equations for boundary value…
A finite element based computational scheme is developed and employed to assess a duality based variational approach to the solution of the linear heat and transport PDE in one space dimension and time, and the nonlinear system of ODEs of…
Computing the Delaunay triangulation (DT) of a given point set in $\mathbb{R}^D$ is one of the fundamental operations in computational geometry. Recently, Funke and Sanders (2017) presented a divide-and-conquer DT algorithm that merges two…
The paper considers the heat transfer characteristics of a thin film flow over a hot horizontal flat plate resulting from a cold vertical liquid jet falling onto a surface. A numerical solution of high accuracy is obtained for large…
A fast inverse heat conduction model (IHCM) is developed for estimating unknown properties of multi-layer composites considering internal heat generation. This work builds on the validated analytical forward models presented in Part I.…
The present study proposes a new efficient and robust algorithm for multi-objectives topology optimization of heat transfer surfaces to achieve heat transfer enhancement with a less pressure drop penalty based on a continuous adjoint…
Mathematical network models are extremely useful to capture complex propagation processes between different regions (nodes), for example the spread of an infectious agent between different countries, or the transport and replication of…
The objective of this work is to investigate the coupling of fluid dynamics, heat transfer and mass transfer during the impact and evaporation of droplets on a heated solid substrate. A laser-based thermoreflectance method is used to…
Reactive transport in permeable porous media is relevant for a variety of applications, but poses a significant challenge due to the range of length and time scales. Multiscale methods that aim to link microstructure with the macroscopic…
This paper develops 'covariant tomography', a local framework for solving Inverse Boundary Value Problems (IBVP) for parallel transport equation on star-shaped domains. By integrating geometric decomposition with specific interior…
This work concentrates on optimization on Riemannian manifolds. The Limited-memory Broyden-Fletcher-Goldfarb-Shanno (LBFGS) algorithm is a commonly used quasi-Newton method for numerical optimization in Euclidean spaces. Riemannian LBFGS…
In many applications such as color image processing, data has more than one piece of information associated with each spatial coordinate, and in such cases the classical optimal mass transport (OMT) must be generalized to handle…
Horizontally extended plane-layer convection flows are characterized by characteristic patterns of turbulent heat transfer due to the convective fluid motion consisting of a nearly-regular ridge network where hot fluid rises and cold fluid…
This work addresses model order reduction for complex moving fronts, which are transported by advection or through a reaction-diffusion process. Such systems are especially challenging for model order reduction since the transport cannot be…
We investigate the concept of rendering production-style content with full path tracing in a data-distributed fashion -- that is, with multiple collaborating nodes and/or GPUs that each store only part of the model. In particular, we…
In this paper we describe a high-resolution transport formulation of the regional level-set approach for an improved prediction of the evolution of complex interface networks. The novelty of this method is twofold: (i) construction of local…
We further develop the new approach, proposed in part I (hep-th/9807072), to computing the heat kernel associated with a Fermion coupled to vector and axial vector fields. We first use the path integral representation obtained for the heat…
Machine learning has been progressively generalised to operate within non-Euclidean domains, but geometrically accurate methods for learning on surfaces are still falling behind. The lack of closed-form Riemannian operators, the…