相关论文: Derivation of a transfer function model for a high…

Computational fluid dynamics (CFD) simulations of complex fluid flows in energy systems are prohibitively expensive due to strong nonlinearities and multiscale-multiphysics interactions. In this work, we present a transformer-based modeling…

Sampling from high-dimensional and structured probability distributions is a fundamental challenge in computational physics, particularly in the context of lattice field theory (LFT), where generating field configurations efficiently is…

We introduce an entirely new class of high-order methods for computational fluid dynamics (CFD) based on the Gaussian Process (GP) family of stochastic functions. Our approach is to use kernel-based GP prediction methods to…

This paper is concerned with networks of interacting linear systems at sites of a multidimensional lattice. The systems are governed by linear ODEs with constant coefficients driven by external inputs, and their internal dynamics and…

Neural network based methods have emerged as a promising paradigm for scientific computing, yet they face critical bottlenecks in high frequency function approximation and partial differential equation (PDE) solving.

In this paper, we develop a phase-field model for binary incompressible (quasi-incompressible) fluid with thermocapillary effects, which allows for the different properties (densities, viscosities and heat conductivities) of each component…

This study presents a novel pressure-based methodology for the efficient numerical solution of a four-equation two-phase diffuse interface model. The proposed methodology has the potential to simulate low-Mach flows with mass transfer. In…

Structure-preserving finite-difference schemes for general nonlinear fourth-order parabolic equations on the one-dimensional torus are derived. Examples include the thin-film and the Derrida-Lebowitz-Speer-Spohn equations. The schemes…

In this paper, we study a machine-learning-based solver for high-dimensional partial differential equations (PDEs). Computing accurate solutions efficiently for such problems remains challenging because of the curse of dimensionality, which…

Effective power flow (PF) modeling critically affects the solution accuracy and computational complexity of large-scale grid optimization problems. Especially for grid optimization involving flexible topology to enhance resilience,…

We use a novel parameterization of the flowing Hamiltonian to show that the flow equations based on continuous unitary transformations, as proposed by Wegner, can be implemented through a nonlinear partial differential equation involving…

A model for diffusion on a cubic lattice with a random distribution of traps is developed. The traps are redistributed at certain time intervals. Such models are useful for describing systems showing dynamic disorder, such as ion-conducting…

We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several…

This letter presents a probabilistic omnidirectional millimeter-wave path loss model based on real-world 28 GHz and 73 GHz measurements collected in New York City. The probabilistic path loss approach uses a free space line-of-sight…

A theoretical and computational finite element study of modified Navier-Stokes Equations coupled with energy conservation governing the flow and heat transfer in complex domains with hybrid nanofluid$(HNF)$ is carried out. The apriori error…

We present a new direct logarithmically optimal in theory and fast in practice algorithm to implement the high order finite element method on multi-dimensional rectangular parallelepipeds for solving PDEs of the Poisson kind. The key points…

A finite-size-scaling (FSS) theory is proposed for various models in complex networks. In particular, we focus on the FSS exponent, which plays a crucial role in analyzing numerical data for finite-size systems. Based on the…

We develop a method of driving a Markov processes through a continuous flow. In particular, at the level of the transition functions we investigate an approach of adding a first order operator to the generator of a Markov process, when the…

The result provided in this paper helps complete a unified picture of the scaling behavior in heavy-tailed stochastic models for transmission of packet traffic on high-speed communication links. Popular models include infinite source…

We develop a lumped parameter model to describe and predict the mass release of (absorption from) an arbitrary shaped body of any dimension in a large environment. Through the one-to-one analogy between diffusion-dominated mass transfer…