相关论文: Generalized Patch Dynamics Scheme in Equation-free…
Frequency-domain channel extrapolation is effective in reducing pilot overhead for massive multiple-input multiple-output (MIMO) systems. Recently, Deep learning (DL) based channel extrapolator has become a promising candidate for modeling…
We present an extension of the PatchworkMHD code [1], itself an MHD-capable extension of the Patchwork code [2], for which several algorithms presented here were co-developed. Its purpose is to create a multipatch scheme compatible with…
We consider one dimensional lattice diffusion model on a microscale grid with many discrete diffusivity values which repeat periodicially. Computer algebra explores how the dynamics of small coupled `patches' predict the slow emergent…
Deep learning networks are typically trained by Stochastic Gradient Descent (SGD) methods that iteratively improve the model parameters by estimating a gradient on a very small fraction of the training data. A major roadblock faced when…
In order to better model high-dimensional sequential data, we propose a collaborative multi-output Gaussian process dynamical system (CGPDS), which is a novel variant of GPDSs. The proposed model assumes that the output on each dimension is…
A general framework for the development of high-order compact schemes has been proposed recently. The core steps of the schemes are composed of the following. 1). Based on a kinetic model equation, from a generalized initial distribution of…
We introduce an algorithm based on Generalized Dual Method (GDM) to efficiently study the dynamics of a particle in quasiperiodic environments without the need to use periodic approximations or to save the information of the vertices that…
We develop a multiscale patch scheme for studying the system level characteristics of heterogeneous functional graded beams. The algorithm computes the detailed beam dynamics on the microscale, but only in small patches of the beam domain,…
Diffusion models generate data by learning to reverse a forward process, where samples are progressively perturbed with Gaussian noise according to a predefined noise schedule. From a geometric perspective, each noise schedule corresponds…
The multivariate generalized Pareto distribution (mGPD) is a common method for modeling extreme threshold exceedance probabilities in environmental and financial risk management. Despite its broad applicability, mGPD faces challenges due to…
New implicit and implicit-explicit time-stepping methods for the wave equation in second-order form are described with application to two and three-dimensional problems discretized on overset grids. The implicit schemes are single step,…
Computational multi-scale methods capitalize on a large time-scale separation to efficiently simulate slow dynamics over long time intervals. For stochastic systems, one often aims at resolving the statistics of the slowest dynamics. This…
Diffusion models have garnered significant attention since they can effectively learn complex multivariate Gaussian distributions, resulting in diverse, high-quality outcomes. They introduce Gaussian noise into training data and reconstruct…
Differential equations are pivotal in modeling and understanding the dynamics of various systems, offering insights into their future states through parameter estimation fitted to time series data. In fields such as economy, politics, and…
Long-term biomolecular dynamics are critical for understanding key evolutionary transformations in molecular systems. However, capturing these processes requires extended simulation timescales that often exceed the practical limits of…
Gaussian processes are typically used for smoothing and interpolation on small datasets. We introduce a new Bayesian nonparametric framework -- GPatt -- enabling automatic pattern extrapolation with Gaussian processes on large…
This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady…
This paper presents a multi-temporal formulation for simulating elastoplastic solids under cyclic loading. We leverage the proper generalized decomposition (PGD) to decompose the displacements into multiple time scales, separating the…
Probabilistic approaches for handling count-valued time sequences have attracted amounts of research attentions because their ability to infer explainable latent structures and to estimate uncertainties, and thus are especially suitable for…
In molecular dynamics (MD) simulations, accessing transition probabilities between states is crucial for understanding kinetic information, such as reaction paths and rates. However, standard MD simulations are hindered by the capacity to…