Related papers: Dissipation-assisted operator evolution method for…
We develop a computational method based on Dissipative Particle Dynamics (DPD) that introduces solvent hydrodynamic interactions to coarse-grained models of solutes, such as ions, molecules, or polymers. DPD-solvent (DPDS) is a fully…
Discovering hidden physical laws and identifying governing system parameters from sparse observations are central challenges in computational science and engineering. Existing data-driven methods, such as physics-informed neural networks…
A Bayesian data assimilation scheme is formulated for advection-dominated or hyperbolic evolutionary problems, and observations. The method is referred to as the dynamic likelihood filter because it exploits the model physics to dynamically…
Out-of-distribution (OOD) detectors can act as safety monitors in embedded cyber-physical systems by identifying samples outside a machine learning model's training distribution to prevent potentially unsafe actions. However, OOD detectors…
Inspired by the relation between deep neural network (DNN) and partial differential equations (PDEs), we study the general form of the PDE models of deep neural networks. To achieve this goal, we formulate DNN as an evolution operator from…
While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting,…
We study the directed transport of bosons along a one dimensional lattice in a dissipative setting, where the hopping is only facilitated by coupling to a Markovian reservoir. By combining numerical simulations with a field-theoretic…
In the simulation of differential-algebraic equations (DAEs), it is essential to employ numerical schemes that take into account the inherent structure and maintain explicit or hidden algebraic constraints without altering them. This paper…
The effect of the applied trajectory length on the convergence of the static dielectric constant and the self-diffusion coefficient were examined for the SPC/E water model in the NVT ensemble with different system size at 293 K. Very long…
Multiscale dynamical systems, modeled by high-dimensional stiff ordinary differential equations (ODEs) with wide-ranging characteristic timescales, arise across diverse fields of science and engineering, but their numerical solvers often…
In recent years, deep learning for modeling physical phenomena which can be described by partial differential equations (PDEs) have received significant attention. For example, for learning Hamiltonian mechanics, methods based on deep…
We propose a method for learning dynamical systems from high-dimensional empirical data that combines variational autoencoders and (spatio-)temporal attention within a framework designed to enforce certain scientifically-motivated…
We study the adsorption and desorption kinetics of interacting particles moving on a one-dimensional lattice. Confinement is introduced by limiting the number of particles on a lattice site. Adsorption and desorption are found to proceed at…
Data assimilation (DA) in the geophysical sciences remains the cornerstone of robust forecasts from numerical models. Indeed, DA plays a crucial role in the quality of numerical weather prediction, and is a crucial building block that has…
Correlated driving-and-dissipation equation (CODDE) is an optimized complete second-order quantum dissipation approach, which is originally concerned with the reduced system dynamics only. However, one can actually extract the hybridized…
The methods currently used to determine the scaling exponent of a complex dynamic process described by a time series are based on the numerical evaluation of variance. This means that all of them can be safely applied only to the case where…
We report here a general theory describing photoelectron transportation dynamics in GaAs semiconductor photocathodes. Gradient doping is incorporated in the model through the inclusion of directional carrier drift. The time-evolution of…
Diffusion-based generative models use stochastic differential equations (SDEs) and their equivalent ordinary differential equations (ODEs) to establish a smooth connection between a complex data distribution and a tractable prior…
We consider the real-time evolution of a strongly coupled system of lattice fermions whose dynamics is driven entirely by dissipative Lindblad processes, with linear or quadratic quantum jump operators. The fermion 2-point functions obey a…
We devise a numerical scheme for the time evolution of matrix product operators by adapting the time-dependent variational principle for matrix product states [J. Haegeman et al, Phys. Rev. B 94, 165116 (2016)]. A simple augmentation of the…