Related papers: Optimal estimates of diffusion coefficients from m…
In recent years, diffusion models trained on equilibrium molecular distributions have proven effective for sampling biomolecules. Beyond direct sampling, the score of such a model can also be used to derive the forces that act on molecular…
The augmented, iterated Kalman smoother is applied to system identification for inverse problems in evolutionary differential equations. In the augmented smoother, the unknown, time-dependent coefficients are included in the state vector,…
Diffusion models have been successful on a range of conditional generation tasks including molecular design and text-to-image generation. However, these achievements have primarily depended on task-specific conditional training or…
Using Stokesian dynamics simulations, we examine the flow of a monodisperse, neutrally buoyant, homogeneous suspension of non-Brownian solid spheres in simple shear, starting from a large number of independent hard-sphere distributions and…
The mean square displacement per collision of a molecule immersed in a gas at equilibrium is given by its mean square displacement between two consecutive collisions (mean square free path) corrected by a prefactor in the form of a series.…
Over the past decades, discrete dislocation dynamics simulations have been shown to reliably predict the evolution of dislocation microstructures for micrometer-sized metallic samples. Such simulations provide insight into the governing…
We investigate the hydrodynamic properties of a fluid simulated with a mesoscopic solvent model. Two distinct regimes are identified, the `particle regime' in which the dynamics is gas-like, and the `collective regime' where the dynamics is…
Monte Carlo simulation is one of the most important tools in the study of diffusion processes. For constant diffusion coefficients, an appropriate Gaussian distribution of particle's steplengths can generate exact results, when compared…
Time course measurement of single molecules on a cell surface provides detailed information on the dynamics of the molecules, which is otherwise inaccessible. To extract the quantitative information, single particle tracking (SPT) is…
The influence of periodic and random surface textures on the flow structure and effective slip length in Newtonian fluids is investigated by molecular dynamics (MD) simulations. We consider a situation where the typical pattern size is…
In this article we consider the estimation of static parameters for partially observed diffusion processes with discrete-time observations over a fixed time interval. In particular, when one only has access to time-discretized solutions of…
We model two time and space scales discrete observations by using a unique continuous diffusion process with time dependent coefficient. We define new parameters for the large scale model as functions of the small scale distribution…
Data-dependent metrics are powerful tools for learning the underlying structure of high-dimensional data. This article develops and analyzes a data-dependent metric known as diffusion state distance (DSD), which compares points using a…
Understanding the geometry of learned distributions is fundamental to improving and interpreting diffusion models, yet systematic tools for exploring their landscape remain limited. Standard latent-space interpolations fail to respect the…
The viscosity and self-diffusion constant of a mesoscale hydrodynamic method, dissipative particle dynamics (DPD), are investigated. The viscosity of DPD with finite time step, including the Lowe-Anderson thermostat, is derived analytically…
Parametric estimation for diffusion processes is considered for high frequency observations over a fixed time interval. The processes solve stochastic differential equations with an unknown parameter in the diffusion coefficient. We find…
While efficient distribution learning is no doubt behind the groundbreaking success of diffusion modeling, its theoretical guarantees are quite limited. In this paper, we provide the first rigorous analysis on approximation and…
Dissipative particle dynamics (DPD) is a novel particle method for mesoscale modeling of complex fluids. DPD particles are often thought to represent packets of real atoms, and the physical scale probed in DPD models are determined by the…
We propose score dynamics (SD), a general framework for learning accelerated evolution operators with large timesteps from molecular-dynamics simulations. SD is centered around scores, or derivatives of the transition log-probability with…
We present predictions for the statistical error due to finite sampling in the presence of thermal fluctuations in molecular simulation algorithms. Specifically, we establish how these errors depend on Mach number, Knudsen number, number of…