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We consider the problem of statistical inference for the effective dynamics of multiscale diffusion processes with (at least) two widely separated characteristic time scales. More precisely, we seek to determine parameters in the effective…

Machine learning methods, such as diffusion models, are widely explored as a promising way to accelerate high-fidelity fluid dynamics computation via a super-resolution process from faster-to-compute low-fidelity input. However, existing…

A Computationally Assisted Spectroscopic Technique to measure secondary electron emission coefficients ($\gamma$-CAST) in capacitively-coupled radio-frequency plasmas is proposed. This non-intrusive, sensitive diagnostic is based on a…

Numerical simulations are a powerful tool for the development and improvement of Li-ion batteries. Modeling the mass transport of the involved electrolytic solutions requires precise determination of the corresponding electrolyte…

We investigate the approximation and estimation rates of conditional diffusion transformers (DiTs) with classifier-free guidance. We present a comprehensive analysis for ``in-context'' conditional DiTs under four common data assumptions. We…

The rigid-intensity-shift model of differential phase contrast scanning transmission electron microscopy (DPC-STEM) imaging assumes that the phase gradient imposed on the probe by the sample causes the diffraction pattern intensity to shift…

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…

Classical Density Functional Theory (DFT) is a statistical-mechanical framework to analyze fluids, which accounts for nanoscale fluid inhomogeneities and non-local intermolecular interactions. DFT can be applied to a wide range of…

Pre-trained diffusion models are commonly used to generate clean data (e.g., images) from random noises, effectively forming pairs of noises and corresponding clean images. Distillation on these pre-trained models can be viewed as the…

Discrete diffusion models (DMs) have achieved strong performance in language and other discrete domains, offering a compelling alternative to autoregressive modeling. Yet this performance typically depends on large training datasets,…

Gas phase ultrafast electron diffraction (GUED) has become a powerful technique to directly observe the structural dynamics of photoexcited molecules. GUED reveals information about the nuclear motions that is complementary to the…

A goodness of fit test for the drift coefficient of an ergodic diffusion process is presented. The test is based on the score marked empirical process. The weak convergence of the proposed test statistic is studied under the null hypotheses…

In this article, we carry out a study of long-term behavior of reaction-diffusion systems augmented with self- and cross-diffusion, using an augmented Gray-Scott system as a general example. The methodology remains generic, and is therefore…

We develop several statistical tests of the determinant of the diffusion coefficient of a stochastic differential equation, based on discrete observations on a time interval $[0,T]$ sampled with a time step $\Delta$. Our main contribution…

Major drawback of studying diffusion in multi-component systems is the lack of suitable techniques to estimate the diffusion parameters. In this study, a generalized treatment to determine the intrinsic diffusion coefficients in…

We study, theoretically and experimentally, electromagnetically induced transparency (EIT) in two different solid-state systems. Unlike many implementations in homogeneously broadened media, these systems exhibit inhomogeneous broadening of…

Recent computer simulation results [Barrat {\em et al.}, Physica A 334 (2004) 513] for granular mixtures subject to stochastic driving have shown the validity of the Einstein relation $\epsilon\equiv D/(T_0\lambda)=1$ between the diffusion…

We analyse diffusion at low temperature by bringing the fluctuation-dissipation theorem (FDT) to bear on a physically natural, viscous response-function R(t). The resulting diffusion-law exhibits several distinct regimes of time and…

Nonequilibrium fluctuation-dissipation theorems (FDTs) are one of the most important advances in stochastic thermodynamics over the past two decades. Here we provide rigorous mathematical proofs of two types of nonequilibrium FDTs for…

Accurate prediction of pedestrian trajectories is crucial for improving the safety of autonomous driving. However, this task is generally nontrivial due to the inherent stochasticity of human motion, which naturally requires the predictor…