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We consider the Halfin-Whitt diffusion process $X_d(t)$, which is used, for example, as an approximation to the $m$-server $M/M/m$ queue. We use recently obtained integral representations for the transient density $p(x,t)$ of this diffusion…
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 investigate the application of the discontinuous Petrov-Galerkin (DPG) finite element framework to stationary convection-diffusion problems. In particular, we demonstrate how the quasi-optimal test space norm can be utilized to improve…
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…
Continuous diffusion models have demonstrated remarkable performance in data generation across various domains, yet their efficiency remains constrained by two critical limitations: (1) the local adjacency structure of the forward Markov…
Smoothed dissipative particle dynamics (SDPD) is a widely used particle-based method for modelling soft matter systems at mesoscopic and macroscopic scales, offering thermodynamic consistency and direct control over the fluid's transport…
The radiative transfer equation (RTE) arises in many different areas of science and engineering. In this paper, we propose and investigate a discrete-ordinate discontinuous-streamline diffusion (DODSD) method for solving the RTE, which is a…
This work presents a detailed mathematical model combined with an innovative efficient numerical model to predict heat, air and moisture transfer through porous building materials. The model considers the transient effects of air transport…
Mass transport problems are ubiquitous in diverse fields of physics and engineering. With the development of fractional calculus, many have taken to studying problems of fractional mass transport either through numerical simulations or…
This paper describes a new method for mitigating the effects of atmospheric distortion on observed sequences that include large moving objects. In order to provide accurate detail from objects behind the distorting layer, we solve the…
Single-particle traces of the diffusive motion of molecules, cells, or animals are by-now routinely measured, similar to stochastic records of stock prices or weather data. Deciphering the stochastic mechanism behind the recorded dynamics…
Energy carrier transport and recombination in emerging semiconductors can be directly monitored with optical microscopy, leading to the measurement of the diffusion coefficient (D), a critical property for design of efficient optoelectronic…
Point-based representations have consistently played a vital role in geometric data structures. Most point cloud learning and processing methods typically leverage the unordered and unconstrained nature to represent the underlying geometry…
Deep learning models have achieved remarkable progress in precipitation prediction. However, they still face significant challenges in accurately capturing spatial details of radar images, particularly in regions of high precipitation…
This paper aims to efficiently compute transport maps between probability distributions arising from particle representation of bio-physical problems. We develop a bidirectional DeepParticle (BDP) method to learn and generate solutions…
A semi-Lagrangian Characteristic Mapping method for the solution of the tracer transport equations on the sphere is presented. The method solves for the solution operator of the equations by approximating the inverse of the diffeomorphism…
In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min…
General dynamical transport of classical particles in disordered quasi-1D samples is viewed in the framework of scattering approach. Simple equation for the transfer-matrix is obtained within this unified picture. In the case of diffusive…
Diffusion Probabilistic Models (DPMs) have emerged as the de facto approach for high-fidelity image synthesis, operating diffusion processes on continuous VAE latent, which significantly differ from the text generation methods employed by…
Recent advances in robotic manipulation have highlighted the effectiveness of learning from demonstration. However, while end-to-end policies excel in expressivity and flexibility, they struggle both in generalizing to novel object…