Related papers: The Spatial Regime Conversion Method
We study a large deviation principle for a system of stochastic reaction--diffusion equations (SRDEs) with a separation of fast and slow components and small noise in the slow component. The derivation of the large deviation principle is…
In this paper, we propose stochastic structure-preserving schemes to compute the effective diffusivity for particles moving in random flows. We first introduce the motion of particles using the Lagrangian formulation, which is modeled by…
Establishing appropriate mathematical models for complex systems in natural phenomena not only helps deepen our understanding of nature but can also be used for state estimation and prediction. However, the extreme complexity of natural…
In the stochastic mean-field (SMF) approach, an ensemble of initial values for a selected set of one-body observables is formed by stochastic sampling from a phase-space distribution that reproduces the initial quantum fluctuations.…
Diffusion bridge models establish probabilistic paths between arbitrary paired distributions and exhibit great potential for universal image restoration. Most existing methods merely treat them as simple variants of stochastic interpolants,…
Recent advances in diffusion models hold significant potential in robotics, enabling the generation of diverse and smooth trajectories directly from raw representations of the environment. Despite this promise, applying diffusion models to…
Diffusion models have shown promising capabilities in trajectory generation for planning in offline reinforcement learning (RL). However, conventional diffusion-based planning methods often fail to account for the fact that generating…
Due to storage and bandwidth limitations, videos transmitted over the Internet often exhibit low quality, characterized by low-resolution and compression artifacts. Although video super-resolution (VSR) is an efficient video enhancing…
In this paper, we study stochastic homogenization of a coupled diffusion-reaction system. The diffusion-reaction system is coupled to stochastic differential equations, which govern the changes in the media properties. Though homogenization…
We consider the problem of Bayesian estimation of static parameters associated to a partially and discretely observed diffusion process. We assume that the exact transition dynamics of the diffusion process are unavailable, even up-to an…
By formulating data samples' formation as a Markov denoising process, diffusion models achieve state-of-the-art performances in a collection of tasks. Recently, many variants of diffusion models have been proposed to enable controlled…
We present a multiscale hybrid particle-field scheme for the simulation of relaxation and diffusion behavior of soft condensed matter systems. It combines particle-based Brownian dynamics and field-based local dynamics in an adaptive sense…
Langevin Monte Carlo (LMC) algorithms are popular Markov Chain Monte Carlo (MCMC) methods to sample a target probability distribution, which arises in many applications in machine learning. Inspired by regime-switching stochastic…
To model bio-chemical reaction systems with diffusion one can either use stochastic, microscopic reaction-diffusion master equations or deterministic, macroscopic reaction-diffusion system. The connection between these two models is not…
This paper presents RDCSim, an interactive simulator for reaction--diffusion chemistry (RDC) research, being developed as part of an ongoing project studying how humans interact with unconventional computing systems. While much research…
We study a generic problem of dissipative quantum mechanics, a small local quantum system with discrete states coupled in an arbitrary way (i.e. not necessarily linear) to several infinitely large particle or heat reservoirs. For both…
The stochastic dynamics of biochemical reaction networks can be accurately described by discrete-state Markov processes where each chemical reaction corresponds to a state transition of the process. Due to the largeness problem of the state…
Our study focuses on fractional order compartment models derived from underlying physical stochastic processes, providing a more physically grounded approach compared to models that use the dynamical system approach by simply replacing…
Astrophysical plasmas in relativistic spacetimes, such as black hole accretion flows, are often weakly collisional and require kinetic modeling to capture non-local transport and particle acceleration. However, the extreme scale separation…
Numerous processes across both the physical and biological sciences are driven by diffusion. Partial differential equations (PDEs) are a popular tool for modelling such phenomena deterministically, but it is often necessary to use…