Related papers: A hybrid algorithm for coupling PDE and compartmen…

Systems of reaction-diffusion equations are commonly used in biological models of food chains. The populations and their complicated interactions present numerous challenges in theory and in numerical approximation. In particular,…

Many complex multiphysics systems in fluid dynamics involve using solvers with varied levels of approximations in different regions of the computational domain to resolve multiple spatiotemporal scales present in the flow. The accuracy of…

This work develops effective distributed strategies for the solution of constrained multi-agent stochastic optimization problems with coupled parameters across the agents. In this formulation, each agent is influenced by only a subset of…

Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble forecasting relies on perturbing initial states to capture…

Simulating physical problems involving multi-time scale coupling is challenging due to the need of solving these multi-time scale processes simultaneously. In response to this challenge, this paper proposed an explicit multi-time step…

We consider the problem of estimating the dynamic latent states of an intracellular multiscale stochastic reaction network from time-course measurements of fluorescent reporters. We first prove that accurate solutions to the filtering…

Constructing robots to accomplish long-horizon tasks is a long-standing challenge within artificial intelligence. Approaches using generative methods, particularly Diffusion Models, have gained attention due to their ability to model…

All simulation approaches eventually face limits in computational scalability when applied to large spatiotemporal domains. This challenge becomes especially apparent in molecular-level particle simulations, where high spatial and temporal…

We discuss the distributed matching scheme in accelerators where control of transverse beam phase space, oscillation, and transport is accomplished by flexible distribution of focusing elements beyond dedicated matching sections. Besides…

We introduce a simple and efficient algorithm for diffusion in smoothed particle hydrodynamics (SPH) simulations and apply it to the problem of chemical mixing. Based on the concept of turbulent diffusion, we link the diffusivity of a…

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…

In this paper we propose a compositional framework for the construction of approximations of the interconnection of a class of stochastic hybrid systems. As special cases, this class of systems includes both jump linear stochastic systems…

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,…

The numerical tools to simulate the bidomain model in cardiac electrophysiology are constantly developing due to the great clinical interest and scientific advances in mathematical models and computational power. The bidomain model consists…

Metastable condensed matter typically fluctuates about local energy minima at the femtosecond time scale before transitioning between local minima after nanoseconds or microseconds. This vast scale separation limits the applicability of…

Stochastically evolving geometric systems are studied in shape analysis and computational anatomy for modelling random evolutions of human organ shapes. The notion of geodesic paths between shapes is central to shape analysis and has a…

As compute power increases with time, more involved and larger simulations become possible. However, it gets increasingly difficult to efficiently use the provided computational resources. Especially in particle-based simulations with a…

We consider the numerical solution of coupled volume-surface reaction-diffusion systems having a detailed balance equilibrium. Based on the conservation of mass, an appropriate quadratic entropy functional is identified and an…

We present a coupled atomistic-continuum method for the modeling of defects and interface dynamics of crystalline materials. The method uses atomistic models such as molecular dynamics near defects and interfaces, and continuum models away…

This paper introduces a framework for simulating finite dimensional representations of (jump) diffusion sample paths over finite intervals, without discretisation error (exactly), in such a way that the sample path can be restored at any…