Related papers: Equation-free, multiscale computation for unsteady…
Equation-free approaches have been proposed in recent years for the computational study of multiscale phenomena in engineering problems where evolution equations for the coarse-grained, system-level behavior are not explicitly available. In…
In the context of the recently developed "equation-free" approach to the computer-assisted analysis of complex systems, we illustrate the computation of coarsely self-similar solutions. Dynamic renormalization and fixed point algorithms for…
We discuss certain basic features of the equation-free (EF) approach to modeling and computation for complex/multiscale systems. We focus on links between the equation-free approach and tools from systems and control theory (design of…
We propose a seamless multiscale method which approximates the macroscopic behavior of the passive advection-diffusion equations with steady incompressible velocity fields with multi-spatial scales. The method uses decompositions of the…
The computer-assisted modeling of re-entrant production lines, and, in particular, simulation scalability, is attracting a lot of attention due to the importance of such lines in semiconductor manufacturing. Re-entrant flows lead to…
Building on recent advances in scientific machine learning and generative modeling for computational fluid dynamics, we propose a conditional score-based diffusion model designed for multi-scenarios fluid flow prediction. Our model…
The movement of many organisms can be described as a random walk at either or both the individual and population level. The rules for this random walk are based on complex biological processes and it may be difficult to develop a tractable,…
Stochastic chemical systems with diffusion are modeled with a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic…
We present a Bayesian non-parametric way of inferring stochastic differential equations for both regression tasks and continuous-time dynamical modelling. The work has high emphasis on the stochastic part of the differential equation, also…
We present a simple technique for the computation of coarse-scale steady states of dynamical systems with time scale separation in the form of a "wrapper" around a fine-scale simulator. We discuss how this approach alleviates certain…
We show how the Equation-Free approach for mutliscale computations can be exploited to extract, in a computational strict and systematic way the emergent dynamical attributes, from detailed large-scale microscopic stochastic models, of…
Computational modelling of diffusion in heterogeneous media is prohibitively expensive for problems with fine-scale heterogeneities. A common strategy for resolving this issue is to decompose the domain into a number of non-overlapping…
A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…
In this paper, we develop an efficient numerical solver for unsteady diffusion-type partial differential equations with random coefficients. A major computational challenge in such problems lies in repeatedly handling large-scale linear…
Equation-free modeling aims at extracting low-dimensional macroscopic dynamics from complex high-dimensional systems that govern the evolution of microscopic states. This algorithm relies on lifting and restriction operators that map…
Nonlinear time fractional partial differential equations are widely used in modeling and simulations. In many applications, there are high contrast changes in media properties. For solving these problems, one often uses coarse spatial grid…
Modern `smart' materials have complex microscale structure, often with unknown macroscale closure. The Equation-Free Patch Scheme empowers us to non-intrusively, efficiently, and accurately simulate over large scales through computations on…
A new method is proposed to numerically extract the diffusivity of a (typically nonlinear) diffusion equation from underlying stochastic particle systems. The proposed strategy requires the system to be in local equilibrium and have…
The simulation of stochastic reaction-diffusion systems using fine-grained representations can become computationally prohibitive when particle numbers become large. If particle numbers are sufficiently high then it may be possible to…
We demonstrate how direct simulation of stochastic, individual-based models can be combined with continuum numerical analysis techniques to study the dynamics of evolving diseases. % Sidestepping the necessity of obtaining explicit…