dorsal/arxiv
View SchemaEquation-Free Multiscale Computation: enabling microscopic simulators to perform system-level tasks
| Authors | Ioannis G. Kevrekidis, C. William Gear, James M. Hyman, Panagiotis G. Kevrekidis, Olof Runborg, Constantinos Theodoropoulos |
|---|---|
| Categories | |
| ArXiv ID | physics/0209043 |
| URL | https://arxiv.org/abs/physics/0209043 |
Abstract
We present and discuss a framework for computer-aided multiscale analysis, which enables models at a "fine" (microscopic/stochastic) level of description to perform modeling tasks at a "coarse" (macroscopic, systems) level. These macroscopic modeling tasks, yielding information over long time and large space scales, are accomplished through appropriately initialized calls to the microscopic simulator for only short times and small spatial domains. Our equation-free (EF) approach, when successful, can bypass the derivation of the macroscopic evolution equations when these equations conceptually exist but are not available in closed form. We discuss how the mathematics-assisted development of a computational superstructure may enable alternative descriptions of the problem physics (e.g. Lattice Boltzmann (LB), kinetic Monte Carlo (KMC) or Molecular Dynamics (MD) microscopic simulators, executed over relatively short time and space scales) to perform systems level tasks (integration over relatively large time and space scales,"coarse" bifurcation analysis, optimization, and control) directly. In effect, the procedure constitutes a systems identification based, "closure on demand" computational toolkit, bridging microscopic/stochastic simulation with traditional continuum scientific computation and numerical analysis. We illustrate these ideas through examples from chemical kinetics (LB, KMC), rheology (Brownian Dynamics), homogenization and the computation of "coarsely self-similar" solutions, and discuss various features, limitations and potential extensions of the approach.
{
"annotation_id": "cb615236-4611-48af-9daf-fcbe9c831a3b",
"date_created": "2026-03-02T18:00:39.760000Z",
"date_modified": "2026-03-02T18:00:39.760000Z",
"file_hash": "2e634984cd0e33ecc813d56f8c8ba9b3601e112c76cb95437ebc5f77001fc5ca",
"private": false,
"record": {
"abstract": "We present and discuss a framework for computer-aided multiscale analysis,\nwhich enables models at a \"fine\" (microscopic/stochastic) level of description\nto perform modeling tasks at a \"coarse\" (macroscopic, systems) level. These\nmacroscopic modeling tasks, yielding information over long time and large space\nscales, are accomplished through appropriately initialized calls to the\nmicroscopic simulator for only short times and small spatial domains. Our\nequation-free (EF) approach, when successful, can bypass the derivation of the\nmacroscopic evolution equations when these equations conceptually exist but are\nnot available in closed form. We discuss how the mathematics-assisted\ndevelopment of a computational superstructure may enable alternative\ndescriptions of the problem physics (e.g. Lattice Boltzmann (LB), kinetic Monte\nCarlo (KMC) or Molecular Dynamics (MD) microscopic simulators, executed over\nrelatively short time and space scales) to perform systems level tasks\n(integration over relatively large time and space scales,\"coarse\" bifurcation\nanalysis, optimization, and control) directly. In effect, the procedure\nconstitutes a systems identification based, \"closure on demand\" computational\ntoolkit, bridging microscopic/stochastic simulation with traditional continuum\nscientific computation and numerical analysis. We illustrate these ideas\nthrough examples from chemical kinetics (LB, KMC), rheology (Brownian\nDynamics), homogenization and the computation of \"coarsely self-similar\"\nsolutions, and discuss various features, limitations and potential extensions\nof the approach.",
"arxiv_id": "physics/0209043",
"authors": [
"Ioannis G. Kevrekidis",
"C. William Gear",
"James M. Hyman",
"Panagiotis G. Kevrekidis",
"Olof Runborg",
"Constantinos Theodoropoulos"
],
"categories": [
"physics.comp-ph"
],
"title": "Equation-Free Multiscale Computation: enabling microscopic simulators to perform system-level tasks",
"url": "https://arxiv.org/abs/physics/0209043"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "21b73121-ff49-4e1b-839f-f4c58c84f314",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}