Data-driven variational multiscale reduced order models

Modeling diffusion in random heterogeneous media: Data-driven models, stochastic collocation and the variational multiscale method

In recent years, there has been intense interest in understanding various physical phenomena in random heterogeneous media. Any accurate description/simulation of a process in such media has to satisfactorily account for the twin issues of randomness as well as the multi-length scale variations in the material properties. An accurate model of the material property variation in the system is an ...

Multiscale S-Fraction Reduced-Order Models for Massive Wavefield Simulations

Optimal Control of Multiscale Systems Using Reduced-order Models

We study optimal control of diffusions with slow and fast variables and address a question raised by practitioners: is it possible to first eliminate the fast variables before solving the optimal control problem and then use the optimal control computed from the reduced-order model to control the original, high-dimensional system? The strategy “first reduce, then optimize”—rather than “first op...

Variational Multiscale Models for Charge Transport

This work presents a few variational multiscale models for charge transport in complex physical, chemical and biological systems and engineering devices, such as fuel cells, solar cells, battery cells, nanofluidics, transistors and ion channels. An essential ingredient of the present models, introduced in an earlier paper (Bulletin of Mathematical Biology, 72, 1562-1622, 2010), is the use of di...

Data-Driven Stochastic Multiscale Method

Introduction 1 Randomness manifests itself in many aspects of real-world problems, such as initial/boundary conditions, model parameters, measurements, to name a few. 2 Its effect may span many scales and grow with time through nonlinear interactions, which results in dramatic difference compared with that of the deterministic model. 3 A typical scenario occurring frequently in practice is that...