Related papers: Systematic derivation of hybrid coarse-grained mod…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…
By reducing resolution, coarse-grained models greatly accelerate molecular simulations, unlocking access to long-timescale phenomena, though at the expense of microscopic information. Recovering this fine-grained detail is essential for…
We introduce the Mori-Zwanzig Mode Decomposition (MZMD), a novel data-driven technique for efficient modal analysis of and reduced-order modeling of large-scale spatio-temporal dynamical systems. MZMD represents an extension of Dynamic Mode…
Understanding the emergence of macroscopic irreversible hydrodynamics from the reversible unitary dynamics of isolated quantum many-body systems remains a fundamental challenge. Conventional approaches often force spin density dynamics into…
Reduced-order models that accurately abstract high fidelity models and enable faster simulation is vital for real-time, model-based diagnosis applications. In this paper, we outline a novel hybrid modeling approach that combines machine…
Coarse-graining is central to reducing dimensionality in molecular dynamics, and is typically characterized by a mapping which projects the full state of the system to a smaller class of variables. While extensive literature has been…
The separation between molecular and mesoscopic length and time scales poses a severe limit to molecular simulations of mesoscale phenomena. We describe a hybrid multiscale computational technique which address this problem by keeping the…
Computational modeling of a complex system is limited by the parts of the system with the least information. While detailed models and high-resolution data may be available for parts of a system, abstract relationships are often necessary…
We present a multilevel Monte Carlo simulation method for analysing multi-scale physical systems via a hierarchy of coarse-grained representations, to obtain numerically-exact results, at the most detailed level. We apply the method to a…
Over the last decade, the Lattice Boltzmann method has found major scope for the simulation of a large spectrum of problems in soft matter, from multiphase and multi-component microfluidic flows, to foams, emulsions, colloidal flows, to…
The Weak-form Sparse Identification of Nonlinear Dynamics algorithm (WSINDy) has been demonstrated to offer coarse-graining capabilities in the context of interacting particle systems (https://doi.org/10.1016/j.physd.2022.133406). In this…
The automated construction of coarse-grained models represents a pivotal component in computer simulation of physical systems and is a key enabler in various analysis and design tasks related to uncertainty quantification. Pertinent methods…
Electrostatic interactions between macroions largely govern the equilibrium thermodynamic and dynamical properties of charge-stabilized colloidal suspensions and polyelectrolyte solutions. Predicting the properties of such complex,…
In this work, we present a novel nonlocal nonlinear coarse grid approximation using a machine learning algorithm. We consider unsaturated and two-phase flow problems in heterogeneous and fractured porous media, where mathematical models are…
A careful derivation of the generalized Langevin equation using "Zwanzig flavor" projection operator formalism is presented. We provide arguments why this formalism has better properties compared to alternative projection-operator…
We present a data-driven machine-learning approach for modeling space-time socioeconomic dynamics. Through coarse-graining fine-scale observations, our modeling framework simplifies these complex systems to a set of tractable mechanistic…
Sufficiently accurate finite state models, also called symbolic models or discrete abstractions, allow one to apply fully automated methods, originally developed for purely discrete systems, to formally reason about continuous and hybrid…
A key challenge for soft materials design and coarse-graining simulations is determining interaction potentials between components that give rise to desired condensed-phase structures. In theory, the Ornstein-Zernike equation provides an…
Measurement involves the determination of quantitative estimates of physical quantities from experiment, along with estimates of their associated uncertainties. Herewith an experimental system model is the key to extracting information from…
We show that, near periodic orbits, a class of hybrid models can be reduced to or approximated by smooth continuous-time dynamical systems. Specifically, near an exponentially stable periodic orbit undergoing isolated transitions in a…