Related papers: Reduced models in chemical kinetics via nonlinear …
In the present work, we illustrate the process of constructing a simplified model for complex multi-scale combustion systems. To this end, reduced models of homogeneous ideal gas mixtures of methane and air are first obtained by the novel…
We present a microscopic approach to quantum dissipation and sketch the derivation of the kinetic equation describing the evolution of a simple quantum system in interaction with a complex quantum system. A typical quantum complex system is…
To develop and investigate detailed mathematical models of cellular metabolic processes is one of the primary challenges in systems biology. However, despite considerable advance in the topological analysis of metabolic networks, explicit…
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…
We introduce the optimized dynamic mode decomposition algorithm for constructing an adaptive and computationally efficient reduced order model and forecasting tool for global atmospheric chemistry dynamics. By exploiting a low-dimensional…
Discrete-state, continuous-time Markov models are becoming commonplace in the modelling of biochemical processes. The mathematical formulations that such models lead to are opaque, and, due to their complexity, are often considered…
Dynamic Mode Decomposition (DMD) is a model-order reduction approach, whereby spatial modes of fixed temporal frequencies are extracted from numerical or experimental data sets. The DMD low-rank or reduced operator is typically obtained by…
Dynamical models underpin our ability to understand and predict the behavior of natural systems. Whether dynamical models are developed from first-principles derivations or from observational data, they are predicated on our choice of state…
In this contribution we develop an efficient reduced order model for solving parametrized linear-quadratic optimal control problems with linear time-varying state system. The fully reduced model combines reduced basis approximations of the…
This article is concerned with the asymptotic accuracy of the Computational Singular Perturbation (CSP) method developed by Lam and Goussis to reduce the dimensionality of a system of chemical kinetics equations. The method exploits the…
The determination of a dynamic law of cut is complex and often very difficult to develop. Several formulations were developed, in very complex ways being given that 3 AD crosses from there, the number of variables is much higher than out of…
Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…
The parameterization of simulation-based models is a central yet laborious task in computational chemistry and physics, often driven by human intuition and manual iteration. Automating this task necessitates the definition of suitable…
The simulation of atmospheric flows by means of traditional discretization methods remains computationally intensive, hindering the achievement of high forecasting accuracy in short time frames. In this paper, we apply three reduced order…
Denoising Diffusion Probabilistic Models (DDPMs) are a very popular class of deep generative model that have been successfully applied to a diverse range of problems including image and video generation, protein and material synthesis,…
We present an ``equation-free'' multiscale approach to the simulation of unsteady diffusion in a random medium. The diffusivity of the medium is modeled as a random field with short correlation length, and the governing equations are cast…
In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be…
Metadynamics is a powerful method to accelerate molecular dynamics simulations, but its efficiency critically depends on the identification of collective variables that capture the slow modes of the process. Unfortunately, collective…
Finding informative low-dimensional descriptions of high-dimensional simulation data (like the ones arising in molecular dynamics or kinetic Monte Carlo simulations of physical and chemical processes) is crucial to understanding physical…
Molecular dynamics simulations are widely used across chemistry, physics, and biology, providing quantitative insight into complex processes with atomic detail. However, their limited timescale of a few microseconds is a significant…