Related papers: Data-driven non-Markovian closure models
This work uses the Mori-Zwanzig (M-Z) formalism, a concept originating from non-equilibrium statistical mechanics, as a basis for the development of coarse-grained models of turbulence. The mechanics of the generalized Langevin equation…
We propose a Machine Learning (ML) non-Markovian closure modeling framework for accurate predictions of statistical responses of turbulent dynamical systems subjected to external forcings. One of the difficulties in this statistical closure…
The development of reduced models for complex multiscale problems remains one of the principal challenges in computational physics. The optimal prediction framework of Chorin et al., which is a reformulation of the Mori-Zwanzig (M-Z)…
We describe a paradigm for multiscale modeling that combines the Mori-Zwanzig (MZ) formalism of Statistical Mechanics with the Variational Multiscale (VMS) method. The MZ-VMS approach leverages both VMS scale-separation projectors as well…
Simulation of multiscale problems remains a challenge due to the disparate range of spatial and temporal scales and the complex interaction between the resolved and unresolved scales. This work develops a coarse-grained modeling approach…
Complex dynamical systems are used for predictions in many domains. Because of computational costs, models are truncated, coarsened, or aggregated. As the neglected and unresolved terms become important, the utility of model predictions…
Markov switching models (MSMs) are probabilistic models that employ multiple sets of parameters to describe different dynamic regimes that a time series may exhibit at different periods of time. The switching mechanism between regimes is…
Understanding, predicting and controlling laminar-turbulent boundary-layer transition is crucial for the next generation aircraft design. However, in real flight experiments, or wind tunnel tests, often only sparse sensor measurements can…
Closure models are widely used in simulating complex multiscale dynamical systems such as turbulence and the earth system, for which direct numerical simulation that resolves all scales is often too expensive. For those systems without a…
The Boltzmann equation, a fundamental equation in kinetic theory, serves as a bridge between microscopic particle dynamics and macroscopic continuum mechanics. However, deriving closed macroscopic moment systems from the Boltzmann equation…
In this work, we apply, for the first time to spatially inhomogeneous flows, a recently developed data-driven learning algorithm of Mori-Zwanzig (MZ) operators, which is based on a generalized Koopman's description of dynamical systems. The…
We propose a statistical-stochastic surrogate modeling approach to predict the response of the mean and variance statistics under various initial conditions and external forcing perturbations. The proposed modeling framework extends the…
Closure problems are omnipresent when simulating multiscale systems, where some quantities and processes cannot be fully prescribed despite their effects on the simulation's accuracy. Recently, scientific machine learning approaches have…
Recent advances in learning dynamical systems from data have shown significant promise. However, many existing methods assume access to the full state of the system -- an assumption that is rarely satisfied in practice, where systems are…
This paper presents a theoretical analysis of the closure kinetics of a polymer with hydrodynamic interactions. This analysis, which takes into account the non-Markovian dynamics of the end-to-end vector and relies on the preaveraging of…
We propose a general framework for non-normal multivariate data analysis called multivariate covariance generalized linear models (McGLMs), designed to handle multivariate response variables, along with a wide range of temporal and spatial…
The Koopman operator presents an attractive approach to achieve global linearization of nonlinear systems, making it a valuable method for simplifying the understanding of complex dynamics. While data-driven methodologies have exhibited…
We present a general numerical scheme for the practical implementation of statistical moment closures suitable for modeling complex, large-scale, nonlinear systems. Building on recently developed equation-free methods, this approach…
Only a subset of degrees of freedom are typically accessible or measurable in real-world systems. As a consequence, the proper setting for empirical modeling is that of partially-observed systems. Notably, data-driven models consistently…
While data-driven model reduction techniques are well-established for linearizable mechanical systems, general approaches to reducing non-linearizable systems with multiple coexisting steady states have been unavailable. In this paper, we…