Scientific machine learning for closure models in multiscale problems: A review
Closure problems are omnipresent when simulating multiscale systems, where some
quantities and processes cannot be fully prescribed despite their effects on the simulation's …
quantities and processes cannot be fully prescribed despite their effects on the simulation's …
Data-Driven Learning for the Mori--Zwanzig Formalism: A Generalization of the Koopman Learning Framework
A theoretical framework which unifies the conventional Mori--Zwanzig formalism and the
approximate Koopman learning of deterministic dynamical systems from noiseless …
approximate Koopman learning of deterministic dynamical systems from noiseless …
Learning stochastic dynamics with statistics-informed neural network
We introduce a machine-learning framework named statistics-informed neural network
(SINN) for learning stochastic dynamics from data. This new architecture was theoretically …
(SINN) for learning stochastic dynamics from data. This new architecture was theoretically …
Data-driven construction of stochastic reduced dynamics encoded with non-Markovian features
One important problem in constructing the reduced dynamics of molecular systems is the
accurate modeling of the non-Markovian behavior arising from the dynamics of unresolved …
accurate modeling of the non-Markovian behavior arising from the dynamics of unresolved …
Dynamics of liquids in the large-dimensional limit
In this paper we analytically derive the exact closed dynamical equations for a liquid with
short-ranged interactions in large spatial dimensions using the same statistical mechanics …
short-ranged interactions in large spatial dimensions using the same statistical mechanics …
Data-driven molecular modeling with the generalized Langevin equation
The complexity of molecular dynamics simulations necessitates dimension reduction and
coarse-graining techniques to enable tractable computation. The generalized Langevin …
coarse-graining techniques to enable tractable computation. The generalized Langevin …
Data-driven model reduction for stochastic Burgers equations
F Lu - Entropy, 2020 - mdpi.com
We present a class of efficient parametric closure models for 1D stochastic Burgers
equations. Casting it as statistical learning of the flow map, we derive the parametric form by …
equations. Casting it as statistical learning of the flow map, we derive the parametric form by …
General validity of the second fluctuation-dissipation theorem in the nonequilibrium steady state: Theory and applications
In this paper, we derive a generalized second fluctuation-dissipation theorem (FDT) for
stochastic dynamical systems in the steady state and further show that if the system is highly …
stochastic dynamical systems in the steady state and further show that if the system is highly …
Effective Mori-Zwanzig equation for the reduced-order modeling of stochastic systems
Built upon the hypoelliptic analysis of the effective Mori-Zwanzig (EMZ) equation for
observables of stochastic dynamical systems, we show that the obtained semigroup …
observables of stochastic dynamical systems, we show that the obtained semigroup …
[HTML][HTML] Hypoellipticity and the Mori–Zwanzig formulation of stochastic differential equations
We develop a thorough mathematical analysis of the effective Mori–Zwanzig (EMZ) equation
governing the dynamics of noise-averaged observables in stochastic differential equations …
governing the dynamics of noise-averaged observables in stochastic differential equations …