Related papers: On the estimation of the Mori-Zwanzig memory integ…
We develop a new formulation of deep learning based on the Mori-Zwanzig (MZ) formalism of irreversible statistical mechanics. The new formulation is built upon the well-known duality between deep neural networks and discrete dynamical…
We present a general numerical approach for constructing governing equations for unknown dynamical systems when only data on a subset of the state variables are available. The unknown equations for these observed variables are thus a…
Built upon the hypoelliptic analysis of the effective Mori-Zwanzig (EMZ) equation for observables of stochastic dynamical systems, we show that the obtained semigroup estimates for the EMZ equation can be used to drive prior estimates of…
Developing reduced-order models for turbulent flows, which contain dynamics over a wide range of scales, is an extremely challenging problem. In statistical mechanics, the Mori-Zwanzig (MZ) formalism provides a mathematically formal…
In many time-dependent problems of practical interest the parameters and/or initial conditions entering the equations describing the evolution of the various quantities exhibit uncertainty. One way to address the problem of how this…
We present a formalism that explicitly unifies the commonly used Nakajima-Zwanzig approach for reduced density matrix dynamics with the more versatile Mori theory in the context of nonequilibrium dynamics. Employing a Dyson-type expansion…
In this paper we consider the problem of deriving approximate autonomous dynamics for a number of variables of a dynamical system, which are weakly coupled to the remaining variables. In a previous paper we have used the Ruelle response…
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…
Significant efforts have been devoted in the last decade towards improving the predictivity of coarse-grained models in molecular dynamics simulations and providing a rigorous justification of their use, through a combination of theoretical…
In a recent preprint (arXiv:1211.4285v1) we addressed the problem of constructing reduced models for time-dependent systems described by differential equations which involve uncertain parameters. In the current work, we focus on the…
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…
We present a new method to approximate the Mori-Zwanzig (MZ) memory integral in generalized Langevin equations (GLEs) describing the evolution of smooth observables in high-dimensional nonlinear systems with local interactions. Building…
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…
The ability to efficiently and accurately calculate equilibrium time correlation functions of many-body condensed phase quantum systems is one of the outstanding problems in theoretical chemistry. The Nakajima-Zwanzig-Mori formalism coupled…
Standard projection-based model reduction for dynamical systems incurs closure error because it only accounts for instantaneous dependence on the resolved state. From the Mori-Zwanzig (MZ) perspective, projecting the full dynamics onto a…
We study an approximation method for partially observed Markov decision processes (POMDPs) with continuous spaces. Belief MDP reduction, which has been the standard approach to study POMDPs requires rigorous approximation methods for…
Mathematical approaches from dynamical systems theory are used in a range of fields. This includes biology where they are used to describe processes such as protein-protein interaction and gene regulatory networks. As such networks increase…
Explaining the emergence of stochastic irreversible macroscopic dynamics from time-reversible deterministic microscopic dynamics is one of the key problems in philosophy of physics. The Mori-Zwanzig projection operator formalism, which is…
The Dynamic Mode Decomposition has proved to be a very efficient technique to study dynamic data. This is entirely a data-driven approach that extracts all necessary information from data snapshots which are commonly supposed to be sampled…
We study reinforcement learning with linear function approximation and finite-memory approximations for partially observed Markov decision processes (POMDPs). We first present an algorithm for the value evaluation of finite-memory feedback…