Related papers: Mori-Zwanzig reduced models for uncertainty quanti…
In many time-dependent problems of practical interest the parameters entering the equations describing the evolution of the various quantities exhibit uncertainty. One way to address the problem of how this uncertainty impacts the solution…
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 novel way of constructing reduced models for systems of ordinary differential equations. The reduced models we construct depend on coefficients which measure the importance of the different terms appearing in the model and need…
We examine the challenging problem of constructing reduced models for the long time prediction of systems where there is no timescale separation between the resolved and unresolved variables. In previous work we focused on the case where…
The well-known Mori-Zwanzig theory tells us that model reduction leads to memory effect. For a long time, modeling the memory effect accurately and efficiently has been an important but nearly impossible task in developing a good reduced…
Reduced Order Models (ROMs) of complex, nonlinear dynamical systems often require closure, which is the process of representing the contribution of the unresolved physics on the resolved physics. The Mori-Zwanzig (M-Z) procedure allows one…
While model order reduction is a promising approach in dealing with multi-scale time-dependent systems that are too large or too expensive to simulate for long times, the resulting reduced order models can suffer from instabilities. We have…
We develop rigorous estimates and provably convergent approximations for the memory integral in the Mori-Zwanzig (MZ) formulation. The new theory is built upon rigorous mathematical foundations and is presented for both state-space and…
Reduced order models are computationally inexpensive approximations that capture the important dynamical characteristics of large, high-fidelity computer models of physical systems. This paper applies machine learning techniques to improve…
The Mori-Zwanzig formalism of statistical mechanics is used to estimate the uncertainty caused by underresolution in the solution of a nonlinear dynamical system. A general approach is outlined and applied to a simple example. The noise…
We consider the model reduction problem for linear time-invariant dynamical systems having nonzero (but otherwise indeterminate) initial conditions. Building upon the observation that the full system response is decomposable as a…
Establishing appropriate mathematical models for complex systems in natural phenomena not only helps deepen our understanding of nature but can also be used for state estimation and prediction. However, the extreme complexity of natural…
Machine learning models have emerged as a very effective strategy to sidestep time-consuming electronic-structure calculations, enabling accurate simulations of greater size, time scale and complexity. Given the interpolative nature of…
We present a comparative study of two methods for the reduction of the dimensionality of a system of ordinary differential equations that exhibits time-scale separation. Both methods lead to a reduced system of stochastic differential…
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…
This paper presents a probabilistic approach to represent and quantify model-form uncertainties in the reduced-order modeling of complex systems using operator inference techniques. Such uncertainties can arise in the selection of an…
Propagating uncertainties introduced by chemical reaction rate parameters to high-fidelity numerical simulations of complex combustion devices is necessary to ascertain impact on computational predictions. However, the high cost of detailed…
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…
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…
We study the robustness of system estimation to parametric perturbations in system dynamics and initial conditions. We define the problem of sensitivity-based parametric uncertainty quantification in dynamical system estimation. The main…