Related papers: Data-Driven Mori-Zwanzig: Approaching a Reduced Or…
Dynamic mode decomposition has emerged as a leading technique to identify spatiotemporal coherent structures from high-dimensional data, benefiting from a strong connection to nonlinear dynamical systems via the Koopman operator. In this…
Dynamic Mode Decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly…
This paper deals with the development of a Reduced-Order Model (ROM) to investigate haemodynamics in cardiovascular applications. It employs the use of Proper Orthogonal Decomposition (POD) for the computation of the basis functions and the…
We present a data-driven approach for constructing generalized collisional kinetic models for inhomogeneous plasmas in one-dimensional physical space and three-dimensional velocity space (1D-3V). The collision operator is directly learned…
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…
Stochastic modeling has become a popular approach to quantify uncertainty in flows through heterogeneous porous media. The uncertainty in heterogeneous structure properties is often parameterized by a high-dimensional random variable. This…
This work introduces a non-intrusive model reduction approach for learning reduced models from partially observed state trajectories of high-dimensional dynamical systems. The proposed approach compensates for the loss of information due to…
We present a numerical methodology for construction of reduced order models, ROMs, of fluid flows through the combination of flow modal decomposition and regression analysis. Spectral proper orthogonal decomposition, SPOD, is applied to…
Integrating machine learning techniques in established numerical solvers represents a modern approach to enhancing computational fluid dynamics simulations. Within the lattice Boltzmann method (LBM), the collision operator serves as an…
In this paper, we combine deep learning concepts and some proper orthogonal decomposition (POD) model reduction methods for predicting flow in heterogeneous porous media. Nonlinear flow dynamics is studied, where the dynamics is regarded as…
This paper develops a smooth model identification and self-learning strategy for dynamic systems taking into account possible parameter variations and uncertainties. We have tried to solve the problem such that the model follows the changes…
In spatially extended systems, it is common to find latent variables that are hard, or even impossible, to measure with acceptable precision, but are crucially important for the proper description of the dynamics. This substantially…
The Mori-Zwanzig formalism is a powerful theoretical framework for deriving equations of motion for coarse-grained observables in the form of generalized Langevin equations (GLEs) involving evolution and projection operators. Using a…
Turbulence modeling within the Lattice Boltzmann Method (LBM) framework has long relied on traditional algebraic sub-grid scale (SGS) models, which often suffer from over-dissipation and lack of spatial selectivity near solid boundaries. In…
A central question in modern deep learning is how to design optimizers whose behavior remains stable as the network width $w$ increases. We address this question by interpreting several widely used neural-network optimizers, including…
Lattice gas and lattice Boltzmann methods are recently developed numerical schemes for simulating a variety of physical systems. In this paper a new lattice Boltzmann model for modeling two-dimensional incompressible magnetohydrodynamics…
We develop an optimization-based algorithm for parametric model order reduction (PMOR) of linear time-invariant dynamical systems. Our method aims at minimizing the $\mathcal{H}_\infty \otimes \mathcal{L}_\infty$ approximation error in the…
High-dimensional multivariate spatial-temporal data arise frequently in a wide range of applications; however, there are relatively few statistical methods that can simultaneously deal with spatial, temporal and variable-wise dependencies…
In this work, a new hybrid predictive Reduced Order Model (ROM) is proposed to solve reacting flow problems. This algorithm is based on a dimensionality reduction using Proper Orthogonal Decomposition (POD) combined with deep learning…
This paper develops learning-enabled safe controllers for linear systems subject to system uncertainties and bounded disturbances. Given the disturbance zonotope, the databased closed-loop dynamics (CLDs) are first characterized using a…