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The article focuses on error estimates as well as stability analysis of deep learning methods for stationary and non-stationary viscous Burgers equation in two and three dimensions. The local well-posedness of homogeneous boundary value…
Two comprehensive approaches are considered for constructing projection-based reduced-order computational models for linear dynamical systems. The first one reduces the governing equations written in the descriptor form, using a Galerkin or…
We present results on stabilization for reduced order models (ROM) of partial differential equations using learning. Stabilization is achieved via closure models for ROMs, where we use a model-free extremum seeking (ES) dither-based…
This paper presents a reduced order approach for transient modeling of multiple moving objects in nonlinear crossflows. The Proper Orthogonal Decomposition method and the Galerkin projection are used to construct a reduced version of the…
Data-driven turbulence modeling is experiencing a surge in interest following algorithmic and hardware developments in the data sciences. We discuss an approach using the differentiable physics paradigm that combines known physics with…
We present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The…
Reduced-order models have been widely adopted in fluid mechanics, particularly in the context of Newtonian fluid flows. These models offer the ability to predict complex dynamics, such as instabilities and oscillations, at a considerably…
Nearly all model-reduction techniques project the governing equations onto a linear subspace of the original state space. Such subspaces are typically computed using methods such as balanced truncation, rational interpolation, the…
Piecewise-linear nonlinear systems appear in many engineering disciplines. Prediction of the dynamic behavior of such systems is of great importance from practical and theoretical viewpoint. In this paper, a data-driven model order…
Traditional linear subspace reduced order models (LS-ROMs) are able to accelerate physical simulations, in which the intrinsic solution space falls into a subspace with a small dimension, i.e., the solution space has a small Kolmogorov…
In this paper, feedforward neural networks are presented that have nonlinear weight functions based on look--up tables, that are specially smoothed in a regularization called the diffusion. The idea of such a type of networks is based on…
This work proposes a Bayesian inference method for the reduced-order modeling of time-dependent systems. Informed by the structure of the governing equations, the task of learning a reduced-order model from data is posed as a Bayesian…
This paper studies reduced-order modeling of dynamic networks with strongly connected topology. Given a graph clustering of an original complex network, we construct a quotient graph with less number of vertices, where the edge weights are…
We propose a probabilistic way for reducing the cost of classical projection-based model order reduction methods for parameter-dependent linear equations. A reduced order model is here approximated from its random sketch, which is a set of…
Computationally cheap yet accurate dynamical models are a key requirement for real-time capable nonlinear optimization and model-based control. When given a computationally expensive high-order prediction model, a reduction to a lower-order…
The paper presents a Projection-Based Reduced-Order Model for simulations of high Reynolds turbulent flows. The PBROM are enhanced by incorporating various models of turbulent viscosity and residual closures to model the effects of…
In this paper, we consider queueing systems where the dynamics are non-stationary and state-dependent. For performance analysis of these systems, fluid and diffusion models have been typically used. Although they are proven to be…
This work presents a method for constructing online-efficient reduced models of large-scale systems governed by parametrized nonlinear scalar conservation laws. The solution manifolds induced by transport-dominated problems such as…
We propose a general strategy for reduced order modeling of systems that display highly nonlinear oscillations. By considering a continuous family of forced periodic orbits defined in relation to a stable fixed point and subsequently…
This study presents a systematic machine learning approach for creating efficient hybrid models and discovering sorption uptake models in non-linear advection-diffusion-sorption systems. It demonstrates an effective method to train these…