Related papers: Latent-space time evolution of non-intrusive reduc…

Occupancy mapping has been a key enabler of mobile robotics. Originally based on a discrete grid representation, occupancy mapping has evolved towards continuous representations that can predict the occupancy status at any location and…

Advection-dominated problems are predominantly noticed in nature, engineering systems, and various industrial processes. Traditional linear compression methods, such as proper orthogonal decomposition (POD) and reduced basis (RB) methods…

We propose a numerical pipeline for shape optimization in naval engineering involving two different non-intrusive reduced order method (ROM) techniques. Such methods are proper orthogonal decomposition with interpolation (PODI) and dynamic…

An adaptive approach to using reduced-order models as surrogates in PDE-constrained optimization is introduced that breaks the traditional offline-online framework of model order reduction. A sequence of optimization problems constrained by…

Data-driven reduced order models (ROMs) are combined with the Lippmann-Schwinger integral equation to produce a direct nonlinear inversion method. The ROM is viewed as a Galerkin projection and is sparse due to Lanczos orthogonalization.…

Data-driven modeling for nonlinear fluid flows using sparse convolution-based mapping into a feature space where the dynamics are Markov linear is explored in this article. The underlying principle of low-order models for fluid systems is…

This work aims to advance computational methods for projection-based reduced order models (ROMs) of linear time-invariant (LTI) dynamical systems. For such systems, current practice relies on ROM formulations expressing the state as a…

This paper proposes a supervised machine learning framework for the non-intrusive model order reduction of unsteady fluid flows to provide accurate predictions of non-stationary state variables when the control parameter values vary. Our…

We propose a three-tier machine learning framework based on the next-generation Equation-Free algorithm for learning the spatio-temporal dynamics of mass-constrained complex systems with hidden states, whose dynamics can in principle be…

This paper extends a low-rank tensor decomposition (LRTD) reduced order model (ROM) methodology to simulate viscous flows and in particular to predict a smooth branch of solutions for the incompressible Navier-Stokes equations.…

Interpolatory methods offer a powerful framework for generating reduced-order models (ROMs) for non-parametric or parametric systems with time-varying inputs. Choosing the interpolation points adaptively remains an area of active interest.…

We propose a non-intrusive reduced-order modeling framework for parametrized visco-plastic free-surface flows governed by a shallow-water formulation of Herschel--Bulkley fluids. These flows exhibit strong nonlinearities, non-smooth…

This paper proposes the use of a Spectral method to simulate diffusive moisture transfer through porous materials as a Reduced-Order Model (ROM). The Spectral approach is an a priori method assuming a separated representation of the…

This paper investigates non-intrusive Scientific Machine Learning (SciML) Reduced-Order Models (ROMs) for plasma turbulence simulations. In particular, we focus on Operator Inference (OpInf) to build low-cost physics-based ROMs from data…

This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models. The key ingredient of the approach…

A structure preserving proper orthogonal decomposition reduce-order modeling approach has been developed in [Gong et al. 2017] for the Hamiltonian system, which uses the traditional framework of Galerkin projection-based model reduction but…

The recently developed generalized Fourier-Galerkin method is complemented by a numerical continuation with respect to the kinetic energy, which extends the framework to the investigation of modal interactions resulting in folds of the…

Reduced-order models (ROMs) can efficiently simulate high-dimensional physical systems but lack robust uncertainty quantification methods. Existing approaches are frequently architecture- or training-specific, which limits flexibility and…

Gaussian state space models have been used for decades as generative models of sequential data. They admit an intuitive probabilistic interpretation, have a simple functional form, and enjoy widespread adoption. We introduce a unified…

Reduced-order modelling and low-dimensional surrogate models generated using machine learning algorithms have been widely applied in high-dimensional dynamical systems to improve the algorithmic efficiency. In this paper, we develop a…