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Although projection-based reduced-order models (ROMs) for parameterized nonlinear dynamical systems have demonstrated exciting results across a range of applications, their broad adoption has been limited by their intrusivity: implementing…

We consider high-dimensional asset price models that are reduced in their dimension in order to reduce the complexity of the problem or the effect of the curse of dimensionality in the context of option pricing. We apply model order…

We present a novel reduced order model (ROM) approach for parameterized time-dependent PDEs based on modern learning. The ROM is suitable for multi-query problems and is nonintrusive. It is divided into two distinct stages: A nonlinear…

Model order reduction (MOR) involves offering low-dimensional models that effectively approximate the behavior of complex high-order systems. Due to potential model complexities and computational costs, designing controllers for…

We propose a data-driven model order reduction (MOR) technique for parametrized partial differential equations that exhibit parameter-dependent jump-discontinuities. Such problems have poor-approximability in a linear space and therefore,…

Reduced-order models are indispensable for multi-query or real-time problems. However, there are still many challenges to constructing efficient ROMs for time-dependent parametrized problems. Using a linear reduced space is inefficient for…

Steering a system towards a desired target in a very short amount of time is challenging from a computational standpoint. Indeed, the intrinsically iterative nature of optimal control problems requires multiple simulations of the physical…

The Model Order Reduction (MOR) technique can provide compact numerical models for fast simulation. Different from the intrusive MOR methods, the non-intrusive MOR does not require access to the Full Order Models (FOMs), especially system…

Feedback control synthesis for nonlinear, parameter-dependent fluid flow control problems is considered. The optimal feedback law requires the solution of the Hamilton-Jacobi-Bellman (HJB) PDE suffering the curse of dimensionality. This is…

In this work, we present the novel mathematical framework of latent dynamics models (LDMs) for reduced order modeling of parameterized nonlinear time-dependent PDEs. Our framework casts this latter task as a nonlinear dimensionality…

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…

Reduced order modeling methods are often used as a mean to reduce simulation costs in industrial applications. Despite their computational advantages, reduced order models (ROMs) often fail to accurately reproduce complex dynamics…

Reduced order modeling (ROM) techniques are numerical methods that approximate the solution of parametric partial differential equation (PDE) by properly combining the high-fidelity solutions of the problem obtained for several…

A data-driven parametric model order reduction (MOR) method using a deep artificial neural network is proposed. The present network, which is the least-squares hierarchical variational autoencoder (LSH-VAE), is capable of performing…

A nonintrusive model order reduction method for bilinear stochastic differential equations with additive noise is proposed. A reduced order model (ROM) is designed in order to approximate the statistical properties of high-dimensional…

The numerical simulation of electromagnetic transients in fusion devices is essential for analyzing plasma stability and disruptive events. However, it remains computationally demanding due to the large-scale dense systems arising from…

This paper presents a model order reduction (MOR) approach for high dimensional problems in the analysis of financial risk. To understand the financial risks and possible outcomes, we have to perform several thousand simulations of the…

Multiple model reduction techniques have been proposed to tackle linear and non linear problems. Intrusive model order reduction techniques exhibit high accuracy levels, however, they are rarely used as a standalone industrial tool, because…

The efficient condition assessment of engineered systems requires the coupling of high fidelity models with data extracted from the state of the system `as-is'. In enabling this task, this paper implements a parametric Model Order Reduction…

Moment-based distributionally robust optimization (DRO) provides an optimization framework to integrate statistical information with traditional optimization approaches. Under this framework, one assumes that the underlying joint…