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In this paper, we introduce an uplifted reduced order modeling (UROM) approach through the integration of standard projection based methods with long short-term memory (LSTM) embedding. Our approach has three modeling layers or components.…

Given a set of solution snapshots of a hyperbolic PDE, we are interested in learning a reduced order model (ROM). To this end, we propose a novel decompose then learn approach. We decompose the solution by expressing it as a composition of…

This work aims to interpolate parametrized Reduced Order Model (ROM) basis constructed via the Proper Orthogonal Decomposition (POD) to derive a robust ROM of the system's dynamics for an unseen target parameter value. A novel non-intrusive…

This paper introduces a multifidelity formulation that reduces the computational cost of the proper orthogonal decomposition (POD) of a high-fidelity model by leveraging data from cheaper, lower-fidelity models. POD is a prevalent technique…

Reduced Order Models (ROMs) have been regarded as an efficient alternative to conventional high-fidelity Computational Fluid Dynamics (CFD) for accelerating the design and optimization processes in engineering applications. Many industrial…

We develop a novel deep learning technique, termed Deep Orthogonal Decomposition (DOD), for dimensionality reduction and reduced order modeling of parameter dependent partial differential equations. The approach consists in the construction…

Reduced Order Modeling is of paramount importance for efficiently inferring high-dimensional spatio-temporal fields in parametric contexts, enabling computationally tractable parametric analyses, uncertainty quantification and control.…

This paper proposes a large eddy simulation reduced order model(LES-ROM) framework for the numerical simulation of realistic flows. In this LES-ROM framework, the proper orthogonal decomposition(POD) is used to define the ROM basis and a…

We propose a new reduced order modeling strategy for tackling parametrized Partial Differential Equations (PDEs) with linear constraints, in particular Darcy flow systems in which the constraint is given by mass conservation. Our approach…

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…

The two-layer quasi-geostrophic equations (2QGE) is a simplified model that describes the dynamics of a stratified, wind-driven ocean in terms of potential vorticity and stream function. Its numerical simulation is plagued by a high…

In this paper, we propose a data-driven model reduction method to solve parabolic inverse source problems efficiently. Our method consists of offline and online stages. In the off-line stage, we explore the low-dimensional structures in the…

The current study aims to evaluate and investigate the development of projection-based reduced-order models (ROMs) for efficient and accurate RDE simulations. Specifically, we focus on assessing the projection-based ROM construction…

Within the environmental context, numerical modeling is a promising approach to assessing the energy efficiency of buildings. Resilient buildings need to be designed, and capable of adapting to future extreme heat. Simulations are required…

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,…

Digital twins have emerged as a key technology for optimizing the performance of engineering products and systems. High-fidelity numerical simulations constitute the backbone of engineering design, providing an accurate insight into the…

This study presents a collection of purely data-driven workflows for constructing reduced-order models (ROMs) for distributed dynamical systems. The ROMs we focus on, are data-assisted models inspired by, and templated upon, the theory of…

Simulating physical systems governed by Lagrangian dynamics often entails solving partial differential equations (PDEs) over high-resolution spatial domains, leading to significant computational expense. Reduced-order modeling (ROM)…

Reduced Order Models (ROMs) are of considerable importance in many areas of engineering in which computational time presents difficulties. Established approaches employ projection-based reduction such as Proper Orthogonal Decomposition,…

Many AI problems, in robotics and other domains, are goal-based, essentially seeking trajectories leading to various goal states. Reinforcement learning (RL), building on Bellman's optimality equation, naturally optimizes for a single goal,…