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In recent years, large-scale numerical simulations played an essential role in estimating the effects of explosion events in urban environments, for the purpose of ensuring the security and safety of cities. Such simulations are…
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…
In a recent work, we proposed a graph-based manifold learning scheme for the nonlinear Galerkin-reduction of quasi-static solid mechanical problems [1]. The resulting nonlinear approximation spaces can closely and flexibly represent…
Suitable reduced order models (ROMs) are computationally efficient tools in characterizing key dynamical and statistical features of nature. In this paper, a systematic multiscale stochastic ROM framework is developed for complex systems…
This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…
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…
In aircraft design, structural optimization and uncertainty quantification concerning transonic aeroelastic issues are computationally impractical, because the iterative process requires great number of aeroelastic analysis. Emerging…
A novel reduced order model (ROM) for incompressible flows is developed by performing a Galerkin projection based on a fully (space and time) discrete full order model (FOM) formulation. This 'discretize-then-project' approach requires no…
Scientific and engineering problems often involve parametric partial differential equations (PDEs), such as uncertainty quantification, optimizations, and inverse problems. However, solving these PDEs repeatedly can be prohibitively…
Nonlinear manifold learning (ML) based reduced-order models (ROMs) can substantially improve the quality of nonlinear flow-field modeling. However, noise and the lack of physical information often distort the dimensionality-reduction…
Reduced order models (ROM) can represent spatiotemporal processes in significantly fewer dimensions and can be solved many orders faster than their governing partial differential equations (PDEs). For example, using a proper orthogonal…
We present an efficient data-driven regression approach for constructing reduced-order models (ROMs) of reaction-diffusion systems exhibiting pattern formation. The ROMs are learned non-intrusively from available training data of physically…
Numerous cutting-edge scientific technologies originate at the laboratory scale, but transitioning them to practical industry applications is a formidable challenge. Traditional pilot projects at intermediate scales are costly and…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…
In this work we propose a novel method to ensure important entropy inequalities are satisfied semi-discretely when constructing reduced order models (ROMs) on nonlinear reduced manifolds. We are in particular interested in ROMs of systems…
Time domain simulations are crucial for analyzing transient behavior and broadband responses in electromagnetic problems. However, conventional numerical methods such as finite element method in time domain (FEMTD) and finite difference…
Reduced Order Modelling (ROM) has been widely used to create lower order, computationally inexpensive representations of higher-order dynamical systems. Using these representations, ROMs can efficiently model flow fields while using…
This work presents a non-intrusive reduced-order modeling framework for dynamical systems with spatially localized features characterized by slow singular value decay. The proposed approach builds upon two existing methodologies for reduced…
In recent years, data-driven deep learning models have gained significant interest in the analysis of turbulent dynamical systems. Within the context of reduced-order models (ROMs), convolutional autoencoders (CAEs) pose a universally…
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…