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This paper presents a physics-based data-driven method to learn predictive reduced-order models (ROMs) from high-fidelity simulations, and illustrates it in the challenging context of a single-injector combustion process. The method…

Standard ROMs generally yield spurious numerical oscillations in the simulation of convection-dominated flows. Regularized ROMs use explicit ROM spatial filtering to decrease these spurious numerical oscillations. The Leray ROM is a…

Parameter-efficient fine-tuning (PEFT) is widely studied for its effectiveness and efficiency in the era of large language models. Low-rank adaptation (LoRA) has demonstrated commendable performance as a popular and representative method.…

In this paper, we propose SubLoRA, a rank determination method for Low-Rank Adaptation (LoRA) based on submodular function maximization. In contrast to prior approaches, such as AdaLoRA, that rely on first-order (linearized) approximations…

We present a comparative computational study of two stabilized Reduced Order Models (ROMs) for the simulation of convection-dominated incompressible flow (Reynolds number of the order of a few thousands). Representative solutions in the…

Cardio-mechanical models can be used to support clinical decision-making. Unfortunately, the substantial computational effort involved in many cardiac models hinders their application in the clinic, despite the fact that they may provide…

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…

Standard stochastic optimization methods are brittle, sensitive to stepsize choices and other algorithmic parameters, and they exhibit instability outside of well-behaved families of objectives. To address these challenges, we investigate…

In this paper, we present a deep learning-based reduced-order model (DL-ROM) for the stability prediction of unsteady 3D fluid-structure interaction systems. The proposed DL-ROM has the format of a nonlinear state-space model and employs a…

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…

Effectively integrating molecular graph structures with Large Language Models (LLMs) is a key challenge in drug discovery. Most existing multi-modal alignment methods typically process these structures by fine-tuning the LLM or adding a…

Convection-dominated problems are known for their slow Kolmogorov $n$-width decays and are challenging for model order reduction (MOR). In this work, we propose a hybrid surrogate modeling approach and a non-intrusive variant that overcome…

We present a globally convergent method to accelerate density-based topology optimization using projection-based reduced-order models (ROMs) and trust-region methods. To accelerate topology optimization, we replace the large-scale finite…

This paper deals with model order reduction of parametrical dynamical systems. We consider the specific setup where the distribution of the system's trajectories is unknown but the following two sources of information are available:…

Programmable arrays of optical traps enable the assembly of configurations of single atoms to perform controlled experiments on quantum many-body systems. Finding the sequence of control operations to transform an arbitrary configuration of…

In this paper we propose a new reduced order model (ROM) to the imcompressible Stokes equations. Numerical experiments show that our ROM is accurate and efficient. Under some assumptions on the problem data, we prove that the convergence…

A classical reduced order model for dynamical problems involves spatial reduction of the problem size. However, temporal reduction accompanied by the spatial reduction can further reduce the problem size without losing accuracy much, which…

Lie groups and their actions are ubiquitous in the description of physical systems, and we explore implications in the setting of model order reduction (MOR). We present a novel framework of MOR via Lie groups, called MORLie, in which…

Lattice-like structures can provide a combination of high stiffness with light weight that is useful in many applications, but a resolved finite element mesh of such structures results in a computationally expensive discretization. This…

In our previous work, a reduced order model (ROM) for a stochastic system was made, where noisy data was projected onto principal component analysis (PCA)-derived basis vectors to obtain an accurate reconstruction of the noise-free data.…