Related papers: Online adaptive basis construction for nonlinear m…
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…
To balance the quality and inference cost of a Foundation Model (FM, such as large language models (LLMs)) powered software, people often opt to train a routing model that routes requests to FMs with different sizes and capabilities.…
We introduce a transformation framework that can be utilized to develop online algorithms with low $\epsilon$-approximate regret in the random-order model from offline approximation algorithms. We first give a general reduction theorem that…
In this work, the dual-weighted residual (DWR) method is applied to obtain a certified incremental proper orthogonal decomposition (POD) based reduced order model. A novel approach called MORe DWR (Model Order Rduction with Dual-Weighted…
Nonlinear aeroelastic reduced-order models (ROMs) based on machine learning or artificial intelligence algorithms can be complex and computationally demanding to train, meaning that for practical aeroelastic applications, the conservative…
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…
Overparameterized models have recently challenged conventional learning theory by exhibiting improved generalization beyond the interpolation limit, a phenomenon known as benign overfitting. This work introduces Adaptive Benign Overfitting…
We initiate the study of numerical linear algebra in the sliding window model, where only the most recent $W$ updates in a stream form the underlying data set. We first introduce a unified row-sampling based framework that gives randomized…
We investigate an optimization problem governed by an elliptic partial differential equation with uncertain parameters. We introduce a robust optimization framework that accounts for uncertain model parameters. The resulting non-linear…
In this paper, we propose a novel online optimization algorithm built by combining ideas from control theory and system identification. The foundation of our algorithm is a control-based design that makes use of the internal model of the…
e consider the experimental design problem in an online environment, an important practical task for reducing the variance of estimates in randomized experiments which allows for greater precision, and in turn, improved decision making. In…
We investigate boosted online regression and propose a novel family of regression algorithms with strong theoretical bounds. In addition, we implement several variants of the proposed generic algorithm. We specifically provide theoretical…
Nonlinear parametric inverse problems appear in many applications and are typically very expensive to solve, especially if they involve many measurements. These problems pose huge computational challenges as evaluating the objective…
In many applications, retrieval-augmented generation (RAG) drives tool use and function calling by embedding the (user) queries and matching them to pre-specified tool/function descriptions. In this paper, we address an embedding…
This work develops an active learning framework to intelligently enrich data-driven reduced-order models (ROMs) of parametric dynamical systems, which can serve as the foundation of virtual assets in a digital twin. Data-driven ROMs are…
Finite element model updating is a mature discipline for linear structures, yet its extension to nonlinear regimes remains an open challenge. This paper presents a methodology that combines nonlinear model order reduction (NMOR) based on…
Low-rank representation~(LRR) has been a significant method for segmenting data that are generated from a union of subspaces. It is, however, known that solving the LRR program is challenging in terms of time complexity and memory…
Slip is a very common phenomena present in wheeled mobile robotic systems. It has undesirable consequences such as wasting energy and impeding system stability. To tackle the challenge of mobile robot trajectory tracking under slippery…
We study unconstrained Online Linear Optimization with Lipschitz losses. Motivated by the pursuit of instance optimality, we propose a new algorithm that simultaneously achieves ($i$) the AdaGrad-style second order gradient adaptivity; and…
In this paper we extend the hierarchical model reduction framework based on reduced basis techniques for the application to nonlinear partial differential equations. The major new ingredient to accomplish this goal is the introduction of…