English
Related papers

Related papers: Online adaptive basis construction for nonlinear m…

200 papers

We consider a framework for the construction of iterative schemes for operator equations that combine low-rank approximation in tensor formats and adaptive approximation in a basis. Under fairly general assumptions, we obtain a rigorous…

Numerical Analysis · Mathematics 2014-03-17 Markus Bachmayr , Wolfgang Dahmen

Offline model-based optimization (MBO) seeks to discover high-performing designs using only a fixed dataset of past evaluations. Most existing methods rely on learning a surrogate model via regression and implicitly assume that good…

Machine Learning · Computer Science 2026-03-05 Shen-Huan Lyu , Rong-Xi Tan , Ke Xue , Yi-Xiao He , Yu Huang , Qingfu Zhang , Chao Qian

In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in…

Numerical Analysis · Mathematics 2024-06-07 Anna Ivagnes , Giovanni Stabile , Gianluigi Rozza

In this work, we develop reduced order models (ROMs) to predict solutions to a multiscale kinetic transport equation with a diffusion limit under the parametric setting. When the underlying scattering effect is not sufficiently strong, the…

Numerical Analysis · Mathematics 2025-05-14 Tianyu Jin , Zhichao Peng , Yang Xiang

In this paper, we focus on the reduced basis methodology in the context of non-linear non-affinely parametrized partial differential equations in which affine decomposition necessary for the reduced basis methodology are not obtained [4,…

Analysis of PDEs · Mathematics 2015-04-24 Cécile Daversin , Christophe Prud'Homme

A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…

Computational Physics · Physics 2015-12-02 Martin Servin , Da Wang

We study the problem of system identification and adaptive control in partially observable linear dynamical systems. Adaptive and closed-loop system identification is a challenging problem due to correlations introduced in data collection.…

Machine Learning · Computer Science 2020-06-25 Sahin Lale , Kamyar Azizzadenesheli , Babak Hassibi , Anima Anandkumar

The paper investigates the problem of estimating the state of a time-varying system with a linear measurement model; in particular, the paper considers the case where the number of measurements available can be smaller than the number of…

Systems and Control · Electrical Eng. & Systems 2021-04-07 Guido Cavraro , Emiliano Dall'Anese , Joshua Comden , Andrey Bernstein

The reduced basis method (RBM) empowers repeated and rapid evaluation of parametrized partial differential equations through an offline-online decomposition, a.k.a. a learning-execution process. A key feature of the method is a greedy…

Numerical Analysis · Mathematics 2020-09-16 Jiahua Jiang , Yanlai Chen

This paper presents a two-stage online algorithm for recovery of low-rank parameter matrix in non-stationary stochastic systems. The first stage applies the recursive least squares (RLS) estimator combined with its singular value…

Systems and Control · Electrical Eng. & Systems 2025-06-25 Yanxin Fu , Junbao Zhou , Yu Hu , Wenxiao Zhao

The emerging field of learning-augmented online algorithms uses ML techniques to predict future input parameters and thereby improve the performance of online algorithms. Since these parameters are, in general, real-valued functions, a…

Machine Learning · Computer Science 2022-05-26 Keerti Anand , Rong Ge , Amit Kumar , Debmalya Panigrahi

Solving complex partial differential equations is vital in the physical sciences, but often requires computationally expensive numerical methods. Reduced-order models (ROMs) address this by exploiting dimensionality reduction to create fast…

Machine Learning · Computer Science 2025-09-11 Robert Stephany , Youngsoo Choi

Non-stationary online learning has drawn much attention in recent years. In particular, dynamic regret and adaptive regret are proposed as two principled performance measures for online convex optimization in non-stationary environments. To…

Machine Learning · Computer Science 2025-09-10 Peng Zhao , Yan-Feng Xie , Lijun Zhang , Zhi-Hua Zhou

Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…

Machine Learning · Computer Science 2026-01-16 Andrew F. Ilersich , Kevin Course , Prasanth B. Nair

This work proposes a technique for constructing a statistical closure model for reduced-order models (ROMs) applied to stationary systems modeled as parameterized systems of algebraic equations. The proposed technique extends the…

Numerical Analysis · Mathematics 2024-12-20 Stefano Pagani , Andrea Manzoni , Kevin Carlberg

Dynamical systems, for instance in model predictive control, often contain unknown parameters, which must be determined during system operation. Online or on-the-fly parameter identification methods are therefore necessary. The challenge of…

Optimization and Control · Mathematics 2021-04-05 Barbara Kaltenbacher , Tram Thi Ngoc Nguyen

This work addresses inverse linear optimization where the goal is to infer the unknown cost vector of a linear program. Specifically, we consider the data-driven setting in which the available data are noisy observations of optimal…

Optimization and Control · Mathematics 2021-12-07 Rishabh Gupta , Qi Zhang

Model order reduction techniques simplify high-dimensional dynamical systems by deriving lower-dimensional models that retain essential system characteristics. These techniques are crucial for the controller design of complex systems while…

Systems and Control · Electrical Eng. & Systems 2026-03-18 Behrad Samari , Henrik Sandberg , Karl H. Johansson , Abolfazl Lavaei

When data is collected in an adaptive manner, even simple methods like ordinary least squares can exhibit non-normal asymptotic behavior. As an undesirable consequence, hypothesis tests and confidence intervals based on asymptotic normality…

Statistics Theory · Mathematics 2023-03-23 Koulik Khamaru , Yash Deshpande , Tor Lattimore , Lester Mackey , Martin J. Wainwright

Data-driven black-box model-based optimization (MBO) problems arise in a great number of practical application scenarios, where the goal is to find a design over the whole space maximizing a black-box target function based on a static…

Machine Learning · Computer Science 2023-10-20 Mingcheng Chen , Haoran Zhao , Yuxiang Zhao , Hulei Fan , Hongqiao Gao , Yong Yu , Zheng Tian