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Dynamic mode decomposition (DMD) is a powerful data-driven technique for construction of reduced-order models of complex dynamical systems. Multiple numerical tests have demonstrated the accuracy and efficiency of DMD, but mostly for…

Numerical Analysis · Mathematics 2021-07-28 Hannah Lu , Daniel M. Tartakovsky

The fast simulation of dynamical systems is a key challenge in many scientific and engineering applications, such as weather forecasting, disease control, and drug discovery. With the recent success of deep learning, there is increasing…

Machine Learning · Computer Science 2024-10-02 Zezheng Song , Jiaxin Yuan , Haizhao Yang

There have been growing interests in leveraging experimental measurements to discover the underlying partial differential equations (PDEs) that govern complex physical phenomena. Although past research attempts have achieved great success…

Machine Learning · Computer Science 2023-05-23 Chengping Rao , Pu Ren , Yang Liu , Hao Sun

The discovery of Partial Differential Equations (PDEs) is an essential task for applied science and engineering. However, data-driven discovery of PDEs is generally challenging, primarily stemming from the sensitivity of the discovered…

Machine Learning · Statistics 2024-03-27 Aoxue Chen , Yifan Du , Liyao Mars Gao , Guang Lin

The modern machine learning methods allow one to obtain the data-driven models in various ways. However, the more complex the model is, the harder it is to interpret. In the paper, we describe the algorithm for the mathematical equations…

Neural and Evolutionary Computing · Computer Science 2021-09-09 Alexander Hvatov , Mikhail Maslyaev

Ordinary and partial differential equations (ODEs/PDEs) play a paramount role in analyzing and simulating complex dynamic processes across all corners of science and engineering. In recent years machine learning tools are aspiring to…

Machine Learning · Computer Science 2021-06-11 Sifan Wang , Paris Perdikaris

Augmenting mechanistic ordinary differential equation (ODE) models with machine-learnable structures is an novel approach to create highly accurate, low-dimensional models of engineering systems incorporating both expert knowledge and…

Dynamical Systems · Mathematics 2022-06-22 Sandor Beregi , David A. W. Barton , Djamel Rezgui , Simon A. Neild

Physical attacks against object detection have gained increasing attention due to their significant practical implications. However, conducting physical experiments is extremely time-consuming and labor-intensive. Moreover, physical…

Computer Vision and Pattern Recognition · Computer Science 2025-06-03 Jiawei Lian , Jianhong Pan , Lefan Wang , Yi Wang , Lap-Pui Chau , Shaohui Mei

In this work, we present a method which determines optimal multi-step dynamic mode decomposition (DMD) models via entropic regression, which is a nonlinear information flow detection algorithm. Motivated by the higher-order DMD (HODMD)…

Machine Learning · Statistics 2024-06-19 Christopher W. Curtis , Erik Bollt , Daniel Jay Alford-Lago

Multi-dimensional breakage is a ubiquitous phenomenon in natural systems, yet the systematic discovery of underlying governing equations remains a long-standing challenge. Current inverse solution techniques are restricted to…

Computational Engineering, Finance, and Science · Computer Science 2025-08-20 Suet Lin Leong , Firnaaz Ahamed , Yong Kuen Ho

Data-driven methods have recently made great progress in the discovery of partial differential equations (PDEs) from spatial-temporal data. However, several challenges remain to be solved, including sparse noisy data, incomplete candidate…

Computational Physics · Physics 2021-09-28 Hao Xu , Dongxiao Zhang , Junsheng Zeng

Anomaly detection in multivariate time series is essential across domains such as healthcare, cybersecurity, and industrial monitoring, yet remains fundamentally challenging due to high-dimensional dependencies, the presence of…

Machine Learning · Computer Science 2026-02-10 Xiaona Zhou , Constantin Brif , Ismini Lourentzou

Evaluating large language models (LLMs) today rests on fixed benchmarks that apply the same set of items to any model, producing ceiling and floor effects that mask capability gaps. We argue that the most informative evaluation signal lies…

Artificial Intelligence · Computer Science 2026-05-27 Haoxiang Wang , Da Yu , Huishuai Zhang

As large language models continue to advance, their application in educational contexts remains underexplored and under-optimized. In this paper, we address this gap by introducing the first diverse benchmark tailored for educational…

Computation and Language · Computer Science 2026-01-07 Bin Xu , Yu Bai , Huashan Sun , Yiguan Lin , Siming Liu , Xinyue Liang , Yaolin Li , Zhuangzhi Dong , Jingren Zhang , Yufan Deng , Xinyu Zou , Yang Gao , Heyan Huang

This paper presents a machine learning framework for Bayesian systems identification from noisy, sparse and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of recent developments in differentiable…

Machine Learning · Computer Science 2020-04-21 Yibo Yang , Mohamed Aziz Bhouri , Paris Perdikaris

The estimation of static parameters in dynamical systems and control theory has been extensively studied, with significant progress made in estimating varying parameters in specific system types. Suppose, in the general case, we have data…

Optimization and Control · Mathematics 2025-07-10 Jamiree Harrison , Enoch Yeung

The dynamic mode decomposition (DMD) is a data-driven method used for identifying the dynamics of complex nonlinear systems. It extracts important characteristics of the underlying dynamics using measured time-domain data produced either by…

Numerical Analysis · Mathematics 2020-11-24 Ion Victor Gosea , Igor Pontes Duff

Dynamical systems are essential to model various phenomena in physics, finance, economics, and are also of current interest in machine learning. A central modeling task is investigating parameter sensitivity, whether tuning atmospheric…

Numerical Analysis · Mathematics 2026-01-14 Rishi Leburu , Levon Nurbekyan , Lars Ruthotto

The data-driven models allow one to define the model structure in cases when a priori information is not sufficient to build other types of models. The possible way to obtain physical interpretation is the data-driven differential equation…

Neural and Evolutionary Computing · Computer Science 2019-06-11 Michail Maslyaev , Alexander Hvatov , Anna Kalyuzhnaya

Existing benchmarks for analytical database systems such as TPC-DS and TPC-H are designed for static reporting scenarios. The main metric of these benchmarks is the performance of running individual SQL queries over a synthetic database. In…

Databases · Computer Science 2018-04-10 Philipp Eichmann , Carsten Binnig , Tim Kraska , Emanuel Zgraggen