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Related papers: Minimum Reduced-Order Models via Causal Inference

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In this paper, we consider the problem of causal order discovery within the framework of monotonic Structural Causal Models (SCMs), which have gained attention for their potential to enable causal inference and causal discovery from…

Machine Learning · Computer Science 2024-10-29 Ali Izadi , Martin Ester

We develop an unsupervised machine learning algorithm for the automated discovery and identification of traveling waves in spatio-temporal systems governed by partial differential equations (PDEs). Our method uses sparse regression and…

Computational Physics · Physics 2020-05-20 Ariana Mendible , Steven L. Brunton , Aleksandr Y. Aravkin , Wes Lowrie , J. Nathan Kutz

This paper develops an interpretable, non-intrusive reduced-order modeling technique using regularized kernel interpolation. Existing non-intrusive approaches approximate the dynamics of a reduced-order model (ROM) by solving a data-driven…

Computational Engineering, Finance, and Science · Computer Science 2026-01-26 Alejandro N Diaz , Shane A McQuarrie , John T Tencer , Patrick J Blonigan

We consider the problem of identifying the causal direction between two discrete random variables using observational data. Unlike previous work, we keep the most general functional model but make an assumption on the unobserved exogenous…

Artificial Intelligence · Computer Science 2016-11-16 Murat Kocaoglu , Alexandros G. Dimakis , Sriram Vishwanath , Babak Hassibi

In this document, some general results in approximation theory and matrix analysis with applications to sparse identification of time series models and nonlinear discrete-time dynamical systems are presented. The aforementioned theoretical…

Numerical Analysis · Mathematics 2021-08-04 Fredy Vides

Reduced Order Modeling is of paramount importance for efficiently inferring high-dimensional spatio-temporal fields in parametric contexts, enabling computationally tractable parametric analyses, uncertainty quantification and control.…

Machine Learning · Computer Science 2025-02-18 Matteo Tomasetto , Jan P. Williams , Francesco Braghin , Andrea Manzoni , J. Nathan Kutz

High-fidelity simulations of mixing and combustion processes are generally computationally demanding and time-consuming, hindering their wide application in industrial design and optimization. The present study proposes parametric reduced…

Fluid Dynamics · Physics 2023-08-29 Chenxu Ni , Siyu Ding , Xingjian Wang

Interpolation-based trust-region methods are an important class of algorithms for Derivative-Free Optimization which rely on locally approximating an objective function by quadratic polynomial interpolation models, frequently built from…

Optimization and Control · Mathematics 2013-06-25 Afonso S. Bandeira , Katya Scheinberg , Luis Nunes Vicente

In this paper, we study the system identification problem for sparse linear time-invariant systems. We propose a sparsity promoting block-regularized estimator to identify the dynamics of the system with only a limited number of input-state…

Systems and Control · Computer Science 2018-08-28 Salar Fattahi , Somayeh Sojoudi

Reduced order modeling (ROM) provides an efficient framework to compute solutions of parametric problems. Basically, it exploits a set of precomputed high-fidelity solutions --- computed for properly chosen parameters, using a full-order…

Numerical Analysis · Mathematics 2019-11-19 Nicola Demo , Marco Tezzele , Gianluigi Rozza

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…

Computational Physics · Physics 2020-07-14 Renee Swischuk , Boris Kramer , Cheng Huang , Karen Willcox

The vast majority of reduced-order models (ROMs) first obtain a low dimensional representation of the problem from high-dimensional model (HDM) training data which is afterwards used to obtain a system of reduced complexity. Unfortunately,…

Numerical Analysis · Mathematics 2023-09-14 Victor Zucatti , Matthew J. Zahr

Large-dimensional empirical data in science and engineering frequently have a low-rank structure and can be represented as a combination of just a few eigenmodes. Because of this structure, we can use just a few spatially localized sensor…

Statistical Mechanics · Physics 2025-09-16 Andrei A. Klishin , J. Nathan Kutz , Krithika Manohar

Reduced order modeling methods are often used as a mean to reduce simulation costs in industrial applications. Despite their computational advantages, reduced order models (ROMs) often fail to accurately reproduce complex dynamics…

Inferring the causal direction and causal effect between two discrete random variables X and Y from a finite sample is often a crucial problem and a challenging task. However, if we have access to observational and interventional data, it…

Machine Learning · Statistics 2020-10-16 Peter Gmeiner

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:…

Methodology · Statistics 2017-05-10 Patrick Héas , Cédric Herzet

Reduced order modeling (ROM) techniques are numerical methods that approximate the solution of parametric partial differential equation (PDE) by properly combining the high-fidelity solutions of the problem obtained for several…

Numerical Analysis · Mathematics 2023-08-08 M. Girfoglio , L. Scandurra , F. Ballarin , G. Infantino , F. Nicolò , A. Montalto , G. Rozza , R. Scrofani , M. Comisso , F. Musumeci

Predicting the effect of interventions with many possible variations, e.g., therapeutic content that affects mental health outcomes or an earnings call transcript that drives movement in share price, is useful across several domains.…

Machine Learning · Computer Science 2026-05-27 Nikita Dhawan , Arnav Paruthi , Andrew Kim , Lovedeep Gondara , Jekaterina Novikova , Chris J. Maddison

While data-driven techniques are powerful tools for reduced-order modeling of systems with chaotic dynamics, great potential remains for leveraging known physics (i.e. a full-order model (FOM)) to improve predictive capability. We develop a…

Machine Learning · Computer Science 2025-07-30 Alex Guo , Michael D. Graham

Establishing appropriate mathematical models for complex systems in natural phenomena not only helps deepen our understanding of nature but can also be used for state estimation and prediction. However, the extreme complexity of natural…

Machine Learning · Computer Science 2024-03-27 Cheng Fang , Jinqiao Duan