English
Related papers

Related papers: On the representation of energy-preserving quadrat…

200 papers

Many-query computations, in which a computational model for an engineering system must be evaluated many times, are crucial in design and control. For systems governed by partial differential equations (PDEs), typical high-fidelity…

Numerical Analysis · Mathematics 2024-02-09 Tomoki Koike , Elizabeth Qian

Scientific machine learning for inferring dynamical systems combines data-driven modeling, physics-based modeling, and empirical knowledge. It plays an essential role in engineering design and digital twinning. In this work, we primarily…

Machine Learning · Computer Science 2024-01-09 Pawan Goyal , Igor Pontes Duff , Peter Benner

This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models. The key ingredient of the approach…

Numerical Analysis · Mathematics 2022-12-29 Rudy Geelen , Stephen Wright , Karen Willcox

We propose neural network operator inference (NN-OpInf): a structure-preserving, composable, and minimally restrictive operator inference framework for the non-intrusive reduced-order modeling of dynamical systems. The approach learns…

Machine Learning · Computer Science 2026-03-10 Eric Parish , Anthony Gruber , Patrick Blonigan , Irina Tezaur

This work explores the physics-driven machine learning technique Operator Inference (OpInf) for predicting the state of chaotic dynamical systems. OpInf provides a non-intrusive approach to infer approximations of polynomial operators in…

In this paper, we develop a novel class of linear energy-preserving integrating factor methods for the 2D nonlinear Schr\"odinger equation with wave operator (NLSW), combining the scalar auxiliary variable approach and the integrating…

Numerical Analysis · Mathematics 2022-09-27 Xuelong Gu , Wenjun Cai , Chaolong Jiang , Yushun Wang

This work develops a non-intrusive, data-driven surrogate modeling framework based on Operator Inference (OpInf) for rapidly solving parameter-dependent matrix equations in many-query settings. Motivated by the requirements of the OpInf…

Numerical Analysis · Mathematics 2025-11-21 Xuelian Wen , Qiuqi Li , Juan Zhang

This work formulates a new approach to reduced modeling of parameterized, time-dependent partial differential equations (PDEs). The method employs Operator Inference, a scientific machine learning framework combining data-driven learning…

Computational Engineering, Finance, and Science · Computer Science 2025-06-16 Shane A McQuarrie , Parisa Khodabakhshi , Karen E Willcox

Mechanical systems are often characterized only by their response to certain loads known from experiments or simulations. The obtained data can be used for various purposes: system analysis, design of mathematical models, or construction of…

Dynamical Systems · Mathematics 2026-01-05 Yevgeniya Filanova , Igor Pontes Duff , Pawan Goyal , Peter Benner

Existing model reduction techniques for high-dimensional models of conservative partial differential equations (PDEs) encounter computational bottlenecks when dealing with systems featuring non-polynomial nonlinearities. This work presents…

Numerical Analysis · Mathematics 2025-10-21 Harsh Sharma , Juan Diego Draxl Giannoni , Boris Kramer

Numerical simulations of complex multiphysics systems, such as char combustion considered herein, yield numerous state variables that inherently exhibit physical constraints. This paper presents a new approach to augment Operator Inference…

Computational Physics · Physics 2026-05-15 Hyeonghun Kim , Boris Kramer

Operator inference learns low-dimensional dynamical-system models with polynomial nonlinear terms from trajectories of high-dimensional physical systems (non-intrusive model reduction). This work focuses on the large class of physical…

Numerical Analysis · Mathematics 2021-07-07 Nihar Sawant , Boris Kramer , Benjamin Peherstorfer

We present a new scientific machine learning method that learns from data a computationally inexpensive surrogate model for predicting the evolution of a system governed by a time-dependent nonlinear partial differential equation (PDE), an…

Numerical Analysis · Mathematics 2022-02-28 Elizabeth Qian , Ionut-Gabriel Farcas , Karen Willcox

Recently, a whole class of evergy-preserving integrators has been derived for the numerical solution of Hamiltonian problems. In the mainstream of this research, we have defined a new family of symplectic integrators depending on a real…

Numerical Analysis · Mathematics 2010-09-30 Luigi Brugnano , Felice Iavernaro , Donato Trigiante

This paper investigates convex quadratic optimization problems involving $n$ indicator variables, each associated with a continuous variable, particularly focusing on scenarios where the matrix $Q$ defining the quadratic term is positive…

Optimization and Control · Mathematics 2024-04-15 Aaresh Bhathena , Salar Fattahi , Andrés Gómez , Simge Küçükyavuz

This paper presents a data-driven, nested Operator Inference (OpInf) approach for learning physics-informed reduced-order models (ROMs) from snapshot data of high-dimensional dynamical systems. The approach exploits the inherent hierarchy…

Machine Learning · Computer Science 2025-08-18 Nicole Aretz , Karen Willcox

Thus far, sparse representations have been exploited largely in the context of robustly estimating functions in a noisy environment from a few measurements. In this context, the existence of a basis in which the signal class under…

Data Structures and Algorithms · Computer Science 2009-06-26 Mohamed-Ali Belabbas , Patrick J. Wolfe

This paper derives predictive reduced-order models for rocket engine combustion dynamics via Operator Inference, a scientific machine learning approach that blends data-driven learning with physics-based modeling. The non-intrusive nature…

Computational Engineering, Finance, and Science · Computer Science 2021-10-19 Shane A. McQuarrie , Cheng Huang , Karen E. Willcox

In this paper, we investigate projection-based intrusive and data-driven non-intrusive model order reduction methods in numerical simulation of rotating thermal shallow water equation (RTSWE) in parametric and non-parametric form.…

Numerical Analysis · Mathematics 2023-07-19 Süleyman Yıldız , Murat Uzunca , Bülent Karasözen

Hamiltonian Operator Inference has been introduced in [Sharma, H., Wang, Z., Kramer, B., Physica D: Nonlinear Phenomena, 431, p.133122, 2022] to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. This approach…

Numerical Analysis · Mathematics 2024-05-10 Yuwei Geng , Jasdeep Singh , Lili Ju , Boris Kramer , Zhu Wang
‹ Prev 1 2 3 10 Next ›