no code implementations • 1 Mar 2024 • Igor Pontes Duff, Pawan Goyal, Peter Benner
To this aim, we investigate the stability characteristics of control systems with energy-preserving nonlinearities, thereby identifying conditions under which such systems are bounded-input bounded-state stable.
no code implementations • 27 Feb 2024 • Ion Victor Gosea, Luisa Peterson, Pawan Goyal, Jens Bremer, Kai Sundmacher, Peter Benner
In this work, we address the challenge of efficiently modeling dynamical systems in process engineering.
no code implementations • 13 Sep 2023 • Ali Forootani, Pawan Goyal, Peter Benner
To do this, we make use of neural networks to learn an implicit representation based on measurement data so that not only it produces the output in the vicinity of the measurements but also the time-evolution of output can be described by a dynamical system.
no code implementations • 26 Aug 2023 • Pawan Goyal, Igor Pontes Duff, Peter Benner
In this work, we propose inference formulations to learn quadratic models, which are stable by design.
no code implementations • 26 Aug 2023 • Pawan Goyal, Süleyman Yıldız, Peter Benner
We demonstrate the capabilities of deep learning in acquiring compact symplectic coordinate transformation and the corresponding simple dynamical models, fostering data-driven learning of nonlinear canonical Hamiltonian systems, even those with continuous spectra.
no code implementations • 2 Aug 2023 • Süleyman Yıldız, Pawan Goyal, Thomas Bendokat, Peter Benner
By leveraging this, we obtain quadratic dynamics that are Hamiltonian in a transformed coordinate system.
no code implementations • 9 Jun 2023 • Harshit Kapadia, Lihong Feng, Peter Benner
When repeated evaluations for varying parameter configurations of a high-fidelity physical model are required, surrogate modeling techniques based on model order reduction are desired.
no code implementations • 1 Jun 2023 • Jingjing Zhang, Jan Heiland, Peter Benner, Xin Du
We show that our FDSC scheme is capable to approximate the solid in-band performance while maintaining acceptable out-of-band performance with regard to global time horizons as well as localized time horizons.
no code implementations • 19 Feb 2023 • Pawan Goyal, Benjamin Peherstorfer, Peter Benner
While extracting information from data with machine learning plays an increasingly important role, physical laws and other first principles continue to provide critical insights about systems and processes of interest in science and engineering.
no code implementations • 16 Feb 2023 • Kirandeep Kour, Sergey Dolgov, Peter Benner, Martin Stoll, Max Pfeffer
High-dimensional data in the form of tensors are challenging for kernel classification methods.
no code implementations • 24 Jan 2023 • Pawan Goyal, Igor Pontes Duff, Peter Benner
Machine-learning technologies for learning dynamical systems from data play an important role in engineering design.
no code implementations • 1 Nov 2022 • Pawan Goyal, Peter Benner
To simplify this task, we aim to identify a coordinate transformation that allows us to represent the dynamics of nonlinear systems using a common, simple model structure.
no code implementations • 19 May 2022 • Pawan Goyal, Peter Benner
In our methodology, the main innovation can be seen in the integration of deep neural networks with the neural ordinary differential equations (ODEs) approach.
no code implementations • 25 Nov 2021 • Pawan Goyal, Peter Benner
It is, however, observed that the dynamics of high-fidelity models often evolve in low-dimensional manifolds.
no code implementations • NeurIPS Workshop DLDE 2021 • Pawan Goyal, Peter Benner
We demonstrate the effectiveness of the proposed method to learning models using data obtained from various differential equations.
no code implementations • 27 Jul 2021 • Karim Cherifi, Pawan Goyal, Peter Benner
Mathematical models are essential to analyze and understand the dynamics of complex systems.
2 code implementations • 11 May 2021 • Pawan Goyal, Peter Benner
Discovering dynamical models to describe underlying dynamical behavior is essential to draw decisive conclusions and engineering studies, e. g., optimizing a process.
no code implementations • 10 Mar 2021 • Sridhar Chellappa, Lihong Feng, Peter Benner
Then, for the available low-fidelity snapshots of the output variable, we apply the pivoted QR decomposition or the discrete empirical interpolation method to identify a set of sparse sampling locations in the parameter domain.
Numerical Analysis Numerical Analysis
1 code implementation • 3 Mar 2021 • Pawan Goyal, Peter Benner
In this work, we suggest combining the operator inference with certain deep neural network approaches to infer the unknown nonlinear dynamics of the system.
1 code implementation • 13 Oct 2020 • Peter Benner, Pawan Goyal, Jan Heiland, Igor Pontes Duff
To that end, we utilize the intrinsic structure of the Navier-Stokes equations for incompressible flows and show that learning dynamics of the velocity and pressure can be decoupled, thus leading to an efficient operator inference approach for learning the underlying dynamics of incompressible flows.
no code implementations • 12 Oct 2020 • Anke Stoll, Peter Benner
This study also gives an application of machine learning methods on small punch test data for the determination of the property ultimate tensile strength for various materials.
1 code implementation • 28 Jul 2020 • Süleyman Yıldız, Pawan Goyal, Peter Benner, Bülent Karasözen
This paper discusses a non-intrusive data-driven model order reduction method that learns low-dimensional dynamical models for a parametrized shallow water equation.
Numerical Analysis Numerical Analysis
no code implementations • 12 Mar 2020 • Pawan Goyal, Hussam Al Daas, Peter Benner
In this work, we propose a new problem formulation in such a way that we seek to recover an image that is of low-rank and has sparsity in a transformed domain.
1 code implementation • 22 Feb 2020 • Peter Benner, Pawan Goyal, Boris Kramer, Benjamin Peherstorfer, Karen Willcox
The proposed method learns operators for the linear and polynomially nonlinear dynamics via a least-squares problem, where the given non-polynomial terms are incorporated in the right-hand side.
1 code implementation • 12 Feb 2020 • Kirandeep Kour, Sergey Dolgov, Martin Stoll, Peter Benner
An increasing amount of collected data are high-dimensional multi-way arrays (tensors), and it is crucial for efficient learning algorithms to exploit this tensorial structure as much as possible.
2 code implementations • 9 Dec 2019 • Peter Benner, Claudia Draxl, Andreas Marek, Carolin Penke, Christian Vorwerk
Our method is freely available in the current release of the ELPA library.
Numerical Analysis Data Structures and Algorithms Mathematical Software Numerical Analysis 65Y05, 15B57 G.1.3; G.4
1 code implementation • 31 Oct 2019 • Peter Benner, Pawan Goyal, Paul Van Dooren
In this paper, we study the identification problem of a passive system from tangential interpolation data.
no code implementations • 20 Nov 2018 • Maximilian Behr, Peter Benner, Jan Heiland
The differential Sylvester equation and its symmetric version, the differential Lyapunov equation, appear in different fields of applied mathematics like control theory, system theory, and model order reduction.
Numerical Analysis 15A24, 65F60, 65L05
1 code implementation • 21 Sep 2018 • Peter Benner, Christian Himpe
A standard approach for model reduction of linear input-output systems is balanced truncation, which is based on the controllability and observability properties of the underlying system.
Optimization and Control Systems and Control Numerical Analysis 93A15, 93B11, 93B20