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Found 29 papers, 9 papers with code
Stability-Certified Learning of Control Systems with Quadratic Nonlinearities
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.
Learning reduced-order Quadratic-Linear models in Process Engineering using Operator Inference
In this work, we address the challenge of efficiently modeling dynamical systems in process engineering.
A Robust SINDy Approach by Combining Neural Networks and an Integral Form
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.
Deep Learning for Structure-Preserving Universal Stable Koopman-Inspired Embeddings for Nonlinear Canonical Hamiltonian Dynamics
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.
Guaranteed Stable Quadratic Models and their applications in SINDy and Operator Inference
In this work, we propose inference formulations to learn quadratic models, which are stable by design.
Data-Driven Identification of Quadratic Representations for Nonlinear Hamiltonian Systems using Weakly Symplectic Liftings
By leveraging this, we obtain quadratic dynamics that are Hamiltonian in a transformed coordinate system.
Active-Learning-Driven Surrogate Modeling for Efficient Simulation of Parametric Nonlinear Systems
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.
Frequency-dependent Switching Control for Disturbance Attenuation of Linear Systems
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.
Rank-Minimizing and Structured Model Inference
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.
A weighted subspace exponential kernel for support tensor machines
High-dimensional data in the form of tensors are challenging for kernel classification methods.
Inference of Continuous Linear Systems from Data with Guaranteed Stability
Machine-learning technologies for learning dynamical systems from data play an important role in engineering design.
Generalized Quadratic Embeddings for Nonlinear Dynamics using Deep Learning
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.
Neural ODEs with Irregular and Noisy Data
In our methodology, the main innovation can be seen in the integration of deep neural networks with the neural ordinary differential equations (ODEs) approach.
Learning Low-Dimensional Quadratic-Embeddings of High-Fidelity Nonlinear Dynamics using Deep Learning
It is, however, observed that the dynamics of high-fidelity models often evolve in low-dimensional manifolds.
Learning Dynamics from Noisy Measurements using Deep Learning with a Runge-Kutta Constraint
We demonstrate the effectiveness of the proposed method to learning models using data obtained from various differential equations.
A Greedy Data Collection Scheme For Linear Dynamical Systems
Mathematical models are essential to analyze and understand the dynamics of complex systems.
Discovery of Nonlinear Dynamical Systems using a Runge-Kutta Inspired Dictionary-based Sparse Regression Approach
Discovering dynamical models to describe underlying dynamical behavior is essential to draw decisive conclusions and engineering studies, e. g., optimizing a process.
A Training Set Subsampling Strategy for the Reduced Basis Method
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
LQResNet: A Deep Neural Network Architecture for Learning Dynamic Processes
In this work, we suggest combining the operator inference with certain deep neural network approaches to infer the unknown nonlinear dynamics of the system.
Operator Inference and Physics-Informed Learning of Low-Dimensional Models for Incompressible Flows
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.
Machine Learning for Material Characterization with an Application for Predicting Mechanical Properties
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.
Data-Driven Learning of Reduced-order Dynamics for a Parametrized Shallow Water Equation
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
Low-Rank and Total Variation Regularization and Its Application to Image Recovery
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.
Operator inference for non-intrusive model reduction of systems with non-polynomial nonlinear terms
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.
Efficient Structure-preserving Support Tensor Train Machine
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.
High Performance Solution of Skew-symmetric Eigenvalue Problems with Applications in Solving the Bethe-Salpeter Eigenvalue Problem
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
Identification of Port-Hamiltonian Systems from Frequency Response Data
In this paper, we study the identification problem of a passive system from tangential interpolation data.
Solution Formulas for Differential Sylvester and Lyapunov Equations
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
Cross-Gramian-Based Dominant Subspaces
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
