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09/13/2023
A Robust SINDy Approach by Combining Neural Networks and an Integral Form
The discovery of governing equations from data has been an active field ...
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08/26/2023
Deep Learning for Structure-Preserving Universal Stable Koopman-Inspired Embeddings for Nonlinear Canonical Hamiltonian Dynamics
Discovering a suitable coordinate transformation for nonlinear systems e...
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08/26/2023
Guaranteed Stable Quadratic Models and their applications in SINDy and Operator Inference
Scientific machine learning for learning dynamical systems is a powerful...
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08/07/2023
Parameterized Interpolation of Passive Systems
We study the tangential interpolation problem for a passive transfer fun...
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08/04/2023
Linearly Implicit Global Energy Preserving Reduced-order Models for Cubic Hamiltonian Systems
This work discusses the model reduction problem for large-scale multi-sy...
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08/02/2023
Data-Driven Identification of Quadratic Symplectic Representations of Nonlinear Hamiltonian Systems
We present a framework for learning Hamiltonian systems using data. This...
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07/20/2023
Accurate error estimation for model reduction of nonlinear dynamical systems via data-enhanced error closure
Accurate error estimation is crucial in model order reduction, both to o...
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06/30/2023
Towards a Benchmark Framework for Model Order Reduction in the Mathematical Research Data Initiative (MaRDI)
The race for the most efficient, accurate, and universal algorithm in sc...
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06/09/2023
Active-Learning-Driven Surrogate Modeling for Efficient Simulation of Parametric Nonlinear Systems
When repeated evaluations for varying parameter configurations of a high...
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05/10/2023
Parametric Dynamic Mode Decomposition for nonlinear parametric dynamical systems
A non-intrusive model order reduction (MOR) method that combines feature...
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04/27/2023
Structured interpolation for multivariate transfer functions of quadratic-bilinear systems
High-dimensional/high-fidelity nonlinear dynamical systems appear natura...
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02/19/2023
Rank-Minimizing and Structured Model Inference
While extracting information from data with machine learning plays an in...
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02/16/2023
A weighted subspace exponential kernel for support tensor machines
High-dimensional data in the form of tensors are challenging for kernel ...
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01/24/2023
Inference of Continuous Linear Systems from Data with Guaranteed Stability
Machine-learning technologies for learning dynamical systems from data p...
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01/23/2023
Dominant Subspaces of High-Fidelity Nonlinear Structured Parametric Dynamical Systems and Model Reduction
In this work, we investigate a model order reduction scheme for high-fid...
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01/13/2023
Multi-fidelity error estimation accelerates greedy model reduction of complex dynamical systems
Model order reduction usually consists of two stages: the offline stage ...
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11/01/2022
Generalized Quadratic-Embeddings for Nonlinear Dynamics using Deep Learning
The engineering design process (e.g., control and forecasting) relies on...
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09/12/2022
Riccati-feedback Control of a Two-dimensional Two-phase Stefan Problem
We discuss the feedback control problem for a two-dimensional two-phase ...
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06/03/2022
A unifying framework for tangential interpolation of structured bilinear control systems
In this paper, we consider the structure-preserving model order reductio...
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05/19/2022
Neural ODEs with Irregular and Noisy Data
Measurement noise is an integral part while collecting data of a physica...
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03/31/2022
Krylov techniques for low-rank ADI
One of the most computationally expensive steps of the low-rank ADI meth...
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03/16/2022
A Structure-Preserving Divide-and-Conquer Method for Pseudosymmetric Matrices
We devise a spectral divide-and-conquer scheme for matrices that are sel...
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11/25/2021
Learning Low-Dimensional Quadratic-Embeddings of High-Fidelity Nonlinear Dynamics using Deep Learning
Learning dynamical models from data plays a vital role in engineering de...
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11/12/2021
A low-rank solution method for Riccati equations with indefinite quadratic terms
Algebraic Riccati equations with indefinite quadratic terms play an impo...
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10/12/2021
Fast A Posteriori State Error Estimation for Reliable Frequency Sweeping in Microwave Circuits via the Reduced-Basis Method
We develop a compact, reliable model order reduction approach for fast f...
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10/07/2021
Palindromic linearization and numerical solution of nonsymmetric algebraic T-Riccati equations
We identify a relationship between the solutions of a nonsymmetric algeb...
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09/28/2021
Solution decomposition for the nonlinear Poisson-Boltzmann equation using the range-separated tensor format
The Poisson-Boltzmann equation (PBE) is an implicit solvent continuum mo...
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09/23/2021
Learning Dynamics from Noisy Measurements using Deep Learning with a Runge-Kutta Constraint
Measurement noise is an integral part while collecting data of a physica...
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09/13/2021
Learning reduced order models from data for hyperbolic PDEs
Given a set of solution snapshots of a hyperbolic PDE, we are interested...
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08/05/2021
Next-Gen Gas Network Simulation
To overcome many-query optimization, control, or uncertainty quantificat...
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05/11/2021
Discovery of Nonlinear Dynamical Systems using a Runge-Kutta Inspired Dictionary-based Sparse Regression Approach
Discovering dynamical models to describe underlying dynamical behavior i...
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05/02/2021
Data-Driven Model Order Reduction for Problems with Parameter-Dependent Jump-Discontinuities
We propose a data-driven model order reduction (MOR) technique for param...
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04/26/2021
Inf-Sup-Constant-Free State Error Estimator for Model Order Reduction of Parametric Systems in Electromagnetics
A reliable model order reduction process for parametric analysis in elec...
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04/14/2021
Stable and Efficient Computation of Generalized Polar Decompositions
We present methods for computing the generalized polar decomposition of ...
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03/10/2021
A Training Set Subsampling Strategy for the Reduced Basis Method
We present a subsampling strategy for the offline stage of the Reduced B...
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03/03/2021
LQResNet: A Deep Neural Network Architecture for Learning Dynamic Processes
Mathematical modeling is an essential step, for example, to analyze the ...
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02/27/2021
Reduced basis method for the nonlinear Poisson-Boltzmann equation regularized by the range-separated canonical tensor format
The Poisson-Boltzmann equation (PBE) is a fundamental implicit solvent c...
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11/24/2020
Model Order Reduction for Gas and Energy Networks
To counter the volatile nature of renewable energy sources, gas networks...
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11/12/2020
Parallel Algorithms for Tensor Train Arithmetic
We present efficient and scalable parallel algorithms for performing mat...
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10/13/2020
Operator Inference and Physics-Informed Learning of Low-Dimensional Models for Incompressible Flows
Reduced-order modeling has a long tradition in computational fluid dynam...
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10/13/2020
Structure-Preserving Model Reduction for Dissipative Mechanical Systems
Suppressing vibrations in mechanical models, usually described by second...
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10/12/2020
Machine Learning for Material Characterization with an Application for Predicting Mechanical Properties
Currently, the growth of material data from experiments and simulations ...
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09/17/2020
Data-Driven Snapshot Calibration via Monotonic Feature Matching
Snapshot matrices of hyperbolic equations have a slow singular value dec...
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09/03/2020
A rational Even-IRA algorithm for the solution of T-even polynomial eigenvalue problems
In this work we present a rational Krylov subspace method for solving re...
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09/02/2020
Space and Chaos-Expansion Galerkin POD Low-order Discretization of PDEs for Uncertainty Quantification
The quantification of multivariate uncertainties in partial differential...
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08/24/2020
A Low-rank Method for Parameter-dependent Fluid-structure Interaction Discretizations With Hyperelasticity
In aerospace engineering and boat building, fluid-structure interaction ...
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08/20/2020
Efficient and Accurate Algorithms for Solving the Bethe-Salpeter Eigenvalue Problem for Crystalline Systems
Optical properties of materials related to light absorption and scatteri...
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07/28/2020
Data-Driven Learning of Reduced-order Dynamics for a Parametrized Shallow Water Equation
This paper discusses a non-intrusive data-driven model order reduction m...
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07/22/2020
Structure-Preserving Interpolation for Model Reduction of Parametric Bilinear Systems
In this paper, we present an interpolation framework for structure-prese...
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06/11/2020