A5022294841- Model Reduction and Neural Networks
- Numerical methods for differential equations
- Advanced Numerical Methods in Computational Mathematics
- Real-time simulation and control systems
- Neural Networks and Applications
- Electric Power System Optimization
- Dynamics and Control of Mechanical Systems
- Numerical methods in engineering
- Electromagnetic Simulation and Numerical Methods
- Robotic Mechanisms and Dynamics
- Control Systems and Identification
- Climate Change Policy and Economics
- Stellar, planetary, and galactic studies
- Geological formations and processes
- Metallurgy and Material Forming
- Time Series Analysis and Forecasting
- Capital Investment and Risk Analysis
- Inertial Sensor and Navigation
- Control and Stability of Dynamical Systems
- Advanced Mathematical Modeling in Engineering
- Smart Grid Energy Management
- Advanced Thermodynamics and Statistical Mechanics
- Power System Optimization and Stability
- Fatigue and fracture mechanics
- Hydraulic and Pneumatic Systems
University of Twente
2022-2024
Cornell University
2019-2022
Helmholtz-Institute Ulm
2017
University of Duisburg-Essen
2015
.Classical model reduction techniques project the governing equations onto linear subspaces of high-dimensional state-space. For problems with slowly decaying Kolmogorov- \(n\) -widths such as certain transport-dominated problems, however, classical linear-subspace reduced-order models (ROMs) low dimension might yield inaccurate results. Thus, concept ROMs has to be extended more general concepts, like order teduction (MOR) on manifolds. Moreover, we are dealing Hamiltonian systems, it is...
Abstract As an extension of (Progress in industrial mathematics at ECMI 2018, pp. 469–475, 2019), this paper is concerned with a new mathematical model for intraday electricity trading involving both renewable and conventional generation. The allows to incorporate market data e.g. half-spread immediate price impact. optimal generation strategy agent derived as the viscosity solution second-order Hamilton–Jacobi–Bellman (HJB) equation which no closed-form can be given. We construct numerical...
In this paper, we consider model order reduction (MOR) methods for problems with slowly decaying Kolmogorov $n$-widths as, e.g., certain wave-like or transport-dominated problems. To overcome barrier within MOR, nonlinear projections are used, which often realized numerically using autoencoders. These autoencoders generally consist of a encoder and decoder involve costly training the hyperparameters to obtain good approximation quality reduced system. facilitate process, show that extending...
The retreat of alpine glaciers impacts and intensifies geomorphological processes in proglacial zones, driven by increased sediment availability altered hydrological regimes. These dynamic systems transfer from glacial sources to downstream fluvial networks, profoundly influencing flux morphology. This study investigates dynamics within gravel plains the Jamtal Valley (Tyrol, Austria), focusing on DEM difference (DoD) analysis combined with grain size distribution (GSD) mapping as key tools...
Using nonlinear projections and preserving structure in model order reduction (MOR) are currently active research fields. In this paper, we provide a novel differential geometric framework for on smooth manifolds, which emphasizes the nature of objects involved. The crucial ingredient is construction an embedding low-dimensional submanifold compatible map, discuss several options. Our general allows capturing generalizing existing MOR techniques, such as preservation Lagrangian- or...
Summary In this contribution we introduce a novel space‐time formulation for non‐linear elasticity, able to calculate large deformations and displacements with high efficiency using structured unstructured meshes in the cylinder without changing required regularity thus, enabling use of Lagrangian shape functions including tetrahedron hypertetrahedron or tesseract elements. The common indiscriminate treatment spatial temporal directions allows us remove one major bottlenecks parallel...
In this contribution, we derive an a posteriori error estimator for the second-order wave equation motivated by energy-based priori estimates Bernardi and Süli ["Time Space Adaptivity Second-order Wave Equation." Mathematical Models Methods in Applied Sciences 15 (2): 199–225]. This estimate (which is valid general discretisations) then used to POD-Greedy reduced basis approach parameterised equation. The quantitative performance of online-efficient shown illustrative example, keeping mind...
For projection-based linear-subspace model order reduction (MOR), it is well known that the Kolmogorov n-width describes best-possible error for a reduced (ROM) of size n. In this paper, we provide approximation bounds ROMs on polynomially mapped manifolds. particular, show depend polynomial degree p mapping function as linear underlying problem. This results in (n,p)-width, which lower bound ROM manifolds and
We consider variational inequalities with different trial and test spaces a possibly noncoercive bilinear form. Well-posedness is shown under general conditions that are, e.g., valid for the space-time formulation of parabolic inequalities. Moreover, we prove an estimate error Petrov--Galerkin approximation in terms residual. For arising independent final time.
In the construction of a stellarator, manufacturing and assembling coil system is dominant cost. These coils need to satisfy strict engineering tolerances, if those are not met project could be canceled as in case National Compact Stellarator Experiment (NCSX) [25]. Therefore, our goal find configurations that increase tolerances without compromising performance magnetic field. this paper, we develop gradient-based stochastic optimization model which seeks robust stellarator high dimensions....
Symplectic model order reduction is a structure-preserving technique for Hamiltonian systems. Apart from theoretical results like the preservation of stability, it has been demonstrated to give improved numerical compared classical MOR techniques. A key element in this procedure choice good symplectic reduced basis (ROB). In our work, we introduce so-called canonizable systems energy coordinates. For such with assumption periodic solution, derive globally optimal ROB sense proper...
Abstract In this contribution, we apply space-time formulation on constrained rigid body dynamics. particular, discretize directly Hamilton’s principle using appropriate approximation spaces for the variational problem. Moreover, make use of a rotationless bodies, and thus have to define Lagrange multipliers as well. Livens’ principle, introducing independent quantities position, velocity, momentum, where latter can be considered multipliers, concept formulation. Finally, demonstrate...
We consider variational inequalities with different trial and test spaces a possibly noncoercive bilinear form. Well-posedness has been shown under general conditions that are e.g. valid for the space-time formulation of parabolic inequalities. Fine discretizations such problems resolve in large scale thus long computing times. To reduce size these problems, we use Reduced Basis Method (RBM). Combining RBM formulation, residual based error estimator derived [Glas Urban (2014)]. In this...
For projection-based linear-subspace model order reduction (MOR), it is well known that the Kolmogorov n-width describes best-possible error for a reduced (ROM) of size n. In this paper, we provide approximation bounds ROMs on polynomially mapped manifolds. particular, show depend polynomial degree p mapping function as linear underlying problem. This results in (n, p)-width, which lower bound ROM manifolds and
Using nonlinear projections and preserving structure in model order reduction (MOR) are currently active research fields. In this paper, we provide a novel differential geometric framework for on smooth manifolds, which emphasizes the nature of objects involved. The crucial ingredient is construction an embedding low-dimensional submanifold compatible map, discuss several options. Our general allows capturing generalizing existing MOR techniques, such as preservation Lagrangian- or...
Classical model reduction techniques project the governing equations onto linear subspaces of high-dimensional state-space. For problems with slowly decaying Kolmogorov-n-widths such as certain transport-dominated problems, however, classical linear-subspace reduced-order models (ROMs) low dimension might yield inaccurate results. Thus, concept ROMs has to be extended more general concepts, like Model Order Reduction (MOR) on manifolds. Moreover, we are dealing Hamiltonian systems, it is...
Abstract In this contribution we apply space-time formulation on constrained multibody dynamics. particular, discretize directly Hamilton’s principle using appropriate approximation spaces for the variational problem. Moreover, make use of a rotationless rigid bodies and thus, have to define in Lagrange multipliers as well. Livens’ principle, introducing independent quantities position, velocity momentum, where latter can be considered concept body formulation. Finally, demonstrate...
This work presents two novel approaches for the symplectic model reduction of high-dimensional Hamiltonian systems using data-driven quadratic manifolds. Classical employ linear subspaces representing system states in a reduced-dimensional coordinate system. While these approximations respect nature systems, basis can suffer from slowly decaying Kolmogorov $N$-width, especially wave-type problems, which then requires large size. We propose different methods based on recently developed...
We present a novel technique based on deep learning and set theory which yields exceptional classification prediction results. Having access to sufficiently large amount of labelled training data, our methodology is capable predicting the labels test data almost always even if entirely unrelated data. In other words, we prove in specific setting that as long one has enough points, quality irrelevant.