-
Martin Stoll (TU Chemnitz)17/02/2025, 09:00Talk
Gaussian processes are a versatile tool in statistics and machine learning. They are suitable candidates to generate surrogate models that come with integrated uncertainty quantification of the reduced model. The quality of the model heavily depends on the choice of the hyperparameters and to train these on the given data many linear algebra challenges arise. In this talk we will briefly...
Go to contribution page -
Heike Faßbender (TU Braunschweig)17/02/2025, 09:45Talk
Finding the unique stabilizing solution $X = X^H$ of a large-scale continuous-time algebraic Riccati equation (CARE) $0 = R(X) := A^HX + XA + C^HC - XBB^HX$ with a large, sparse n-x-n matrix $A$, an $n\times m$ matrix $B$ and a $p\times n$ matrix $C$ is of interest in a number of applications. It is assumed, that $B$ and $C^H$ have full column and row rank, respectively, with $m$, $p << n$....
Go to contribution page -
Martin Köhler (Max Planck Institute for Dynamics of Complex Technical Systems)17/02/2025, 11:00Talk
The solution of Sylvester-like matrix equations still constitutes a core task in systems and control theory, with their solution also being required in the extensive field of eigenvalue analysis. In addition to numerous iterative algorithms, Bartels and Stewart presented an algorithm for dense matrices in the 1970s. This algorithm has been improved over the last two decades by the introduction...
Go to contribution page -
Jonas Schulze (MPI DCTS)17/02/2025, 11:30Talk
Reduced rank extrapolation (RRE) is an acceleration method typically used to accelerate the iterative solution of nonlinear systems of equations using a fixed-point process. In this context, the iterates are vectors generated from a fixed-point mapping function. However, when considering the iterative solution of large-scale matrix equations, the iterates are low-rank matrices generated from a...
Go to contribution page -
Mr Harshit Kapadia (Max Planck Institute for Dynamics of Complex Technical Systems)17/02/2025, 12:00Talk
We present a novel tensor empirical interpolation method operating within the tensor t-product framework. Compared to traditional empirical interpolation, our approach significantly enhances the reconstruction accuracy of tensor-valued datasets by using optimally placed sparse sensor measurements along the dimension of interest. This improvement is achieved by preserving the native tensor...
Go to contribution page -
Bonan Sun (Max Planck Institute Dynamics of Complex Technical System)17/02/2025, 16:00Talk
In this talk, we introduce a mesh-free two-level hybrid Tucker tensor format for the approximation of multivariate functions. This new format combines the product Chebyshev interpolation with the ALS-based Tucker decomposition of the coefficients tensor. The benefits of this tensor approximation are two-fold. On the one hand, it allows to avoid the rank-structured approximation of functional...
Go to contribution page -
Dr Anshul Prajapati (Max Planck Institute for Dynamics of Complex Technical Systems)17/02/2025, 16:30Talk
Let $G, H \in \mathbb{C}^{n,n}$ be Hermitian and $S \in \mathbb{C}^{n,n}$ be a symmetric matrix. We consider the problem of maximizing the Rayleigh quotient of $G$ with respect to constraints involving symmetric matrix $S$ and Hermitian matrix $H$. More precisely, we compute
$$
Go to contribution page
\begin{align}
m(G,H,S):=\sup\bigg{ \frac{v^Gv}{v^v} :~v\in \mathbb{C}^{n} \setminus {0},\,v^TSv=0,\,... -
Eda Oktay (MPI DCTS)17/02/2025, 17:00Talk
Interest in communication-avoiding orthogonalization schemes for high-performance computing has been growing recently. In this talk, we discuss some open questions about the numerical stability of various block classical Gram-Schmidt variants that have been proposed in the past few years. We introduce an abstract framework, the flexibility of which allows for new rigorous bounds on the loss of...
Go to contribution page -
Serkan Gugercin (Virginia Tech)17/02/2025, 17:45Talk
In this talk, we revisit the L2 optimal approximation problem through various formulations and applications, exploring its rich mathematical structure and diverse implications. We begin with the classical case where the optimal approximant is a rational function, highlighting how Hermite interpolation at specific reflected points emerges as the necessary condition for optimality. Building on...
Go to contribution page -
Prof. Thomas Richter (Otto-von-Guericke Universität Magdeburg)18/02/2025, 09:00Talk
We consider an elastic solid, e.g. a ball, which sinks towards the ground in a container filled with a liquid. The ball bounces off the bottom.
From a mathematical point of view, it is not clear what exactly happens. Assuming that the Navier-Stokes equations describe the situation, contact should not occur. The common hypothesis is that if the surface of the sphere is assumed to be...
Go to contribution page -
Carolin Mehlmann18/02/2025, 09:45Talk
Sea ice is one of the important components in global circulation models used for weather forecasting and especially for climate prediction. Sea ice is modeled as a 2D layer between the atmosphere and the ocean. While sea ice covers only the polar regions of the Earth, the sea ice component usually takes on the role of a coupler between the ocean and the atmosphere and is responsible for all...
Go to contribution page -
Leonidas Gkimisis (MPI Magdeburg)18/02/2025, 11:00Talk
spatially localized features characterized by slow singular value decay. The proposed approach builds upon two existing methodologies for reduced and full-order non-intrusive modeling, namely Operator Inference (OpInf) and sparse Full-Order Model (sFOM) inference. We decompose the domain into two complementary subdomains which exhibit fast and slow singular value decay, accordingly. The...
Go to contribution page -
Feliks Nüske (MPI for Dynamics of Complex Technical Systems)18/02/2025, 11:30Talk
Metastablility is a phenomenon which often inhibits the efficient simulation of dynamical systems, or the generation of samples from high-dimensional probability measures. In particular, metastability is frequently encountered in computer simulations of biological macromolecules using molecular dynamics. It is well-known that metastable transitions and their time scales are encoded in the...
Go to contribution page -
Lei Guo (Max Planck Institute for Dynamics of Complex Technical Systems)18/02/2025, 12:00Talk
Stochastic dynamics with metastability are a recurring theme in many scientific disciplines, for instance, in simulations of macro-molecules, in climate systems, and in applications of uncertainty quantification. Metastability describes the existence of long-lived macro-states in a dynamical system's state space, such that transitions between these macro-states are rare events. It is thus...
Go to contribution page -
Sridhar Chellappa (Max Planck Institute for Dynamics of Complex Technical Systems)18/02/2025, 13:30Talk
Reconstructing nonlinear parametric functions based on sparse measurements or partially observed sensor data is an important problem arising in a number of practical applications such as climate science, fluid dynamics, and biology. To achieve accurate approximation, two crucial aspects need to be considered: (a) choosing the optimal location for data sampling and (b) identifying a suitable...
Go to contribution page -
Hamdullah Yücel18/02/2025, 14:00Talk
In this talk, we present an adaptive based algorithm to solve a robust shape structural optimization problem governed by a linear elasticity model that accounts for uncertainties in the loading and material inputs. A posteriori error estimators are developed to adjust both the sample size and the spatial domain. Within the dual-weighted residual framework, a weighted goal functional is...
Go to contribution page -
Shuwen Sun (MPI Magdeburg)18/02/2025, 14:30Talk
With the capability of modern computers for processing large amounts of data, machine learning (ML) is being more and more applied in computational science. Many of the ML learning methods aim to accurately predict the whole solution vector of dynamical systems via data compression, such as convolutional autoencoder. These works focus on predicting only the quantities of interests (QoIs) or...
Go to contribution page -
Ion Victor Gosea (MPI Magdeburg)18/02/2025, 15:00Talk
Parametrized nonlinear dynamical systems often arise upon discretizing parametrized partial differential equations (PDEs). Typically, the former tends to be of a large scale, i.e., the number of state variables could be significantly high (the state vector is denoted with x(t, p), p is the vector of parameters, the nonlinearity is f(x(t, p), p), while the matrices corresponding to the linear...
Go to contribution page -
Ashwin Nayak (CSC group)18/02/2025, 15:30Poster
Accurate simulations of gas flow within pipeline networks provide crucial insights for transmission and design operators. This importance intensifies with the growing integration of hydrogen-blended fuels in hydrogen-based energy systems. Existing models predominantly address single-component, one-dimensional flow within individual pipe segments, interconnected at network junctions. Recently,...
Go to contribution page -
Xiaobo Liu (Max Planck Institute for Dynamics of Complex Technical Systems)18/02/2025, 15:30Poster
In the usual one-precision environment the Bartels--Stewart algorithm is the standard algorithm for solving small dense Sylvester matrix equations AX+XB=C. their algorithm consists of three steps, including the computation of the Schur decompositions, the substitution for solving the Sylvester equation with quasi-triangular coefficients, and the final recovering transformation.
In the new...
Go to contribution page -
Pavan L. Veluvali (Max Planck Institute for Dynamics of Complex Technical Systems)18/02/2025, 15:30Poster
Numerical algorithms and computational tools are essential for managing and analyzing complex data processing tasks. As meta-data and parameter-driven simulations have become more prevalent, the need for automated workflows to reproduce computational experiments across platforms has significantly increased. In general, a computational workflow is defined as a step-by-step description for...
Go to contribution page -
Jan Lilienblum (Max-Planck-Institute for Dynamics of Complex Technical Systems)18/02/2025, 15:30Poster
The class of bilinear dynamical systems often arises in the description and approximation of large-scale nonlinear systems with analytic nonlinearities. This bilinear structure allows the extension of various established model order reduction (MOR) approaches, from their linear counterparts. In this work, our aim is to introduce a realization-free, data-based MOR method, inspired by the...
Go to contribution page -
Chenzi Wang (MPI magdeburg)18/02/2025, 15:30Poster
The increasing complexity in design and manufacturing has driven the need for advanced techniques for fast modeling problems with high-dimensional parameter spaces. Avoiding high-fidelity finite element models while achieving fast and accurate simulations in such contexts is challenging. Projection-based parametric model order reduction (pMOR) has drawn significant attention in recent years....
Go to contribution page -
Yevgeniya Filanova18/02/2025, 15:30Poster
Operator inference (OpInf) is a method for non-intrusive reduced modeling, i.e., identifying small surrogate models from data. In this poster, we consider second-order ODE systems, which are typically used to model mechanical vibrations. The variety of load cases requires specific adaptations of the OpInf method, taking into account different approaches to modeling the corresponding problems,...
Go to contribution page -
Maximilian Bindhak (Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg)18/02/2025, 15:30Poster
pyMOR, a Python toolbox for building reduced order models, supports a variety of solver backends, such as dune-gdt, FEniCS, NGSolve, NumPy and potentially MPI distributed variants. An abstract interface, the VectorArray, is used to wrap vectors and matrices from these backends on which pyMOR's algorithms work. For compatibility reasons direct access of entries has to be avoided, which...
Go to contribution page -
Minakshi Verma18/02/2025, 15:30Poster
This poster introduces an approach to solving the Generalised eigenvalue problems arising from the tensor- based Extended Dynamic Mode Decomposition (EDMD). The Extended Dynamic Mode Decomposition (EDMD) is a data-driven technique used for approximating the Koopman operator, a linear operator which is particularly useful for understanding the behavior of nonlinear dynamical systems from...
Go to contribution page -
Shaimaa Monem18/02/2025, 15:30Poster
We introduce a novel reduction bases to accelerate the nonlinear term evaluation of constraints projections on different mesh elements. Our method determines an approximate reduced subspace that is computed on the constrained elements (vertices, triangles, tetrahedrons) which show the largest deformation on the provided set training snapshots. We achieve low error bounds by incorporating the...
Go to contribution page -
Luís Tadeu Nascimento Pires (Max Planck Institute for Dynamics of Complex Technical Systems)18/02/2025, 15:30Poster
Solving the Schrödinger equation is a central task in quantum chemistry. Diffusion Monte Carlo (DMC) is a stochastic method that utilizes the connection between this equation and those governing diffusion phenomena to obtain accurate estimates of the eigenvalues and eigenfunctions involved.
Go to contribution page
This is made possible by the well-known Feynman-Kac formula, which allows the Schrödinger equation to... -
Dr Jens Saak (Max Planck Institute for Dynamics of Complex Technical Systems)18/02/2025, 15:30Poster
For the standard algebraic generalized Riccati equation
$C^TQC+ A^TXE + E^TXA -E^TXBR^{-1}B^TXE = 0$
different algorithms inspired by the low-rank alternating directions implicit (LR-ADI) iteration and Krylov subspace projection have successfully been applied, based on the $ZZ^T$ factorization of the iterates, when $Q, R$ are both symmetric, and $Q\geq0$ and $R>0$.
In this...
Go to contribution page -
Vahid Nateghi18/02/2025, 15:30Poster
In this work, we show how kernel-based approximation to the Koopman generator – the kgEDMD algorithm – can be used to identify implied timescales and meta-stable sets in stochastic dynamical systems, and to learn a coarse-grained dynamics on reduced variables, which retains the essential kinetic properties of the full model. The centerpiece of this study is a learning method to identify an...
Go to contribution page -
Sergii Chuiko (Donbass State Pedagogical University, Donetsk region, Slavyansk, Ukraine)18/02/2025, 15:30Poster
We study the problem of constructing solutions [1, 2] $X \in \mathbb{R}^{\alpha \times \beta}$ of a linear matrix equation
Go to contribution page
$LX = F, F \in \mathbb{R}^{\gamma \times \delta},$ (1)
where $L : \mathbb{R}^{\alpha \times \beta} \rightarrow \mathbb{R}^{\gamma \times \delta}$ is a linear bounded matrix functional. A partial case of the matrix algebraic equation (1) is the well-known Sylvester and... -
Hauke Sprink (MPI Magdeburg)18/02/2025, 15:30Poster
Biomolecular processes often involve transitions between metastable states governing molecular function. Extracting this information is challenging due to the high dimensionality of simulation data. Kernel methods are a powerful tool for automated analysis of complex systems, yet their need for pairwise kernel evaluations leads to scalability issues, particularly in large datasets.
Go to contribution page
To address... -
Yevgeniia Yevgenieva (Max Planck Institute for Dynamics of Complex Technical Systems)18/02/2025, 15:30Poster
We analyze two classes of mathematical models describing chemical reactions of the type "$A \to$ product," conducted in tubular reactors. The first class involves nonlinear hyperbolic partial differential equations modeling a plug flow reactor (PFR) in the presence of an inert component. For this system, an isoperimetric optimal control problem is formulated to maximize the mean product yield...
Go to contribution page -
Sara Grundel18/02/2025, 15:30Poster
The poster will present a comparison of different Port Hamiltonian models focusing on the interconnection of two or more PH models to generate a new PH model. Starting from a standard linear finite dimensional system a few steps will be presented how one could model the generalized framework of nonlinear and infinite dimenisonal systems. Some examples will be shown in the context of...
Go to contribution page -
Xuelian Wang (MPI)18/02/2025, 15:30Poster
There have been a number of works in the literature dealing with the stabilization of processes with input delays for a reaction-diffusion partial differential equation, mainly by using finite-time control strategies, where their settling time depends on the initial conditions. However, in many practical applications, it is difficult or even impossible to obtain system initial values in...
Go to contribution page -
Dr Süleyman Yildiz (Group of Computational Methods in Systems and Control Theory (CSC), Max Planck Institute for Dynamics of Complex Technical Systems)18/02/2025, 15:30Poster
We present a novel machine learning approach to develop energy-preserving reduced-order models (ROMs) by exploiting the multi-symplectic structure of partial differential equations (PDEs). Traditional energy-preserving ROMs often rely on the symplectic Galerkin projection, which requires fully discrete operators - often unavailable in black-box PDE solvers. Our method circumvents this...
Go to contribution page -
Konrad Janik (Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg)18/02/2025, 15:30Poster
The numerical integration of Hamiltonian systems is a central topic in computational physics and theoretical chemistry. Intrinsic structure-preserving symplectic networks (SympNets) [1] are a widely used tool when it comes to learning symplectic integrators for Hamiltonian systems from data. More often then not Hamiltonian systems of interest depend on a set of parameters. Currently, SympNets...
Go to contribution page -
Fan Wang (MPI-Magdeburg)18/02/2025, 15:30Poster
Model-order Reduction (MOR) is a technique used to reduce the complexity of high-dimensional dynamical systems while preserving their essential properties. It has been been successfully used in many scientific and engineering fields, such as Fluid Dynamics and Control Theory by methods like Proper Orthogonal Decomposition (POD), Autoencoder, Dynamic Mode decomposition (DMD) and so on. However,...
Go to contribution page -
Tobias Breiten (Technische Universität Berlin)18/02/2025, 16:45Talk
Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing and deriving reduced-order models that can replace the full PDE when solving the optimal control problem.
Go to contribution page
Specifically, we explore the use of the shifted... -
Tobias Damm (RPTU Kaiserslautern-Landau)19/02/2025, 09:00Talk
For linear control systems, we study algebraic stability domains which are defined by polynomial inequalities in the complex plane. Based on Kharitonov's characterization via generalized Lyapunov matrix inequalities, we define a suitable pair of Gramians and a balancing transformation. Then we analyze the preservation of these stability domains by balanced truncation. For domains bounded by...
Go to contribution page -
Michael Hinze (Universitat Koblenz)19/02/2025, 09:45Talk
We propose a least-squares formulation for parabolic PDEs in the natural $L^2(0,T;V^*)\times H$ norm which avoids regularity assumptions on the data of the problem, which e.g. appear in the recently proposed First Order System Least Squares (FOSLS) method. For abstract parabolic equations the resulting bilinear form then is symmetric, continuous, and coercive. This among other things paves the...
Go to contribution page -
Jan Heiland19/02/2025, 11:00Talk
The computation of system norms is an important part of system-theoretic model order reduction (MOR). For linear time-invariant (LTI) systems, norms are well-defined and accessible formulas are available and one may well say that the handling of the relevant system norms is what makes the popular MOR methods Balanced Truncation and IRKA performant.
Beyond LTI systems, already the...
Go to contribution page -
Alexander Zuyev19/02/2025, 11:30Talk
This talk addresses the stabilization problem for essentially nonlinear control-affine systems under the Lie Algebra Rank Condition (LARC). Previously, a family of oscillating feedback controls was proposed to stabilize the equilibrium of a driftless system under higher-order controllability assumptions. This stabilization scheme relies on a sampling process, which differs from the classical...
Go to contribution page -
Yongho Kim (Max Planck Institute for Dynamics of Complex Technical System)19/02/2025, 12:00Talk
Model order reduction (MOR) is a method designed to simplify high-dimensional systems by representing their states using a low-dimensional parametrization. It enhances computational efficiency and reduces memory usage but can lead to reduced simulation accuracy and difficulties in preserving system properties, such as sparsity, positivity, and incompressibility. Consequently, choosing an...
Go to contribution page -
Hermann Mena (Max Planck Institute for Dynamics of Complex Technical Systems)Poster
Data-driven modelling and optimisation play a fundamental role in science and engineering. In particular, hybrid models, i.e., those that combine physical models (white-box modelling) with data-driven machine learning approaches (black-box modelling), have great potential for simulating and controlling vector-borne diseases, including dengue virus, yellow fever virus, Chikungunya virus, and...
Go to contribution page
Choose timezone
Your profile timezone: