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Dr Sara GrundelTalks
I will try to give an overview over PMOR methods for linear systems developed within the group but also outside, not claiming completeness. I will also present an interpolator parametric model order reduction method and its extension to MIMO systems.
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Roman Weinhandl (Otto von Guericke University Magdeburg)Talks
In many applications such as parameter-dependent partial differential equations and control theory, matrix equations of the form
$\sum \limits_{k=1}^K A_k X B_k^T=C$
are of interest. For $k$, $N$, $m \in \mathbb{N}$, the matrices involved are $A_k\in \mathbb{R}^{N\times N}$, $B_k \in \mathbb{R}^{m \times m}$, $C \in \mathbb{R}^{N \times m}$ and the unknown is $X \in \mathbb{R}^{N \times...
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Dr Jens Saak (Max Planck Institute for Dynamics of Complex Technical Systems)Talks
Nonlinear model predictive control schemes solving the step-wise local optimization problems via, e.g. ipopt lead to the necessity to solve large KKT systems in each step of the optimizer. The KKT system itself is a saddle point matrix and, due to the outer MPC approach, ideally has Kronecker structure.
Ipopt uses the matrix inertia of the KKT system to accelerate computations. Classic...
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Björn Baran (Max Planck Institute for Dynamics of Complex Technical Systems)Talks
Our goal is the feedback stabilization of a two-dimensional
two-phase Stefan problem, which can model solidification and melting of pure materials.
The solid and liquid phases are separated by an interface.
We want to control and stabilize the interface position.After linearization and discretization, the stabilization problem results in a
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non-autonomous differential Riccati equation... -
Mr Petar Mlinarić (Max Planck Institute for Dynamics of Complex Technical Systems)Talks
We will discuss open problems in our approach to structure-preserving model order reduction using clustering and projection. The first is developing more general a priori error bounds. The second is guaranteeing synchronization-preservation for nonlinear multi-agent systems. Finally, we will discuss potential relation to hyper-reduction.
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Carolin PenkeTalks
The QR decomposition is certainly among the most useful tools in the arsenal of numerical linear algebra, both in real as well as in complex arithmetic. Symplectic orthogonal QR decompositions follow a similar idea. They are less ubiquitous but find use in the context of Hamiltonian eigenvalue problems. We point out that an orthogonal symplectic QR decomposition is in fact the very same thing...
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Alexander ZuyevTalks
The flatness-based approach is a powerful method for solving a variety of control theoretic problems such as motion planning, trajectory tracking, and stabilization of nonlinear systems. This method is limited to control systems with endogenous linearizing feedback, and the idea of parameterizing the trajectories and inputs of such systems in terms of the flat output and its derivatives goes...
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Kirandeep Kour (Max Planck Institute Magdeburg)Talks
The machine learning model for binary classification for tensor input data was proposed in my previous work. The main key point was to compute the kernel matrix for each pair of tensor input data, more efficiently. Along with it, we have explained TT-CP expansion and other theoretical aspects of this model which controls the stability and reliability aspects of it.
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Martin Köhler (Max Planck Institute for Dynamics of Complex Technical Systems)Talks
The Generalized Matrix Sign Function (GMSF) of a Matrix pair $(A,B)$ is typically computed using Newton's method. The naive implementation of the iteration step $A_{k+1} = \frac{1}{2}(A + B A_k^{-1} B)$ takes at least $4\frac{2}{3}m^3$ flops, which makes it a computational tough task. With the help of a preprocessing step, the complexity can be reduced down to $2m^3$ flops. Typical ways to...
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Jennifer Przybilla (Max Planck Institute for Dynamics of Complex Technical Systems)Talks
Dampers are used for instance in structure engineering to stabilize constructions, e.g. buildings, bridges or dams. The dampers are externally included to avoid strong movements caused by external forces with frequencies close to the eigenfrequencies of the structure. We want to optimize these dampers in order to stabilize the constructions against external forces.
Our aim is to optimize...
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Mr Karachalios Dimitrios (Max Planck Institute, DRI group)Talks
The main contribution of this work is to provide new insights for capturing the behavior of hard nonlinearities beyond the classical weakly nonlinear Volterra input-output map (VIOMAP). The VIOMAP approach is a special polynomial map unable to capture hard non-linearities due to the ill-conditioned high polynomial terms. On the other hand, the describing functions (DF) framework allows...
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Mr Sridhar Chellappa (Max Planck Institute for Dynamics of Complex Technical Systems)Talks
The Reduced Basis Method has been quite successful for reducing fully-discretized system of parametric partial differential equations. However, not much is known in terms of applying it to a semi-discretized system of ordinary differential equations, solved by standard black-box solvers, like $\texttt{ode45,ode15s}$, etc. We intend to investigate the question of how $\textit{a posteriori}$ ...
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Davide Palitta (Max Planck Institute for Dynamics of Complex Technical Systems)Talks
The Loewner framework is one of the most successful data-driven model order reduction techniques.
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Given $k$ right interpolation data and $h$ left interpolation data, the standard layout of this approach is composed of two stages.
First, the $kh\times kh$ Loewner matrix $\mathbb{L}$ and shifted Loewner matrix $\mathbb{L}_s$ are constructed. Then, an SVD of $\mathbb{L}_s-\gamma \mathbb{L}$,... -
Christian Himpe (Max Planck Institute for Dynamics of Complex Technical Systems)Talks
Publications on model reduction research typically culminate in the numerical results section, which (supposedly) illustrates or justifies the previous theoretical findings. These numerical experiments generally show results supporting the proposed model reduction algorithm or modification thereof. However, an experimental design or an experiment itself involving model reduction is easily...
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Dr Igor Pontes Duff (Max Planck Institute for Dynamics of Complex Technical Systems)Talks
In this talk, we present a data-driven approach to identify second-order systems of the form
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\begin{equation}
\begin{array}{rcl}
\mathbf{M}\ddot{\mathbf{x}}(t) + \mathbf{D}\dot{\mathbf{x}}(t)+ \mathbf{K}\mathbf{x}(t) &=& \mathbf{B}\mathbf{u}(t),\qquad \mathbf{x}(0) = 0,~\dot{\mathbf{x}}(0) = 0, \
\mathbf{y}(t) &=& \mathbf{C}\mathbf{x}(t).
\end{array}
\end{equation}
These systems... -
Karim Cherifi (MPI Magdeburg)Talks
With the numerous applications of batteries ranging from digital devices to electric cars, accurate modelling of batteries has become an essential part of designing efficient and reliable batteries. Up to now, when modelling batteries, people have been assuming constant particle size of the active materials which does not replicate exactly what is happening in reality. However, with the newly...
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Thanos AntoulasTalks
Newman's bound in rational interpolation and its relation with the Loewner framework will be explored.
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Dr Hussam Al Daas (Max Planck Institute for Dynamics of Complex Technical Systems)Talks
Iterative linear solvers and strategies for accelerating their convergence have been extensively studied by researchers for many decades. Recently, two classes of iterative solvers for tensor-represented systems have proven their effectiveness in solving high dimensional problems. These are low rank Krylov-based solvers and alternating-least-squares-based solvers. Nonetheless, rounding the...
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Pawan GoyalTalks
Recently, operator inference (OpInf) approaches have got a lot of attention. They aim at constructing reduced-order modeling directly from the data, without requiring a discretized full-order model. In a recent paper [Benner et. al '2020], the OpInf problem for nonlinear systems was considered, where analytic nonlinear functions of the governing equation are known. However, there are many...
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Tim MitchellTalks
We present algorithms to compute the extremal value of a real parameter for which a given rational transfer function of a linear time-invariant system remains passive. This quantity is linked to finding a realization of a rational transfer function such that its passivity radius is maximized. We begin by adapting the Hybrid Expansion-Contraction (HEC) algorithm, originally proposed for...
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Mr Harshit Kapadia (Max Planck Institute for Dynamics of Complex Technical Systems)Talks
We present some approaches for obtaining the reduced-order model of incompressible Navier-Stokes equations from the existing literature. The focus of our work is ultimately going to be towards the development of non-intrusive model reduction techniques which would be useful when one has no information about the discretized system. The talk will be given keeping this in mind and potential...
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Dr Lihong Feng (MPI/CSC)Talks
In a recent research, we have proposed two different error estimators for the reduced transfer functions of parametric linear systems. One is based on the dual-residual system; the other is based on the primal-residual system. Theoretically, they should have similar accuracy. Numerically, we find the primal-residual based estimator is more accurate. Same conclusions are drawn for three...
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Dr Neeraj Sarna (Max Planck Institute, Magdeburg)Talks
Let $f:\Omega\times D\to R$ be some parameterized function with the parameter domain $D$. We develop a sparse empirical quadrature to compute $I(\mu) = \int_\Omega f(x,\mu)dx$. To this end, we compute $I(\mu)$ for a set of training parameters and compute the weights of the quadrature using sparse recovery. At least computationally, we observe that the number of non-zero weights in such a...
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Tobias Kasper Skovborg Ritschel (Max Planck Institute for Dynamics of Complex Technical Systems)Talks
In recent work, we have reduced nonlinear second-order power grid models using balanced truncation techniques for quadratic systems. In order to do that, we 1) transform the original system to a first-order system and 2) use lifting to quadratize the first-order system. However, although the original quadratized system reaches steady state, the reduced quadratic system may only reach a partial...
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Steffen Werner (Max Planck Institute for Dynamics of Complex Technical Systems)Talks
As structured interpolation of transfer functions has been proven to be effective in the setting of structured linear and bilinear systems, we are aiming for a similar structure-preserving model order reduction approach for quadratic-bilinear systems, e.g., for quadratic-bilinear mechanical systems \begin{align*} \begin{aligned} 0 & = M\ddot{q}(t) + D\dot{q} + Kq(t)\ & \quad{}+{}...
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Maximilian Behr (Max Planck Institute for Dynamics of Complex Technical Systems)Talks
Let $A,S,X_0\in \mathbb R^{n\times n}$ and $ B \in \mathbb R^{n\times b}$ be. Moreover assume that $S$, $X_0$ are symmetric positive semidefinite.
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We consider
\begin{align}
\dot{X}(t) &= A^T X (t) + X(t) A - X(t) S X(t) + C^T C, \\
X(0)&=X_0.
\end{align}
It is well known that the solution $X$ can be obtained from the Hamiltonian system
\begin{align}
\begin{bmatrix}... -
Ion Victor GoseaTalks
The scope of this contribution is to address some theoretical and numerical aspects concerning the AAA (Adaptive Antoulas-Anderson) algorithm for rational approximation. This method was introduced in 2018 by Nakatsukasa, Sete, and Trefethen and it is based on an interpolation scheme proposed by Antoulas and Anderson in 1986. The AAA algorithm can be viewed as a data-driven iterative procedure...
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Jan HeilandTalks
In the Eulerian formulation, a flow with a free boundary is posed on a domain that changes over time. This time dependency transfers to a time dependency of the discrete operators in a spatially discretized model. In particular, the discrete incompressibility constraint and, thus, the state space for the velocity will depend on time.
Following up on recent developments of POD for adaptive...
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Dr Carmen Gräßle (MPI Magdeburg)Talks
For many problem settings, the underlying dynamics can be described by (systems of) ordinary or partial differential equations based on physical laws and equations. However, many practical applications require highly sophisticated models, which are often impractical for numerical computations due to their complexity. For this reason, model simplifications are often carried out leading to model...
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