Conveners
Contibuted Talk
- Bonan Sun (Max Planck Institute Dynamics of Complex Technical System)
Contibuted Talk
- Minakshi Verma
Contibuted Talk
- Vahid Nateghi
Contibuted Talk
- Yevgeniya Filanova
Contibuted Talk
- Jonas Schulze (MPI DCTS)
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...
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...
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...
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...
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
$$
\begin{align}
m(G,H,S):=\sup\bigg{ \frac{v^Gv}{v^v} :~v\in \mathbb{C}^{n} \setminus {0},\,v^TSv=0,\,...
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...
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...
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...
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...
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...
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...
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...
