Related papers: Model Reduction via Parametrized Locally Invariant…
Parametric model order reduction using reduced basis methods can be an effective tool for obtaining quickly solvable reduced order models of parametrized partial differential equation problems. With speedups that can reach several orders of…
If the dynamics of an evolutionary differential equation system possess a low-dimensional, attracting, slow manifold, there are many advantages to using this manifold to perform computations for long term dynamics, locating features such as…
Scientific and engineering processes deliver massive high-dimensional data sets that are generated as non-linear transformations of an initial state and few process parameters. Mapping such data to a low-dimensional manifold facilitates…
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 this Kolmogorov barrier within MOR, nonlinear…
Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…
In conventional ODE modelling coefficients of an equation driving the system state forward in time are estimated. However, for many complex systems it is practically impossible to determine the equations or interactions governing the…
We examine nonlinear dynamical systems of ordinary differential equations or differential algebraic equations. In an uncertainty quantification, physical parameters are replaced by random variables. The inner variables as well as a quantity…
In this contribution we investigate in mathematical modeling and efficient simulation of biological cells with a particular emphasis on effective modeling of structural properties that originate from active forces generated from…
A reduction method of ODEs not possessing Lie point symmetries makes use of the so called $\lambda$-symmetries (C. Muriel and J. L. Romero, \emph{IMA J. Appl. Math.} \textbf{66}, 111-125, 2001). The notion of covering for an ODE…
Model predictive control is a prominent approach to construct a feedback control loop for dynamical systems. Due to real-time constraints, the major challenge in MPC is to solve model-based optimal control problems in a very short amount of…
In numerous robotics and mechanical engineering applications, among others, data is often constrained on smooth manifolds due to the presence of rotational degrees of freedom. Common datadriven and learning-based methods such as neural…
We investigate an optimization problem governed by an elliptic partial differential equation with uncertain parameters. We introduce a robust optimization framework that accounts for uncertain model parameters. The resulting non-linear…
Prediction for high dimensional time series is a challenging task due to the curse of dimensionality problem. Classical parametric models like ARIMA or VAR require strong modeling assumptions and time stationarity and are often…
Constrained mechanical systems occur in many applications, such as modeling of robots and other multibody systems. In this case, the motion is governed by a system of differential-algebraic equations (DAE), often with large and sparse…
A major goal for reduced-order models of unsteady fluid flows is to uncover and exploit latent low-dimensional structure. Proper orthogonal decomposition (POD) provides an energy-optimal linear basis to represent the flow kinematics, but…
Complex systems are often decomposed into modular subsystems for engineering tractability. Although various equation based white-box modeling techniques make use of such structure, learning based methods have yet to incorporate these ideas…
Regressions created from experimental or simulated data enable the construction of metamodels, widely used in a variety of engineering applications. Many engineering problems involve multi-parametric physics whose corresponding…
This article surveys nonlinear model reduction methods that remain effective in regimes where linear reduced-space approximations are intrinsically inefficient, such as transport-dominated problems with wave-like phenomena and moving…
Spectral submanifolds (SSMs) have recently been shown to provide exact and unique reduced-order models for nonlinear unforced mechanical vibrations. Here we extend these results to periodically or quasiperiodically forced mechanical…
Smooth autonomous dynamical systems modeled by ordinary differential equations (ODEs) cannot robustly and globally stabilize a point in compact, boundaryless manifolds. This obstruction, which is topological in nature, implies that…