Related papers: Adaptive Frequency-limited H2-Model Order Reductio…
In this work we derive a second-order approach to bilevel optimization, a type of mathematical programming in which the solution to a parameterized optimization problem (the "lower" problem) is itself to be optimized (in the "upper"…
Masked Diffusion Models (MDMs) have emerged as one of the most promising paradigms for generative modeling over discrete domains. It is known that MDMs effectively train to decode tokens in a random order, and that this ordering has…
Solving optimal control problems to determine a stabilizing controller involves a significant computational effort. Time-varying optimal control provides a remedy by designing a tracking system, given as an ordinary differential equation,…
We introduce a computationally efficient and accurate reduced order modelling approach for the optimization of spatiotemporally chaotic systems. The proposed method combines quantized local reduced order modelling with adjoint-based…
In this paper, we propose new structured second-order methods and structured adaptive-gradient methods obtained by performing natural-gradient descent on structured parameter spaces. Natural-gradient descent is an attractive approach to…
Iterative first-order methods such as gradient descent and its variants are widely used for solving optimization and machine learning problems. There has been recent interest in analytic or numerically efficient methods for computing…
We introduce an efficient numerical method for second order linear ODEs whose solution may vary between highly oscillatory and slowly changing over the solution interval. In oscillatory regions the solution is generated via a nonoscillatory…
Model order reduction is a technique that is used to construct low-order approximations of large-scale dynamical systems. In this paper, we investigate a balancing based model order reduction method for dynamical systems with a linear…
A method is given for solving an optimal H2 approximation problem for SISO linear time-invariant stable systems. The method, based on constructive algebra, guarantees that the global optimum is found; it does not involve any gradient-based…
We present a novel end-to-end deep learning-based adaptation control algorithm for frequency-domain adaptive system identification. The proposed method exploits a deep neural network to map observed signal features to corresponding…
Sliding mode control (SMC) is a robust and computationally efficient solution for tracking control problems of highly nonlinear systems with a great deal of uncertainty. High frequency oscillations due to chattering phenomena and…
The locally modified finite element method, which is introduced in [Frei, Richter: SINUM 52(2014), p. 2315-2334], is a simple fitted finite element method that is able to resolve weak discontinuities in interface problems. The method is…
This paper proposes an adaptive hyper-reduction method to reduce the computational cost associated with the simulation of parametric particle-based kinetic plasma models, specifically focusing on the Vlasov-Poisson equation. Conventional…
In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in…
Heavy-tailed noise is pervasive in modern machine learning applications, arising from data heterogeneity, outliers, and non-stationary stochastic environments. While second-order methods can significantly accelerate convergence in…
Reduced order modeling methods are often used as a mean to reduce simulation costs in industrial applications. Despite their computational advantages, reduced order models (ROMs) often fail to accurately reproduce complex dynamics…
When balanced truncation is used for model order reduction, one has to solve a pair of Lyapunov equations for two Gramians and uses them to construct a reduced-order model. Although advances in solving such equations have been made, it is…
In traditional topology optimization, the computing time required to iteratively update the material distribution within a design domain strongly depends on the complexity or size of the problem, limiting its application in real engineering…
We consider linear dynamical systems consisting of ordinary differential equations with high dimensionality. The aim of model order reduction is to construct an approximating system of a much lower dimension. Therein, the reduced system may…
We introduce an interpolation framework for H-infinity model reduction founded on ideas originating in optimal-H2 interpolatory model reduction, realization theory, and complex Chebyshev approximation. By employing a Loewner "data-driven"…