相关论文: Numerical simulation of differential-algebraic equ…
A sequential solver for differential-algebraic equations with embedded optimization criteria (DAEOs) was developed to take advantage of the theoretical work done by Deussen et al. Solvers of this type separate the optimization problem from…
Differential-algebraic equations (DAEs) with state-dependent events arise in systems whose continuous dynamics are constrained by algebraic equations and interrupted by mode changes, switching logic, impacts, or state reinitializations.…
Differential-algebraic equations (DAEs) are widely used for modeling of dynamical systems. The difficulty in solving numerically a DAE is measured by its differentiation index. For highly accurate simulation of dynamical systems, it is…
Scientific machine learning is an emerging field that broadly describes the combination of scientific computing and machine learning to address challenges in science and engineering. Within the context of differential equations, this has…
This article proposes modifications of the Parareal algorithm for its application to higher index differential algebraic equations (DAEs). It is based on the idea of applying the algorithm to only the differential components of the equation…
The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this…
The stability of integrators dealing with high order Differential Algebraic Equations (DAEs) is a major issue. The usual procedures give rise to instabilities that are not predicted by the usual linear analysis, rendering the common checks…
In many applications, one needs to learn a dynamical system from its solutions sampled at a finite number of time points. The learning problem is often formulated as an optimization problem over a chosen function class. However, in the…
Recent advances in quantum computing and the increasing availability of quantum hardware have substantially enhanced the practical relevance of quantum approaches to discrete optimization. Among these, the Quadratic Unconstrained Binary…
We present a hybrid a-priori/a-posteriori goal oriented error estimator for a combination of dynamic iteration-based solution of ordinary differential equations discretized by finite elements. Our novel error estimator combines estimates…
Viewing optimization methods as numerical integrators for ordinary differential equations (ODEs) provides a thought-provoking modern framework for studying accelerated first-order optimizers. In this literature, acceleration is often…
Many real-world optimization problems involve uncertain parameters with probability distributions that can be estimated using contextual feature information. In contrast to the standard approach of first estimating the distribution of…
We study the Optimal Control Problem (OCP) for regular linear differential-algebraic systems (DAEs). To this end, we introduce the input index, which allows, on the one hand, to characterize the space of consistent initial values in terms…
This paper addresses the problem of efficiently computing higher-order variational integrators in simulation and trajectory optimization of mechanical systems as those often found in robotic applications. We develop $O(n)$ algorithms to…
We deal with the numerical solution of linear partial differential equations (PDEs) with focus on the goal-oriented error estimates including algebraic errors arising by an inaccurate solution of the corresponding algebraic systems. The…
PDE-Constrained Optimization (PDECO) problems can be accelerated significantly by employing gradient-based methods with surrogate models like neural operators compared to traditional numerical solvers. However, this approach faces two key…
In this paper a novel stochastic optimization and extremum seeking algorithm is presented, one which is based on time-delayed random perturbations and step size adaptation. For the case of a one-dimensional quadratic unconstrained…
The Quantum Approximate Optimization Algorithm (QAOA) has emerged as a promising variational quantum algorithm for addressing NP hard combinatorial optimization problems. However, a significant limitation lies in optimizing its classical…
This paper studies a class of distributed optimization problems with coupled equality constraints in networked systems. Many existing distributed algorithms rely on solving local subproblems via the $\operatorname{argmin}$ operator in each…
Differentiable simulation is a promising toolkit for fast gradient-based policy optimization and system identification. However, existing approaches to differentiable simulation have largely tackled scenarios where obtaining smooth…