相关论文: A Gradient-Based Optimization Method Using the Koo…

Dynamical systems have a wide range of applications in mechanics, electrical engineering, chemistry, and so on. In this work, we propose the adaptive spectral Koopman (ASK) method to solve nonlinear autonomous dynamical systems. This novel…

The Koopman operator plays a crucial role in analyzing the global behavior of dynamical systems. Existing data-driven methods for approximating the Koopman operator or discovering the governing equations of the underlying system typically…

The adaptive spectral Koopman (ASK) method was introduced to numerically solve autonomous dynamical systems that lay the foundation of numerous applications across different fields in science and engineering. Although ASK achieves high…

Quantum optimization, a key application of quantum computing, has traditionally been stymied by the linearly increasing complexity of gradient calculations with an increasing number of parameters. This work bridges the gap between Koopman…

Gradient-based hyperparameter optimization methods update hyperparameters using hypergradients, gradients of a meta criterion with respect to hyperparameters. Previous research used two distinct update strategies: optimizing hyperparameters…

Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for…

Trajectory optimization is a widely used tool in the design and control of dynamical systems. Typically, not only nonlinear dynamics, but also couplings of the initial and final condition through implicit boundary constraints render the…

We propose an alternating optimization algorithm to the nonconvex Koopman operator learning problem for nonlinear dynamic systems. We show that the proposed algorithm will converge to a critical point with rate $O(1/T)$ and $O(\frac{1}{\log…

The Koopman operator enables simplified representations for nonlinear systems in data-driven optimal control, but the accompanying uncertainties inevitably induce deviations in the optimal controller and associated value function. This…

We introduce Kalman Gradient Descent, a stochastic optimization algorithm that uses Kalman filtering to adaptively reduce gradient variance in stochastic gradient descent by filtering the gradient estimates. We present both a theoretical…

We present a new framework for optimal and feedback control of PDEs using Koopman operator-based reduced order models (K-ROMs). The Koopman operator is a linear but infinite-dimensional operator which describes the dynamics of observables.…

A systematic mathematical framework for the study of numerical algorithms would allow comparisons, facilitate conjugacy arguments, as well as enable the discovery of improved, accelerated, data-driven algorithms. Over the course of the last…

Estimation of parameters is a crucial part of model development. When models are deterministic, one can minimise the fitting error; for stochastic systems one must be more careful. Broadly parameterisation methods for stochastic dynamical…

The Koopman operator is a linear but infinite dimensional operator that governs the evolution of scalar observables defined on the state space of an autonomous dynamical system, and is a powerful tool for the analysis and decomposition of…

Koopman operators provide tractable means of learning linear approximations of non-linear dynamics. Many approaches have been proposed to find these operators, typically based upon approximations using an a-priori fixed class of models.…

We present a first-order method for solving constrained optimization problems. The method is derived from our previous work, a modified search direction method inspired by singular value decomposition. In this work, we simplify its…

Combinatorial optimization (CO) problems arise across a broad spectrum of domains, including medicine, logistics, and manufacturing. While exact solutions are often computationally infeasible, many practical applications require…

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…

We propose a first-order method for solving inequality constrained optimization problems. The method is derived from our previous work [12], a modified search direction method (MSDM) that applies the singular-value decomposition of…

The Koopman operator is beneficial for analyzing nonlinear and stochastic dynamics; it is linear but infinite-dimensional, and it governs the evolution of observables. The extended dynamic mode decomposition (EDMD) is one of the famous…