Related papers: Representer Theorem for Learning Koopman Operators
With the advancement of sensing and communication in power networks, high-frequency real-time data from a power network can be used as a resource to develop better monitoring capabilities. In this work, a systematic approach based on…
A dynamical system is a transformation of a phase space, and the transformation law is the primary means of defining as well as identifying the dynamical system. It is the object of focus of many learning techniques. Yet there are many…
Koopman operators are infinite-dimensional operators that linearize nonlinear dynamical systems, facilitating the study of their spectral properties and enabling the prediction of the time evolution of observable quantities. Recent methods…
Soft robots are challenging to model and control as inherent non-linearities (e.g., elasticity and deformation), often requires complex explicit physics-based analytical modeling (e.g., a priori geometric definitions). While machine…
The standard approach for dealing with the ill-posedness of the training problem in machine learning and/or the reconstruction of a signal from a limited number of measurements is regularization. The method is applicable whenever the…
We consider an operator-based latent Markov representation of a stochastic nonlinear dynamical system, where the stochastic evolution of the latent state embedded in a reproducing kernel Hilbert space is described with the corresponding…
Approximate solution of the ensemble representability problem for density operators of arbitrary order is obtained. This solution is closely related to the ``Q condition'' of A.J.Coleman. The representability conditions are formulated in…
Koopman operator theory has gained significant attention in recent years for identifying discrete-time nonlinear systems by embedding them into an infinite-dimensional linear vector space. However, providing stability guarantees while…
Continuous-time stochastic processes underlie many natural and engineered systems. In healthcare, autonomous driving, and industrial control, direct interaction with the environment is often unsafe or impractical, motivating offline…
This paper presents a generalizable methodology for data-driven identification of nonlinear dynamics that bounds the model error in terms of the prediction horizon and the magnitude of the derivatives of the system states. Using…
Koopman operator theory has proven to be a promising approach to nonlinear system identification and global linearization. For nearly a century, there had been no efficient means of calculating the Koopman operator for applied engineering…
A theoretical framework which unifies the conventional Mori-Zwanzig formalism and the approximate Koopman learning is presented. In this framework, the Mori-Zwanzig formalism, developed in statistical mechanics to tackle the hard problem of…
In recent years there has been a considerable drive towards data-driven analysis, discovery and control of dynamical systems. To this end, operator theoretic methods, namely, Koopman operator methods have gained a lot of interest. In…
We present a low-rank Koopman operator formulation for accelerating deformable subspace simulation. Using a Dynamic Mode Decomposition (DMD) parameterization of the Koopman operator, our method learns the temporal evolution of deformable…
The estimation for the region of attraction (ROA) of an asymptotically stable equilibrium point is crucial in the analysis of nonlinear systems. There has been a recent surge of interest in estimating the solution to Zubov's equation, whose…
This paper proposes a method for uncertainty quantification of an autoencoder-based Koopman operator. The main challenge of using the Koopman operator is to design the basis functions for lifting the state. To this end, this paper builds an…
In this paper, we propose linear operator theoretic framework involving Koopman operator for the data-driven identification of power system dynamics. We explicitly account for noise in the time series measurement data and propose robust…
The Koopman Operator (KO) offers a promising alternative methodology to solve ordinary differential equations analytically. The solution of the dynamical system is analyzed in terms of observables, which are expressed as a linear…
In this paper, we consider the problem of learning a first-order theorem prover that uses a representation of beliefs in mathematical claims to construct proofs. The inspiration for doing so comes from the practices of human mathematicians…
A learning method is proposed for Koopman operator-based models with the goal of improving closed-loop control behavior. A neural network-based approach is used to discover a space of observables in which nonlinear dynamics is linearly…