相关论文: Information Shapes Koopman Representation

This paper proposes an information-theoretic representation learning framework, named conditional information flow maximization, to extract noise-invariant sufficient representations for the input data and target task. It promotes the…

Koopman operator theory, a powerful framework for discovering the underlying dynamics of nonlinear dynamical systems, was recently shown to be intimately connected with neural network training. In this work, we take the first steps in…

We present KoopCast, a lightweight yet efficient model for trajectory forecasting in general dynamic environments. Our approach leverages Koopman operator theory, which enables a linear representation of nonlinear dynamics by lifting…

Disentangling complex data to its latent factors of variation is a fundamental task in representation learning. Existing work on sequential disentanglement mostly provides two factor representations, i.e., it separates the data to…

The advent of easy access to large amount of data has sparked interest in directly developing the relationships between input and output of dynamic systems. A challenge is that in addition to the applied input and the measured output, the…

Koopman liftings have been successfully used to learn high dimensional linear approximations for autonomous systems for prediction purposes, or for control systems for leveraging linear control techniques to control nonlinear dynamics. In…

We study a class of dynamical systems modelled as Markov chains that admit an invariant distribution via the corresponding transfer, or Koopman, operator. While data-driven algorithms to reconstruct such operators are well known, their…

Markov processes are widely used mathematical models for describing dynamic systems in various fields. However, accurately simulating large-scale systems at long time scales is computationally expensive due to the short time steps required…

The information bottleneck principle provides an information-theoretic method for representation learning, by training an encoder to retain all information which is relevant for predicting the label while minimizing the amount of other,…

Koopman operator theory is a popular candidate for data-driven modeling because it provides a global linearization representation for nonlinear dynamical systems. However, existing Koopman operator-based methods suffer from shortcomings in…

With the increasing availability of large scale datasets, computational power and tools like automatic differentiation and expressive neural network architectures, sequential data are now often treated in a data-driven way, with a dynamical…

Information bottleneck is an information-theoretic principle of representation learning that aims to learn a maximally compressed representation that preserves as much information about labels as possible. Under this principle, two…

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…

The Information Bottleneck (IB) principle offers an information-theoretic framework for analyzing the training process of deep neural networks (DNNs). Its essence lies in tracking the dynamics of two mutual information (MI) values: between…

Koopman-based learning methods can potentially be practical and powerful tools for dynamical robotic systems. However, common methods to construct Koopman representations seek to learn lifted linear models that cannot capture nonlinear…

Mobile robot navigation can be challenged by system uncertainty. For example, ground friction may vary abruptly causing slipping, and noisy sensor data can lead to inaccurate feedback control. Traditional model-based methods may be limited…

We consider the training process of a neural network as a dynamical system acting on the high-dimensional weight space. Each epoch is an application of the map induced by the optimization algorithm and the loss function. Using this induced…

A turbocharger plays an essential part in reducing emissions and increasing the fuel efficiency of road vehicles. The pulsating flow of exhaust gases, along with high heat exchange from the turbocharger casing, makes developing…

Reinforcement Learning (RL) has made significant strides in various domains, and policy gradient methods like Proximal Policy Optimization (PPO) have gained popularity due to their balance in performance, training stability, and…

In this paper, we propose a novel algorithm for learning the Koopman operator of a dynamical system from a \textit{small} amount of training data. In many applications of data-driven modeling, e.g. biological network modeling,…