相关论文: Augmented Invertible Koopman Autoencoder for long-…

In this thesis, we develop methods to enhance the interpretability of recent representation learning techniques in natural language processing (NLP) while accounting for the unavailability of annotated data. We choose to leverage…

Nonlinear optimal control is vital for numerous applications but remains challenging for unknown systems due to the difficulties in accurately modelling dynamics and handling computational demands, particularly in high-dimensional settings.…

Predicting the evolution of complex systems governed by partial differential equations (PDEs) remains challenging, especially for nonlinear, chaotic behaviors. This study introduces Koopman-inspired Fourier Neural Operators (kFNO) and…

Variational autoencoder (VAE) neural networks can be trained to generate power system states that capture both marginal distribution and multivariate dependencies of historical data. The coordinates of the latent space codes of VAEs have…

Simultaneous recordings from thousands of neurons across multiple brain areas reveal rich mixtures of activity that are shared between regions and dynamics that are unique to each region. Existing alignment or multi-view methods neglect…

This work explores the relationship between state space methods and Koopman operator-based methods for predicting the time-evolution of nonlinear dynamical systems. We demonstrate that extended dynamic mode decomposition with dictionary…

Variational autoencoders (VAE) represent a popular, flexible form of deep generative model that can be stochastically fit to samples from a given random process using an information-theoretic variational bound on the true underlying…

In designing efficient feedback control laws for fluid flow, the modern control theory can serve as a powerful tool if the model can be represented by a linear ordinary differential equation (ODE). However, it is generally difficult to find…

This paper presents an interpretable machine learning approach that characterizes load dynamics within an operator-theoretic framework for electricity load forecasting in power grids. We represent the dynamics of load data using the Koopman…

Koopman-based lifted linear identification have been widely used for data-driven prediction and model predictive control (MPC) of nonlinear systems. It has found applications in flow-control, soft robotics, and unmanned aerial vehicles…

We develop a new generalization of Koopman operator theory that incorporates the effects of inputs and control. Koopman spectral analysis is a theoretical tool for the analysis of nonlinear dynamical systems. Moreover, Koopman is intimately…

We propose a novel filter for sparse big data, called an integrated autoencoder (IAE), which utilizes auxiliary information to mitigate data sparsity. The proposed model achieves an appropriate balance between prediction accuracy,…

Steered-Mixtures-of-Experts (SMoE) models provide sparse, edge-aware representations, applicable to many use-cases in image processing. This includes denoising, super-resolution and compression of 2D- and higher dimensional pixel data.…

Deep generative models have demonstrated their effectiveness in learning latent representation and modeling complex dependencies of time series. In this paper, we present a Smoothness-Inducing Sequential Variational Auto-Encoder (SISVAE)…

Over the last few years, several works have proposed deep learning architectures to learn dynamical systems from observation data with no or little knowledge of the underlying physics. A line of work relies on learning representations where…

This work presents a data-driven Koopman operator-based modeling method using a model averaging technique. While the Koopman operator has been used for data-driven modeling and control of nonlinear dynamics, it is challenging to accurately…

While unsupervised variational autoencoders (VAE) have become a powerful tool in neuroimage analysis, their application to supervised learning is under-explored. We aim to close this gap by proposing a unified probabilistic model for…

This paper proposes Koopman operator-based Stochastic Model Predictive Control (K-SMPC) for enhanced lateral control of autonomous vehicles. The Koopman operator is a linear map representing the nonlinear dynamics in an infinite-dimensional…

Koopman operator theory is a kind of data-driven modelling approach that accurately captures the nonlinearities of mechatronic systems such as vehicles against physics-based methods. However, the infinite-dimensional Koopman operator is…

System representations inspired by the infinite-dimensional Koopman operator (generator) are increasingly considered for predictive modeling. Due to the operator's linearity, a range of nonlinear systems admit linear predictor…