相关论文: Meta-Learning for Koopman Spectral Analysis with S…

A popular technique used to obtain linear representations of nonlinear systems is the so-called Koopman approach, where the nonlinear dynamics are lifted to a (possibly infinite dimensional) linear space through nonlinear functions called…

Real-world time series are often governed by complex nonlinear dynamics. Understanding these underlying dynamics is crucial for precise future prediction. While deep learning has achieved major success in time series forecasting, many…

We propose a meta-learning method for semi-supervised learning that learns from multiple tasks with heterogeneous attribute spaces. The existing semi-supervised meta-learning methods assume that all tasks share the same attribute space,…

Recent advancements in language modeling have shown promising results when applied to time series data. In particular, fine-tuning pre-trained large language models (LLMs) for time series classification tasks has achieved state-of-the-art…

This paper develops data-driven methods to identify eigenfunctions of the Koopman operator associated to a dynamical system and subspaces that are invariant under the operator. We build on Extended Dynamic Mode Decomposition (EDMD), a…

This paper explores learning emulators for parameter estimation with uncertainty estimation of high-dimensional dynamical systems. We assume access to a computationally complex simulator that inputs a candidate parameter and outputs a…

Stochastic neighbor embedding (SNE) and related nonlinear manifold learning algorithms achieve high-quality low-dimensional representations of similarity data, but are notoriously slow to train. We propose a generic formulation of embedding…

The Koopman operator has gained significant attention in recent years for its ability to verify evolutionary properties of continuous-time nonlinear systems by lifting state variables into an infinite-dimensional linear vector space. The…

Learning dynamical models from data plays a vital role in engineering design, optimization, and predictions. Building models describing dynamics of complex processes (e.g., weather dynamics, or reactive flows) using empirical knowledge or…

Recent research on time-series self-supervised models shows great promise in learning semantic representations. However, it has been limited to small-scale datasets, e.g., thousands of temporal sequences. In this work, we make key technical…

Can meta-learning discover generic ways of processing time series (TS) from a diverse dataset so as to greatly improve generalization on new TS coming from different datasets? This work provides positive evidence to this using a broad…

The paper presents a framework for online learning of the Koopman operator using streaming data. Many complex systems for which data-driven modeling and control are sought provide streaming sensor data, the abundance of which can present…

Time series prediction with deep learning methods, especially long short-term memory neural networks (LSTMs), have scored significant achievements in recent years. Despite the fact that the LSTMs can help to capture long-term dependencies,…

Extracting previously unknown patterns and information in time series is central to many real-world applications. In this study, we introduce a novel approach to modeling financial time series using a deep learning model. We use a Long…

Network representation learning, as an approach to learn low dimensional representations of vertices, has attracted considerable research attention recently. It has been proven extremely useful in many machine learning tasks over large…

Quantum computation offers potential exponential speedups for simulating certain physical systems, but its application to nonlinear dynamics is inherently constrained by the requirement of unitary evolution. We propose the quantum Koopman…

Developing agents that can perform complex control tasks from high-dimensional observations is a core ability of autonomous agents that requires underlying robust task control policies and adapting the underlying visual representations to…

Koopman operator theory is a key tool in data assimilation of complex dynamical systems, with the potential to be applied to multimodal data. We formulate the problem of learning Koopman eigenfunctions from observations at arbitrary,…

Koopman operator theory offers a rigorous treatment of dynamics and has been emerging as an alternative modeling and learning-based control method across various robotics sub-domains. Due to its ability to represent nonlinear dynamics as a…

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…