Related papers: Meta-Learning for Koopman Spectral Analysis with S…

Multivariate time series forecasting, which analyzes historical time series to predict future trends, can effectively help decision-making. Complex relations among variables in MTS, including static, dynamic, predictable, and latent…

The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode…

This paper presents a distributed Koopman operator learning framework for modeling unknown nonlinear dynamics using sequential observations from multiple agents. Each agent estimates a local Koopman approximation based on lifted data and…

We present an approach to construct approximate Koopman-type decompositions for dynamical systems depending on static or time-varying parameters. Our method simultaneously constructs an invariant subspace and a parametric family of…

We provide a framework for learning of dynamical systems rooted in the concept of representations and Koopman operators. The interplay between the two leads to the full description of systems that can be represented linearly in a finite…

The Koopman operator provides a linear perspective on non-linear dynamics by focusing on the evolution of observables in an invariant subspace. Observables of interest are typically linearly reconstructed from the Koopman eigenfunctions.…

Analyzing temporal developments is crucial for the accurate prognosis of many medical conditions. Temporal changes that occur over short time scales are key to assessing the health of physiological functions, such as the cardiac cycle.…

Pre-trained Large Language Models (LLMs) encapsulate large amounts of knowledge and take enormous amounts of compute to train. We make use of this resource, together with the observation that LLMs are able to transfer knowledge and…

Meta-learning approaches have shown great success in vision and language domains. However, few studies discuss the practice of meta-learning for large-scale industrial applications. Although e-commerce companies have spent many efforts on…

Data-driven models for nonlinear dynamical systems based on approximating the underlying Koopman operator or generator have proven to be successful tools for forecasting, feature learning, state estimation, and control. It has become well…

Constructing good representations is critical for learning complex tasks in a sample efficient manner. In the context of meta-learning, representations can be constructed from common patterns of previously seen tasks so that a future task…

In research areas with scarce data, representation learning plays a significant role. This work aims to enhance representation learning for clinical time series by deriving universal embeddings for clinical features, such as heart rate and…

Koopman operators linearize nonlinear dynamical systems, making their spectral information of crucial interest. Numerous algorithms have been developed to approximate these spectral properties, and Dynamic Mode Decomposition (DMD) stands…

Graph Neural Networks (GNNs) are a framework for graph representation learning, where a model learns to generate low dimensional node embeddings that encapsulate structural and feature-related information. GNNs are usually trained in an…

The rapid adoption of deep learning has increasingly led to data-driven models replacing classical model-based algorithms, even in domains governed by well-understood physical laws. While data-driven models, such as long short-term memory…

Nonlinear dynamical effects are crucial to the operation of many agile robotic systems. Koopman-based model learning methods can capture these nonlinear dynamical system effects in higher dimensional lifted bilinear models that are amenable…

In the early observation period of a time series, there might be only a few historic observations available to learn a model. However, in cases where an existing prior set of datasets is available, Meta learning methods can be applicable.…

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…

Nonlinear coupled systems are ubiquitous in science and engineering. The analysis and modeling of such systems is challenging due to their high dimensionality and complex interactions among subsystems. In recent years, operator-theoretic…

We propose a machine-learning approach to model long-term out-of-sample dynamics of brain activity from task-dependent fMRI data. Our approach is a three stage one. First, we exploit Diffusion maps (DMs) to discover a set of variables that…