Related papers: Geometric Dictionary Learning of Dynamical Systems…

Geometric deep learning (GDL) deals with supervised learning on data domains that go beyond Euclidean structure, such as data with graph or manifold structure. Due to the demand that arises from application-related data, there is a need to…

Uncovering the underlying ordinary differential equations (ODEs) that govern dynamic systems is crucial for advancing our understanding of complex phenomena. Traditional symbolic regression methods often struggle to capture the temporal…

Observable operator models (OOMs) and related models are one of the most important and powerful tools for modeling and analyzing stochastic systems. They exactly describe dynamics of finite-rank systems and can be efficiently and…

This paper presents a linear dynamical operator described in terms of a rational transfer function, endowed with a well-defined and efficient back-propagation behavior for automatic derivatives computation. The operator enables end-to-end…

Koopman spectral theory has provided a new perspective in the field of dynamical systems in recent years. Modern dynamical systems are becoming increasingly non-linear and complex, and there is a need for a framework to model these systems…

Existing operator learning methods rely on supervised training with high-fidelity simulation data, introducing significant computational cost. In this work, we propose the deep Onsager operator learning (DOOL) method, a novel unsupervised…

A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as `machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time. Special…

Multivariate oscillatory signals from complex systems often exhibit non-stationary dynamics and metastable regime structure, making dynamical interpretation challenging. We introduce a ``dynamical microscope'' framework that converts…

Originally introduced in the fluid mechanics community, dynamic mode decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of nonlinear systems. However, existing DMD theory deals primarily with sequential time…

In this paper, we propose an analysis mechanism based structured Analysis Discriminative Dictionary Learning (ADDL) framework. ADDL seamlessly integrates the analysis discriminative dictionary learning, analysis representation and analysis…

Dynamical systems are used to model a variety of phenomena in which the bifurcation structure is a fundamental characteristic. Here we propose a statistical machine-learning approach to derive lowdimensional models that automatically…

Discovering the symbols and rules that can be used in long-horizon planning from a robot's unsupervised exploration of its environment and continuous sensorimotor experience is a challenging task. The previous studies proposed learning…

The modeling and simulation of high-dimensional multiscale systems is a critical challenge across all areas of science and engineering. It is broadly believed that even with today's computer advances resolving all spatiotemporal scales…

Data assimilation algorithms estimate the state of a dynamical system from partial observations, where the successful performance of these algorithms hinges on costly parameter tuning and on employing an accurate model for the dynamics.…

Data-driven learning is rapidly evolving and places a new perspective on realizing state-space dynamical systems. However, dynamical systems derived from nonlinear ordinary differential equations (ODEs) suffer from limitations in…

Dynamical systems models such as recurrent neural networks (RNNs) are increasingly popular in theoretical neuroscience for hypothesis-generation and data analysis. Evaluating the dynamics in such models is key to understanding their learned…

The feasibility of deep neural networks (DNNs) to address data stream problems still requires intensive study because of the static and offline nature of conventional deep learning approaches. A deep continual learning algorithm, namely…

Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…

DAMON leverages manifold learning and variational autoencoding to achieve obstacle avoidance, allowing for motion planning through adaptive graph traversal in a pre-learned low-dimensional hierarchically-structured manifold graph that…

Differential equations are widely used to describe complex dynamical systems with evolving parameters in nature and engineering. Effectively learning a family of maps from the parameter function to the system dynamics is of great…