Related papers: Generalizing across Temporal Domains with Koopman …

Koopman operators and transfer operators represent dynamical systems through their induced linear action on vector spaces of observables, enabling the use of operator-theoretic techniques to analyze nonlinear dynamics in state space. The…

This paper contributes a theoretical framework for data-driven feedback linearization of nonlinear control-affine systems. We unify the traditional geometric perspective on feedback linearization with an operator-theoretic perspective…

The Koopman operator, as a linear representation of a nonlinear dynamical system, has been attracting attention in many fields of science. Recently, Koopman operator theory has been combined with another concept that is popular in data…

We study the evolution of distributions under the action of an ergodic dynamical system, which may be stochastic in nature. By employing tools from Koopman and transfer operator theory one can evolve any initial distribution of the state…

An important goal common to domain adaptation and causal inference is to make accurate predictions when the distributions for the source (or training) domain(s) and target (or test) domain(s) differ. In many cases, these different…

We address the fundamental question of why deep neural networks generalize by establishing a pointwise generalization theory for fully connected networks. This framework resolves long-standing barriers to characterizing the rich nonlinear…

Foundation models have achieved remarkable success across diverse machine-learning domains through large-scale pretraining on large, diverse datasets. However, pretraining on such datasets introduces significant challenges due to…

Temporal graph learning is pivotal for deciphering dynamic systems, where the core challenge lies in explicitly modeling the underlying evolving patterns that govern network transformation. However, prevailing methods are predominantly…

Deep learning based approaches have been utilized to model and generate graphs subjected to different distributions recently. However, they are typically unsupervised learning based and unconditioned generative models or simply conditioned…

Multivariate time series analysis is becoming an integral part of data analysis pipelines. Understanding the individual time point connections between covariates as well as how these connections change in time is non-trivial. To this aim,…

Continual domain shift poses a significant challenge in real-world applications, particularly in situations where labeled data is not available for new domains. The challenge of acquiring knowledge in this problem setting is referred to as…

The design and analysis of optimal control policies for dynamical systems can be complicated by nonlinear dependence in the state variables. Koopman operators have been used to simplify the analysis of dynamical systems by mapping the flow…

Dynamical systems provide a comprehensive way to study complex and changing behaviors across various sciences. Many modern systems are too complicated to analyze directly or we do not have access to models, driving significant interest in…

Koopman operator theory has served as the basis to extract dynamics for nonlinear system modeling and control across settings, including non-holonomic mobile robot control. There is a growing interest in research to derive robustness…

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…

Analyzing the inner mechanisms of deep neural networks is a fundamental task in machine learning. Existing work provides limited analysis or it depends on local theories, such as fixed-point analysis. In contrast, we propose to analyze…

Approaches based on Koopman operators have shown great promise in forecasting time series data generated by complex nonlinear dynamical systems (NLDS). Although such approaches are able to capture the latent state representation of a NLDS,…

Koopman operator theory has found significant success in learning models of complex, real-world dynamical systems, enabling prediction and control. The greater interpretability and lower computational costs of these models, compared to…

Koopman operator theory provides a framework for nonlinear dynamical system analysis and time-series forecasting by mapping dynamics to a space of real-valued measurement functions, enabling a linear operator representation. Despite the…

An essential problem in domain adaptation is to understand and make use of distribution changes across domains. For this purpose, we first propose a flexible Generative Domain Adaptation Network (G-DAN) with specific latent variables to…