相关论文: Deep learning Markov and Koopman models with physi…
This paper presents a unified and scalable framework for predictive and safe autonomous navigation in dynamic transportation environments by integrating model predictive control (MPC) with distributed Koopman operator learning.…
We present a data-driven modeling strategy to overcome improperly modeled dynamics for systems exhibiting complex spatio-temporal behaviors. We propose a Deep Learning framework to resolve the differences between the true dynamics of the…
Koopman operators are infinite-dimensional operators that linearize nonlinear dynamical systems, facilitating the study of their spectral properties and enabling the prediction of the time evolution of observable quantities. Recent methods…
We present a flexible data-driven method for dynamical system analysis that does not require explicit model discovery. The method is rooted in well-established techniques for approximating the Koopman operator from data and is implemented…
We propose a method for inference on moderately high-dimensional, nonlinear, non-Gaussian, partially observed Markov process models for which the transition density is not analytically tractable. Markov processes with intractable transition…
The Koopman operator is a mathematical tool that allows for a linear description of non-linear systems, but working in infinite dimensional spaces. Dynamic Mode Decomposition and Extended Dynamic Mode Decomposition are amongst the most…
Data-driven machine learning (ML) models are reshaping weather forecasting and have shown the potential to accelerate and surpass traditional physics-based approaches, leading to a second revolution in the field after data assimilation.…
The generalized Langevin equation is used as a model for various coarse-grained physical processes, e.g., the time evolution of the velocity of a given larger particle in an implicitly represented solvent, when the relevant time scales of…
Koopman linear representations have become a popular tool for control design of nonlinear systems, yet it remains unclear when such representations are exact. In this paper, we establish sufficient and necessary conditions under which a…
Nonlinear models and optimization methods have successfully tackled a rapidly growing set of problems in recent years. Indeed, a relatively small toolbox of such models and methods can provide sufficient performance across a large landscape…
Many important problems in the real world don't have unique solutions. It is thus important for machine learning models to be capable of proposing different plausible solutions with meaningful probability measures. In this work we introduce…
Dynamic relational processes, such as e-mail exchanges, bank loans and scientific citations, are important examples of dynamic networks, in which the relational events consistute time-stamped edges. There are contexts where the network…
Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many…
Quantum Machine Learning (QML) is considered to be one of the most promising applications of near term quantum devices. However, the optimization of quantum machine learning models presents numerous challenges arising from the imperfections…
The simulation of quantum many-body systems poses a significant challenge in physics due to the exponential scaling of Hilbert space with the number of particles. Traditional methods often struggle with large system sizes and frustrated…
In recent years there has been a considerable drive towards data-driven analysis, discovery and control of dynamical systems. To this end, operator theoretic methods, namely, Koopman operator methods have gained a lot of interest. In…
Dynamical models estimate and predict the temporal evolution of physical systems. State Space Models (SSMs) in particular represent the system dynamics with many desirable properties, such as being able to model uncertainty in both the…
Among several tasks in Machine Learning, a specially important one is that of inferring the latent variables of a system and their causal relations with the observed behavior. Learning a Hidden Markov Model of given stochastic process is a…
Numerous physics theories are rooted in partial differential equations (PDEs). However, the increasingly intricate physics equations, especially those that lack analytic solutions or closed forms, have impeded the further development of…
We consider the general class of time-homogeneous stochastic dynamical systems, both discrete and continuous, and study the problem of learning a representation of the state that faithfully captures its dynamics. This is instrumental to…