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This paper presents the results of identification of vehicle dynamics using the Koopman operator. The basic idea is to transform the state space of a nonlinear system (a car in our case) to a higher-dimensional space, using so-called basis…
This paper addresses the challenge of overfitting in the learning of dynamical systems by introducing a novel approach for the generation of synthetic data, aimed at enhancing model generalization and robustness in scenarios characterized…
We use Koopman theory for data-driven model reduction of nonlinear dynamical systems with controls. We propose generic model structures combining delay-coordinate encoding of measurements and full-state decoding to integrate reduced Koopman…
The Bayesian inference approach is widely used to tackle inverse problems due to its versatile and natural ability to handle ill-posedness. However, it often faces challenges when dealing with situations involving continuous fields or…
Data generated from dynamical systems with unknown dynamics enable the learning of state observers that are: robust to modeling error, computationally tractable to design, and capable of operating with guaranteed performance. In this paper,…
We propose a deep generative approach to sampling from a conditional distribution based on a unified formulation of conditional distribution and generalized nonparametric regression function using the noise-outsourcing lemma. The proposed…
We present a numerical method to learn an accurate predictive model for an unknown stochastic dynamical system from its trajectory data. The method seeks to approximate the unknown flow map of the underlying system. It employs the idea of…
Markov processes serve as a universal model for many real-world random processes. This paper presents a data-driven approach for learning these models through the spectral decomposition of the infinitesimal generator (IG) of the Markov…
Neural network based generative models with discriminative components are a powerful approach for semi-supervised learning. However, these techniques a) cannot account for model uncertainty in the estimation of the model's discriminative…
One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…
This paper presents a novel episodic method to learn a robot's nonlinear dynamics model and an increasingly optimal control sequence for a set of tasks. The method is based on the {\em Koopman operator} approach to nonlinear dynamical…
This paper proposes a Koopman-based framework for modeling, prediction, and control of unknown nonlinear time-varying systems. We present a novel Koopman-based learning method for predicting the state of unknown nonlinear time-varying…
Iterative algorithms are of utmost importance in decision and control. With an ever growing number of algorithms being developed, distributed, and proprietarized, there is a similarly growing need for methods that can provide classification…
Modeling financial time series by stochastic processes is a challenging task and a central area of research in financial mathematics. As an alternative, we introduce Quant GANs, a data-driven model which is inspired by the recent success of…
Transfer operators offer linear representations and global, physically meaningful features of nonlinear dynamical systems. Discovering transfer operators, such as the Koopman operator, require careful crafted dictionaries of observables,…
Dynamical models identified from data are frequently employed in control system design. However, decoupling system identification from controller synthesis can result in situations where no suitable controller exists after a model has been…
Recent advances in semi-supervised learning with deep generative models have shown promise in generalizing from small labeled datasets ($\mathbf{x},\mathbf{y}$) to large unlabeled ones ($\mathbf{x}$). In the case where the codomain has…
We propose a transfer learning method that utilizes data representations in a semiparametric regression model. Our aim is to perform statistical inference on the parameter of primary interest in the target model while accounting for…
Education is a dynamic field that must be adaptable to sudden changes and disruptions caused by events like pandemics, war, and natural disasters related to climate change. When these events occur, traditional classrooms with traditional or…
This paper describes a method for learning low-dimensional approximations of nonlinear dynamical systems, based on neural-network approximations of the underlying Koopman operator. Extended Dynamic Mode Decomposition (EDMD) provides a…