Related papers: Koopman Learning with Episodic Memory
In the context of an increasing popularity of data-driven models to represent dynamical systems, many machine learning-based implementations of the Koopman operator have recently been proposed. However, the vast majority of those works are…
Human interpretation of the world encompasses the use of symbols to categorize sensory inputs and compose them in a hierarchical manner. One of the long-term objectives of Computer Vision and Artificial Intelligence is to endow machines…
We propose a novel framework for safe navigation in dynamic environments by integrating Koopman operator theory with conformal prediction. Our approach leverages data-driven Koopman approximation to learn nonlinear dynamics and employs…
In this paper, we develop the Koopman operator theory for dynamical systems with symmetry. In particular, we investigate how the Koopman operator and eigenfunctions behave under the action of the symmetry group of the underlying dynamical…
System representations inspired by the infinite-dimensional Koopman operator (generator) are increasingly considered for predictive modeling. Due to the operator's linearity, a range of nonlinear systems admit linear predictor…
We present a new framework for optimal and feedback control of PDEs using Koopman operator-based reduced order models (K-ROMs). The Koopman operator is a linear but infinite-dimensional operator which describes the dynamics of observables.…
Learning dexterous manipulation skills presents significant challenges due to complex nonlinear dynamics that underlie the interactions between objects and multi-fingered hands. Koopman operators have emerged as a robust method for modeling…
In many real-world scenarios, data to train machine learning models becomes available over time. Unfortunately, these models struggle to continually learn new concepts without forgetting what has been learnt in the past. This phenomenon is…
This work presents a novel data-driven framework for constructing eigenfunctions of the Koopman operator geared toward prediction and control. The method leverages the richness of the spectrum of the Koopman operator away from attractors to…
Accurately finding and predicting dynamics based on the observational data with noise perturbations is of paramount significance but still a major challenge presently. Here, for the Hamiltonian mechanics, we propose the Hamiltonian Neural…
Episodic memory is a psychology term which refers to the ability to recall specific events from the past. We suggest one advantage of this particular type of memory is the ability to easily assign credit to a specific state when remembered…
This paper proposes Koopman operator-based Stochastic Model Predictive Control (K-SMPC) for enhanced lateral control of autonomous vehicles. The Koopman operator is a linear map representing the nonlinear dynamics in an infinite-dimensional…
This paper presents a novel learning framework to construct Koopman eigenfunctions for unknown, nonlinear dynamics using data gathered from experiments. The learning framework can extract spectral information from the full nonlinear…
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…
Embedding learning, a.k.a. representation learning, has been shown to be able to model large-scale semantic knowledge graphs. A key concept is a mapping of the knowledge graph to a tensor representation whose entries are predicted by models…
In the era of big data, the sheer volume and complexity of datasets pose significant challenges in machine learning, particularly in image processing tasks. This paper introduces an innovative Autoencoder-based Dataset Condensation Model…
The Koopman operator is beneficial for analyzing nonlinear and stochastic dynamics; it is linear but infinite-dimensional, and it governs the evolution of observables. The extended dynamic mode decomposition (EDMD) is one of the famous…
Koopman Operator Theory has opened the doors to data-driven learning of globally linear representations of complex nonlinear systems. However, current methodologies for Koopman Operator discovery struggle with uncertainty quantification and…
In this paper, a novel Koopman-type inverse operator for linear time-invariant non-minimum phase systems with stochastic disturbances is proposed. This operator employs functions of the desired output to directly calculate the input.…
Reinforcement Learning (RL) has made significant strides in various domains, and policy gradient methods like Proximal Policy Optimization (PPO) have gained popularity due to their balance in performance, training stability, and…