Related papers: Learning dynamical systems: an example from open q…
We define an observable-space framework of Quantum Koopman Algorithms (QKAs) for simulating the dynamics of both linear quantum and nonlinear classical systems, based on approximately closed sets of observables and efficient coherent…
Remote state monitoring over wireless is envisaged to play a pivotal role in enabling beyond 5G applications ranging from remote drone control to remote surgery. One key challenge is to identify the system dynamics that is non-linear with a…
We analyze the performance of Dynamic Mode Decomposition (DMD)-based approximations of the stochastic Koopman operator for random dynamical systems where either the dynamics or observables are affected by noise. For many DMD algorithms, the…
The control of legged robots, particularly humanoid and quadruped robots, presents significant challenges due to their high-dimensional and nonlinear dynamics. While linear systems can be effectively controlled using methods like Model…
This paper explores a simple question: can we model the internal transformations of a neural network using dynamical systems theory? We introduce Koopman autoencoders to capture how neural representations evolve through network layers,…
Time series prediction (TSP) has been widely used in various fields, such as life sciences and finance, to forecast future trends based on historical data. However, to date, there has been relatively little research conducted on the TSP for…
We present that, instead of establishing the equations of motion, one can model-freely reveal the dynamical properties of a black-box system using a learning machine. Trained only by a segment of time series of a state variable recorded at…
The advent of easy access to large amount of data has sparked interest in directly developing the relationships between input and output of dynamic systems. A challenge is that in addition to the applied input and the measured output, the…
In this work, we introduce Dissipative SymODEN, a deep learning architecture which can infer the dynamics of a physical system with dissipation from observed state trajectories. To improve prediction accuracy while reducing network size,…
Recent advances in diffusion-based robot policies have demonstrated significant potential in imitating multi-modal behaviors. However, these approaches typically require large quantities of demonstration data paired with corresponding robot…
The modeling of nonlinear dynamics based on Koopman operator theory, which is originally applicable only to autonomous systems with no control, is extended to non-autonomous control system without approximation to input matrix B. Prevailing…
Experimental data bases are typically very large and high dimensional. To learn from them requires to recognize important features (a pattern), often present at scales different to that of the recorded data. Following the experience…
Exact numerical simulations of dynamics of open quantum systems often require immense computational resources. We demonstrate that a deep artificial neural network comprised of convolutional layers is a powerful tool for predicting…
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…
The Koopman operator framework can be used to identify a data-driven model of a nonlinear system. Unfortunately, when the data is corrupted by noise, the identified model can be biased. Additionally, depending on the choice of lifting…
This paper introduces a novel approach for modeling the dynamics of soft robots, utilizing a differentiable filter architecture. The proposed approach enables end-to-end training to learn system dynamics, noise characteristics, and temporal…
The Koopman operator has become a celebrated tool in modern dynamical systems theory for analyzing and interpreting both models and datasets. The linearity of the Koopman operator means that important characteristics about it, and in turn…
The Koopman operator and its data-driven approximations, such as extended dynamic mode decomposition (EDMD), are widely used for analysing, modelling, and controlling nonlinear dynamical systems. However, when the true Koopman…
Dynamic sampling mechanisms in deep learning architectures have demonstrated utility across many computer vision models, though the theoretical analysis of these structures has not yet been unified. In this paper we connect the various…
Physical learning is an emerging paradigm in science and engineering whereby (meta)materials acquire desired macroscopic behaviors by exposure to examples. So far, it has been applied to static properties such as elastic moduli and…