相关论文: Augmented Invertible Koopman Autoencoder for long-…

Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular numerical algorithm for Koopman spectral analysis; however, we often…

Understanding intraventricular hemodynamics requires compact and physically interpretable representations of the underlying flow structures, as characteristic flow patterns are closely associated with cardiovascular conditions and can…

While Koopman-based techniques like extended Dynamic Mode Decomposition are nowadays ubiquitous in the data-driven approximation of dynamical systems, quantitative error estimates were only recently established. To this end, both sources of…

We present the Koopman State Estimator (KoopSE), a framework for model-free batch state estimation of control-affine systems that makes no linearization assumptions, requires no problem-specific feature selections, and has an inference…

It is hard to identify nonlinear biological models strictly from data, with results that are often sensitive to experimental conditions. Automated experimental workflows and liquid handling enables unprecedented throughput, as well as the…

We propose a cross-domain latent modulation mechanism within a variational autoencoders (VAE) framework to enable improved transfer learning. Our key idea is to procure deep representations from one data domain and use it as perturbation to…

We introduce the Rigged Dynamic Mode Decomposition (Rigged DMD) algorithm, which computes generalized eigenfunction decompositions of Koopman operators. By considering the evolution of observables, Koopman operators transform complex…

Probabilistic forecasting of complex phenomena is paramount to various scientific disciplines and applications. Despite the generality and importance of the problem, general mathematical techniques that allow for stable long-term forecasts…

We propose a novel algorithm for quantizing continuous latent representations in trained models. Our approach applies to deep probabilistic models, such as variational autoencoders (VAEs), and enables both data and model compression. Unlike…

Optimization of rotating electrical machines is both time- and computationally expensive. Because of the different parametrization, design optimization is commonly executed separately for each machine technology. In this paper, we present…

Multivariate Time Series forecasting has been an increasingly popular topic in various applications and scenarios. Recently, contrastive learning and Transformer-based models have achieved good performance in many long-term series…

Data-driven flow-field reconstruction typically relies on autoencoder architectures that compress high-dimensional states into low-dimensional latent representations. However, classical approaches such as variational autoencoders (VAEs)…

The Koopman operator lifts nonlinear dynamical systems into a functional space of observables, where the dynamics are linear. In this paper, we provide three different Koopman representations for hybrid systems. The first is specific to…

Extended Dynamic Mode Decomposition (EDMD) is an algorithm that approximates the action of the Koopman operator on an $N$-dimensional subspace of the space of observables by sampling at $M$ points in the state space. Assuming that the…

Koopman operators linearize nonlinear dynamical systems, making their spectral information of crucial interest. Numerous algorithms have been developed to approximate these spectral properties, and Dynamic Mode Decomposition (DMD) stands…

Simulations of large-scale dynamical systems require expensive computations. Low-dimensional parametrization of high-dimensional states such as Proper Orthogonal Decomposition (POD) can be a solution to lessen the burdens by providing a…

Recently Autoencoder(AE) based models are widely used in the field of anomaly detection. A model trained with normal data generates a larger restoration error for abnormal data. Whether or not abnormal data is determined by observing the…

While proper orthogonal decomposition (POD)-based surrogates are widely explored for hydrodynamic applications, the use of Koopman autoencoders for real-world coastal-ocean modelling remains relatively limited. This paper introduces a…

Using the information theory, this study provides insights into how the construction of latent space of autoencoder (AE) using deep neural network (DNN) training finds a smooth low-dimensional manifold in the stiff dynamical system. Our…

We present a coupled Variational Auto-Encoder (VAE) method that improves the accuracy and robustness of the probabilistic inferences on represented data. The new method models the dependency between input feature vectors (images) and weighs…