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A new variational mode decomposition (VMD) based deep learning approach is proposed in this paper for time series forecasting problem. Firstly, VMD is adopted to decompose the original time series into several sub-signals. Then, a…
Offline estimation of the dynamical model of a Markov Decision Process (MDP) is a non-trivial task that greatly depends on the data available in the learning phase. Sometimes the dynamics of the model is invariant with respect to some…
Modal analysis has long been consolidated as a basic tool to interpret dynamics and build low-order models of mechanical, thermal, and fluid systems. Eigenmodes arising from the spectral decomposition of the underlying linearized dynamics…
We propose a new method for computing Dynamic Mode Decomposition (DMD) evolution matrices, which we use to analyze dynamical systems. Unlike the majority of existing methods, our approach is based on a variational formulation consisting of…
Numerical approximation methods for the Koopman operator have advanced considerably in the last few years. In particular, data-driven approaches such as dynamic mode decomposition (DMD) and its generalization, the extended-DMD (EDMD), are…
Diffusion models are a powerful tool for probabilistic forecasting, yet most applications in high-dimensional complex systems predict future states individually. This approach struggles to model complex temporal dependencies and fails to…
Although instantaneous interactions are unphysical, a large variety of maximum entropy statistical inference methods match the model-inferred and the empirically-measured equal-time correlation functions. Focusing on collective motion of…
Modelling biological or engineering swarms is challenging due to the inherently high dimension of the system, despite the often low-dimensional emergent dynamics. Most existing swarm modelling approaches are based on first principles and…
Masked Diffusion Models (MDMs) offer flexible, non-autoregressive generation, but this freedom introduces a challenge: final output quality is highly sensitive to the decoding order. We are the first to formalize this issue, attributing the…
Model usage is the central challenge of model-based reinforcement learning. Although dynamics model based on deep neural networks provide good generalization for single step prediction, such ability is over exploited when it is used to…
Denoising Diffusion Models (DDMs) have become a popular tool for generating high-quality samples from complex data distributions. These models are able to capture sophisticated patterns and structures in the data, and can generate samples…
Methods for out-of-distribution (OOD) detection that scale to 3D data are crucial components of any real-world clinical deep learning system. Classic denoising diffusion probabilistic models (DDPMs) have been recently proposed as a robust…
Reliable and accurate prediction of time series plays a crucial role in maritime industry, such as economic investment, transportation planning, port planning and design, etc. The dynamic growth of maritime time series has the predominantly…
A Multiregression Dynamic Model (MDM) is a class of multivariate time series that represents various dynamic causal processes in a graphical way. One of the advantages of this class is that, in contrast to many other Dynamic Bayesian…
Extracting the latent underlying structures of complex nonlinear local and nonlocal flows is essential for their analysis and modeling. In this work, we attempt to provide a consistent framework through Koopman theory and its related…
A data-driven and equation-free approach is proposed and discussed to model ships maneuvers in waves, based on the dynamic mode decomposition (DMD). DMD is a dimensionality-reduction/reduced-order modeling method, which provides a linear…
This paper discusses the application of Dynamic Mode Decomposition (DMD) to the extraction of modal properties of linear mechanical systems, i.e., experimental modal analysis (EMA). First, theoretical background of the DMD is briefly…
Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…
Discrete diffusion models have emerged as powerful tools for high-quality data generation. Despite their success in discrete spaces, such as text generation tasks, the acceleration of discrete diffusion models remains under-explored. In…
Identifying hidden dynamics from observed data is a significant and challenging task in a wide range of applications. Recently, the combination of linear multistep methods (LMMs) and deep learning has been successfully employed to discover…