Related papers: $K^2$VAE: A Koopman-Kalman Enhanced Variational Au…

Time-series forecasting often faces challenges due to data volatility, which can lead to inaccurate predictions. Variational Mode Decomposition (VMD) has emerged as a promising technique to mitigate volatility by decomposing data into…

Reliable uncertainty quantification is critical in multivariate time series forecasting problems arising in domains such as energy systems and transportation networks, among many others. Although Transformer-based architectures have…

Long-term time series forecasting (LTSF) involves predicting a large number of future values of a time series based on the past values. This is an essential task in a wide range of domains including weather forecasting, stock market…

This paper proposes a unified family of learnable Koopman operator parameterizations that integrate linear dynamical systems theory with modern deep learning forecasting architectures. We introduce four learnable Koopman…

In today's data-driven landscape, time series forecasting is pivotal in decision-making across various sectors. Yet, the proliferation of more diverse time series data, coupled with the expanding landscape of available forecasting methods,…

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…

The variational autoencoder (VAE) framework is a popular option for training unsupervised generative models, featuring ease of training and latent representation of data. The objective function of VAE does not guarantee to achieve the…

Wind energy is a widely distributed, renewable, and environmentally friendly energy source that plays a crucial role in mitigating global warming and addressing energy shortages. Nevertheless, wind power generation is characterized by…

This paper presents VAEneu, an innovative autoregressive method for multistep ahead univariate probabilistic time series forecasting. We employ the conditional VAE framework and optimize the lower bound of the predictive distribution…

Principal Component Analysis (PCA) minimizes the reconstruction error given a class of linear models of fixed component dimensionality. Probabilistic PCA adds a probabilistic structure by learning the probability distribution of the PCA…

Due to the non-stationary nature, the distribution of real-world multivariate time series (MTS) changes over time, which is known as distribution drift. Most existing MTS forecasting models greatly suffer from distribution drift and degrade…

We develop a Bayesian framework for variable selection in linear regression with autocorrelated errors, accommodating lagged covariates and autoregressive structures. This setting occurs in time series applications where responses depend on…

We propose a variational autoencoder (VAE) approach for parameter estimation in nonlinear mixed-effects models based on ordinary differential equations (NLME-ODEs) using longitudinal data from multiple subjects. In moderate dimensions,…

We introduce Flexi-VAE, a data-driven framework for efficient single-shot forecasting of nonlinear parametric partial differential equations (PDEs), eliminating the need for iterative time-stepping while maintaining high accuracy and…

Multi-scale decomposition architectures have emerged as predominant methodologies in time series forecasting. However, real-world time series exhibit noise interference across different scales, while heterogeneous information distribution…

Time series forecasting is critical for decision-making across dynamic domains such as energy, finance, transportation, and cloud computing. However, real-world time series often exhibit non-stationarity, including temporal distribution…

We study the Extended Kalman Filter in constant dynamics, offering a bayesian perspective of stochastic optimization. We obtain high probability bounds on the cumulative excess risk in an unconstrained setting. In order to avoid any…

Long-horizon dynamical prediction is fundamental in robotics and control, underpinning canonical methods like model predictive control. Yet, many systems and disturbance phenomena are difficult to model due to effects like nonlinearity,…

This paper proposes a novel approach for modeling and controlling nonlinear systems with varying parameters. The approach introduces the use of a parameter-varying Koopman operator (PVKO) in a lifted space, which provides an efficient way…

Variational Autoencoder (VAE) is widely used as a generative model to approximate a model's posterior on latent variables by combining the amortized variational inference and deep neural networks. However, when paired with strong…