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Short-term load forecasting (STLF) is challenging due to complex time series (TS) which express three seasonal patterns and a nonlinear trend. This paper proposes a novel hybrid hierarchical deep learning model that deals with multiple…

Multivariate geo-sensory time series prediction is challenging because of the complex spatial and temporal correlation. In urban water distribution systems (WDS), numerous spatial-correlated sensors have been deployed to continuously…

In this paper we introduce a new framework to train an Echo State Network to predict real valued time-series. The method consists in projecting the output of the internal layer of the network on a space with lower dimensionality, before…

Unsupervised structure learning in high-dimensional time series data has attracted a lot of research interests. For example, segmenting and labelling high dimensional time series can be helpful in behavior understanding and medical…

Nudging is an empirical data assimilation technique that incorporates an observation-driven control term into the model dynamics. The trajectory of the nudged system approaches the true system trajectory over time, even when the initial…

State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse…

Recurrent Neural Networks (RNNs) have demonstrated their outstanding ability in sequence tasks and have achieved state-of-the-art in wide range of applications, such as industrial, medical, economic and linguistic. Echo State Network (ESN)…

The El Ni\~{n}o-Southern Oscillation (ENSO) is a dominant mode of interannual climate variability, yet the mechanisms limiting its long-lead predictability remain unclear. Here we develop a physics-guided Deep Echo State Network (DESN) that…

Motivated by objects such as electric fields or fluid streams, we study the problem of learning stochastic fields, i.e. stochastic processes whose samples are fields like those occurring in physics and engineering. Considering general…

I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…

Chaos arises in many complex dynamical systems, from weather to power grids, but is difficult to accurately model using data-driven emulators, including neural operator architectures. For chaotic systems, the inherent sensitivity to initial…

We introduce a robust framework for learning various generalized Hamiltonian dynamics from noisy, sparse phase-space data and in an unsupervised manner based on variational Bayesian inference. Although conservative, dissipative, and…

In this paper, we develop a kernel learning backward SDE filter method to estimate the state of a stochastic dynamical system based on its partial noisy observations. A system of forward backward stochastic differential equations is used to…

A vast majority of spiking neural networks (SNNs) are trained based on inductive biases that are not necessarily a good fit for several critical tasks that require low-latency and power efficiency. Inferring brain behavior based on the…

Artificial neural networks (ANNs) are known to be powerful methods for many hard problems (e.g. image classification, speech recognition or time series prediction). However, these models tend to produce black-box results and are often…

Latent linear dynamical systems with Bernoulli observations provide a powerful modeling framework for identifying the temporal dynamics underlying binary time series data, which arise in a variety of contexts such as binary decision-making…

Ocean current, fluid mechanics, and many other spatio-temporal physical dynamical systems are essential components of the universe. One key characteristic of such systems is that certain physics laws -- represented as ordinary/partial…

In reservoir computing, an input sequence is processed by a recurrent neural network, the reservoir, which transforms it into a spatial pattern that a shallow readout network can then exploit for tasks such as memorization and time-series…

This study analyzes Graph Neural Networks (GNNs) for distribution system state estimation (DSSE) by employing an interpretable Graph Neural Additive Network (GNAN) and by utilizing an edge-conditioned message-passing mechanism. The…

We propose the Automatic-differentiated Physics-Informed Echo State Network (API-ESN). The network is constrained by the physical equations through the reservoir's exact time-derivative, which is computed by automatic differentiation. As…