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Understanding how deep neural networks learn remains a fundamental challenge in modern machine learning. A growing body of evidence suggests that training dynamics undergo a distinct phase transition, yet our understanding of this…

El Ni\~no-Southern Oscillation (ENSO) exerts global climate and societal impacts, but real-time prediction with lead times beyond one year remains challenging. Dynamical models suffer from large biases and uncertainties, while deep learning…

We introduce a data-driven learning framework that assimilates two powerful ideas: ideal large eddy simulation (LES) from turbulence closure modeling and neural stochastic differential equations (SDE) for stochastic modeling. The ideal LES…

Convolutional neural networks (CNNs) have achieved remarkable performance in various fields, particularly in the domain of computer vision. However, why this architecture works well remains to be a mystery. In this work we move a small step…

We present a new model, Predictive State Recurrent Neural Networks (PSRNNs), for filtering and prediction in dynamical systems. PSRNNs draw on insights from both Recurrent Neural Networks (RNNs) and Predictive State Representations (PSRs),…

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…

The robotic systems continuously interact with complex dynamical systems in the physical world. Reliable predictions of spatiotemporal evolution of these dynamical systems, with limited knowledge of system dynamics, are crucial for…

The success of deep learning techniques over the last decades has opened up a new avenue of research for weather forecasting. Here, we take the novel approach of using a neural network to predict full probability density functions at each…

This work presents a novel methodology for analysis and control of nonlinear fluid systems using neural networks. The approach is demonstrated on four different study cases being the Lorenz system, a modified version of the…

Neural networks for structured data like graphs have been studied extensively in recent years. To date, the bulk of research activity has focused mainly on static graphs. However, most real-world networks are dynamic since their topology…

It is widely accepted that the complex dynamics characteristic of recurrent neural circuits contributes in a fundamental manner to brain function. Progress has been slow in understanding and exploiting the computational power of recurrent…

Recently, a general data driven numerical framework has been developed for learning and modeling of unknown dynamical systems using fully- or partially-observed data. The method utilizes deep neural networks (DNNs) to construct a model for…

The study of deep recurrent neural networks (RNNs) and, in particular, of deep Reservoir Computing (RC) is gaining an increasing research attention in the neural networks community. The recently introduced Deep Echo State Network (DeepESN)…

We propose an end-to-end trained neural networkarchitecture to robustly predict the complex dynamics of fluid flows with high temporal stability. We focus on single-phase smoke simulations in 2D and 3D based on the incompressible…

In this paper, we explore the predictive capabilities of echo state networks (ESNs) for the generalized Kuramoto-Sivashinsky (gKS) equation, an archetypal nonlinear PDE that exhibits spatiotemporal chaos. Our research focuses on predicting…

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)…

Neural networks are known to be effective function approximators. Recently, deep neural networks have proven to be very effective in pattern recognition, classification tasks and human-level control to model highly nonlinear realworld…

In the field of complex dynamics, multistable attractors have been gaining a significant attention due to its unpredictability in occurrence and extreme sensitivity to initial conditions. Co-existing attractors are abundant in diverse…

Differential equations are a ubiquitous tool to study dynamics, ranging from physical systems to complex systems, where a large number of agents interact through a graph with non-trivial topological features. Data-driven approximations of…

Forecasting time series with extreme events has been a challenging and prevalent research topic, especially when the time series data are affected by complicated uncertain factors, such as is the case in hydrologic prediction. Diverse…