There is a growing consensus that solutions to complex science and engineering problems
require novel methodologies that are able to integrate traditional physics-based modeling …

Abstract Machine learning (ML) methods have become an important tool for modelling and
forecasting complex high-dimensional spatiotemporal datasets such as those found in …

A common strategy for the dimensionality reduction of nonlinear partial differential equations
(PDEs) relies on the use of the proper orthogonal decomposition (POD) to identify a reduced …

ABSTRACT Neural Ordinary Differential Equations (ODEs) are a promising approach to
learn dynamical models from time-series data in science and engineering applications. This …

We investigate the applicability of the machine learning based reduced order model (ML-
ROM) to three-dimensional complex flows. As an example, we consider a turbulent channel …

We apply supervised machine learning techniques to a number of regression problems in
fluid dynamics. Four machine learning architectures are examined in terms of their …

We propose a customized convolutional neural network based autoencoder called a
hierarchical autoencoder, which allows us to extract nonlinear autoencoder modes of flow …

A data-driven framework is proposed towards the end of predictive modeling of complex
spatio-temporal dynamics, leveraging nested non-linear manifolds. Three levels of neural …

Dynamical models underpin our ability to understand and predict the behaviour of natural
systems. Whether dynamical models are developed from first-principles derivations or from …

Complex system simulation has been playing an irreplaceable role in understanding,
predicting, and controlling diverse complex systems. In the past few decades, the multi-scale …