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Collecting time series data spatially distributed in many locations is often important for analyzing climate change and its impacts on ecosystems. However, comprehensive spatial data collection is not always feasible, requiring us to…
In this paper, we introduce a modular deep neural network (DNN) framework for data-driven reduced order modeling of dynamical systems relevant to fluid flows. We propose various deep neural network architectures which numerically predict…
We propose a physics-informed data-driven framework for urban wind estimation. This framework validates and incorporates the Reynolds number independence for flows under various working conditions, thus allowing the extrapolation for wind…
We present data driven kinematic models for the motion of bubbles in high-Re turbulent fluid flows based on recurrent neural networks with long-short term memory enhancements. The models extend empirical relations, such as Maxey-Riley (MR)…
A framework is proposed to generate a phenomenological model that extracts the essence of a dynamical system (DS) with large degrees of freedom using machine learning. For a given microscopic DS, the optimum transformation to a small number…
We propose a physics-aware machine learning method to time-accurately predict extreme events in a turbulent flow. The method combines two radically different approaches: empirical modelling based on reservoir computing, which learns the…
Establishing appropriate mathematical models for complex systems in natural phenomena not only helps deepen our understanding of nature but can also be used for state estimation and prediction. However, the extreme complexity of natural…
We design scalable neural networks adapted to translational symmetries in dynamical systems, capable of inferring untrained high-dimensional dynamics for different system sizes. We train these networks to predict the dynamics of…
The prediction of time series is a challenging task relevant in such diverse applications as analyzing financial data, forecasting flow dynamics or understanding biological processes. Especially chaotic time series that depend on a long…
Reconstructing the KAM dynamics diagram of Hamiltonian system from the time series of a limited number of parameters is an outstanding question in nonlinear science, especially when the Hamiltonian governing the system dynamics are unknown.…
We assume that we are given a time series of data from a dynamical system and our task is to learn the flow map of the dynamical system. We present a collection of results on how to enforce constraints coming from the dynamical system in…
To predict the future evolution of dynamical systems purely from observations of the past data is of great potential application. In this work, a new formulated paradigm of reservoir computing is proposed for achieving model-free…
Reduced-order dynamical models play a central role in developing our understanding of predictability of climate irrespective of whether we are dealing with the actual climate system or surrogate climate-models. In this context, the…
High-dimensional multivariate longitudinal data, which arise when many outcome variables are measured repeatedly over time, are becoming increasingly common in social, behavioral and health sciences. We propose a latent variable model for…
The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…
We consider a test problem for Navier-Stokes solvers based on the flow around a cylinder that exhibits chaotic behavior, to examine the behavior of various numerical methods. We choose a range of Reynolds numbers for which the flow is…
Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…
Forecasting production reliably and anticipating changes in the behavior of rock-fluid systems are the main challenges in petroleum reservoir engineering. This project proposes to deal with this problem through a data-driven approach and…
I present a data-driven predictive modeling tool that is applicable to high-dimensional chaotic systems with unstable periodic orbits. The basic idea is using deep neural networks to learn coordinate transformations between the trajectories…
We propose a recurrent neural network for a "model-free" simulation of a dynamical system with unknown parameters without prior knowledge. The deep learning model aims to jointly learn the nonlinear time marching operator and the effects of…