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Neural networks have been used to solve different types of large data related problems in many different fields.This project takes a novel approach to solving the Navier-Stokes Equations for turbulence by training a neural network using…

In many applications, it is important to reconstruct a fluid flow field, or some other high-dimensional state, from limited measurements and limited data. In this work, we propose a shallow neural network-based learning methodology for such…

In this study, we explore the application of an artificial recurrent neural network (RNN) called Long Short-Term Memory (LSTM) as an alternative to a turbulent Reynolds-Averaged Navier-Stokes (RANS) model. The LSTM models are utilized to…

Owing to their superior modeling capabilities, gated Recurrent Neural Networks, such as Gated Recurrent Units (GRUs) and Long Short-Term Memory networks (LSTMs), have become popular tools for learning dynamical systems. This paper aims to…

We explore the influence of precision of the data and the algorithm for the simulation of chaotic dynamics by neural networks techniques. For this purpose, we simulate the Lorenz system with different precisions using three different neural…

Neural networks are a promising technique for parameterizing sub-grid-scale physics (e.g. moist atmospheric convection) in coarse-resolution climate models, but their lack of interpretability and reliability prevents widespread adoption.…

A fully-convolutional neural-network model is used to predict the streamwise velocity fields at several wall-normal locations by taking as input the streamwise and spanwise wall-shear-stress planes in a turbulent open channel flow. The…

Learning for control of dynamical systems with formal guarantees remains a challenging task. This paper proposes a learning framework to simultaneously stabilize an unknown nonlinear system with a neural controller and learn a neural…

Learning-based methods could provide solutions to many of the long-standing challenges in control. However, the neural networks (NNs) commonly used in modern learning approaches present substantial challenges for analyzing the resulting…

We present a method for parametrizing sub-grid processes in the Shallow Water equations. We define coarse variables and local spatial averages and use a feed-forward neural network to learn sub-grid fluxes. Our method results in a local…

In this paper, we synthesize two aperiodic-sampled deep neural network (DNN) control schemes, based on the closed-loop tracking stability guarantees. By means of the integral quadratic constraint coping with the input-output behaviour of…

Computational Fluid Dynamics (CFD) is a hugely important subject with applications in almost every engineering field, however, fluid simulations are extremely computationally and memory demanding. Towards this end, we present Lat-Net, a…

Neural network controllers have become popular in control tasks thanks to their flexibility and expressivity. Stability is a crucial property for safety-critical dynamical systems, while stabilization of partially observed systems, in many…

Neural networks can be used as approximations of several complex control schemes such as model predictive control. We show in this paper which properties deep neural networks with rectifier linear units as activation functions need to…

Handling regime shifts and non-stationary time series in deep learning systems presents a significant challenge. In the case of online learning, when new information is introduced, it can disrupt previously stored data and alter the model's…

In this paper a novel model-free algorithm is proposed. This algorithm can learn the nearly optimal control law of constrained-input systems from online data without requiring any a priori knowledge of system dynamics. Based on the concept…

Small-scale liquid flows on solid surfaces provide convincing details in liquid animation, but they are difficult to be simulated with efficiency and fidelity, mostly due to the complex nature of the surface tension at the contact front…

Recurrent neural networks are capable of learning the dynamics of an unknown nonlinear system purely from input-output measurements. However, the resulting models do not provide any stability guarantees on the input-output mapping. In this…

In this document, a neural network is employed in order to estimate the solution of the initial value problem in the context of non linear trajectories. Such trajectories can be subject to gravity, thrust, drag, centrifugal force,…

This paper studies the design of neural network (NN)-based controllers for unknown nonlinear systems, using contraction analysis. A Neural Ordinary Differential Equation (NODE) system is constructed by approximating the unknown draft…