Approximating the Solution of Surface Wave Propagation Using Deep Neural Networks

Partial differential equations formalise the understanding of the behaviour of the physical world that humans acquire through experience and observation. Through their numerical solution, such equations are used to model and predict the evolution of dynamical systems. However, such techniques require extensive computational resources and assume the physics are prescribed \textit{a priori}. Here, we propose a neural network capable of predicting the evolution of a specific physical phenomenon: propagation of surface waves enclosed in a tank, which, mathematically, can be described by the Saint-Venant equations. The existence of reflections and interference makes this problem non-trivial. Forecasting of future states (i.e. spatial patterns of rendered wave amplitude) is achieved from a relatively small set of initial observations. Using a network to make approximate but rapid predictions would enable the active, real-time control of physical systems, often required for engineering design. We used a deep neural network comprising of three main blocks: an encoder, a propagator with three parallel Long Short-Term Memory layers, and a decoder. Results on a novel, custom dataset of simulated sequences produced by a numerical solver show reasonable predictions for as long as 80 time steps into the future on a hold-out dataset. Furthermore, we show that the network is capable of generalising to two other initial conditions that are qualitatively different from those seen at training time

Characterizing Evaporation Ducts Within the Marine Atmospheric Boundary Layer Using Artificial Neural Networks

We apply a multilayer perceptron machine learning (ML) regression approach to infer electromagnetic (EM) duct heights within the marine atmospheric boundary layer (MABL) using sparsely sampled EM propagation data obtained within a bistatic context. This paper explains the rationale behind the selection of the ML network architecture, along with other model hyperparameters, in an effort to demystify the process of arriving at a useful ML model. The resulting speed of our ML predictions of EM duct heights, using sparse data measurements within MABL, indicates the suitability of the proposed method for real-time applications.Comment: 13 pages, 7 figure

Surrogate modelling and uncertainty quantification based on multi-fidelity deep neural network

To reduce training costs, several Deep neural networks (DNNs) that can learn from a small set of HF data and a sufficient number of low-fidelity (LF) data have been proposed. In these established neural networks, a parallel structure is commonly proposed to separately approximate the non-linear and linear correlation between the HF- and LF data. In this paper, a new architecture of multi-fidelity deep neural network (MF-DNN) was proposed where one subnetwork was built to approximate both the non-linear and linear correlation simultaneously. Rather than manually allocating the output weights for the paralleled linear and nonlinear correction networks, the proposed MF-DNN can autonomously learn arbitrary correlation. The prediction accuracy of the proposed MF-DNN was firstly demonstrated by approximating the 1-, 32- and 100-dimensional benchmark functions with either the linear or non-linear correlation. The surrogating modelling results revealed that MF-DNN exhibited excellent approximation capabilities for the test functions. Subsequently, the MF DNN was deployed to simulate the 1-, 32- and 100-dimensional aleatory uncertainty propagation progress with the influence of either the uniform or Gaussian distributions of input uncertainties. The uncertainty quantification (UQ) results validated that the MF-DNN efficiently predicted the probability density distributions of quantities of interest (QoI) as well as the statistical moments without significant compromise of accuracy. MF-DNN was also deployed to model the physical flow of turbine vane LS89. The distributions of isentropic Mach number were well-predicted by MF-DNN based on the 2D Euler flow field and few experimental measurement data points. The proposed MF-DNN should be promising in solving UQ and robust optimization problems in practical engineering applications with multi-fidelity data sources