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Obtaining the solutions of high-dimensional partial differential equations (PDEs) seems to be difficult by utilizing the classical numerical methods. Recently, deep neural networks (DNNs) techniques have received special attentions in solving high–dimensional problems in PDEs. In this study, our quest is to investigate some newly introduced data-driven deep learning-based approaches and compare their performance in terms of their efficiency and faster training towards high-dimensional PDEs. However, the comparison is carried out based on different activation functions, number of layers and gradient based optimizers. We consider some benchmark problems in our numerical experiments which includes Burgers equation, Diffusion-reaction equation and Allen-Cahn Equations. [ABSTRACT FROM AUTHOR]

The problem of function fitting for certain geophysical problem such as Control Source Electro-Magnetic (CSEM) can be solved using a partially recurrent network called Elman Neural Networks (ENN). ENN is one of the subclasses of partial recurrent neural networks. A Recurrent Neural Network (RNN) is an important class of neural networks where connections between units form a directed cycle. The Elman network differs from conventional neural network structure, in that it has addition layer (context layer) with feedback connection from the output of the hidden layer to its input. This feedback path allows Elman networks to recognize and generate temporal patterns, as well as spatial patterns. ENN has an advantage of having a low probability of being affected by external noise. Also, it can be trained to act as an independent system simulator. This study presents an application of ENN in function fitting for CSEM data. The synthetic training data has been generated using Computer Simulation Technology (CST) software. As a preliminary study, the data set was selected carefully representing a no hydrocarbon reservoir CSEM simulation. The trained Elman network shows an encouraging good fitting with MSE as low as 0.000275. [ABSTRACT FROM PUBLISHER]

Controlled Source Electro-Magnetic (CSEM) sounding technique which is an alternative name for Sea Bed Logging (SBL) Is a recent effective resistivity sensing technology used in finding, testing and evaluating hydrocarbon reservoirs. Both sea water and hydrocarbon (target) depths can cause a significant impact when analyzing and interpreting data from CSEM environment. This paper looks at the feasibility of applying artificial neural network to the scaled marine environment data for finding and evaluating hydrocarbon reservoirs. Artificial Neural Network (ANN) Is non-linear predictive models that resemble biological neural network in structure and learn through process of training. One of the advantage of ANN is the ability' to be used as an arbitrary' function approximation mechanism which 'learns' from observed data. Data collected from the experiments of different depths and target positions are used to obtain the neural network training model, while Mean Square Error is for model accuracy evaluation. Preliminary results show that the Artificial Neural Network has a potential in modeling the CSEM environment. [ABSTRACT FROM AUTHOR]