Neural Network Methods for Boundary Value Problems Defined in Arbitrarily Shaped Domains

Partial differential equations (PDEs) with Dirichlet boundary conditions defined on boundaries with simple geometry have been succesfuly treated using sigmoidal multilayer perceptrons in previous works. This article deals with the case of complex boundary geometry, where the boundary is determined by a number of points that belong to it and are closely located, so as to offer a reasonable representation. Two networks are employed: a multilayer perceptron and a radial basis function network. The later is used to account for the satisfaction of the boundary conditions. The method has been successfuly tested on two-dimensional and three-dimensional PDEs and has yielded accurate solutions

Predictive Behavior of a Computational Foot/Ankle Model through Artificial Neural Networks

Computational models are useful tools to study the biomechanics of human joints. Their predictive performance is heavily dependent on bony anatomy and soft tissue properties. Imaging data provides anatomical requirements while approximate tissue properties are implemented from literature data, when available. We sought to improve the predictive capability of a computational foot/ankle model by optimizing its ligament stiffness inputs using feedforward and radial basis function neural networks. While the former demonstrated better performance than the latter per mean square error, both networks provided reasonable stiffness predictions for implementation into the computational model

Supervised ANN vs. unsupervised SOM to classify EEG data for BCI: why can GMDH do better?

Construction of a system for measuring the brain activity (electroencephalogram (EEG)) and recognising thinking patterns comprises significant challenges, in addition to the noise and distortion present in any measuring technique. One of the most major applications of measuring and understanding EGG is the brain-computer interface (BCI) technology. In this paper, ANNs (feedforward back -prop and Self Organising Maps) for EEG data classification will be implemented and compared to abductive-based networks, namely GMDH (Group Methods of Data Handling) to show how GMDH can optimally (i.e. noise and accuracy) classify a given set of BCI’s EEG signals. It is shown that GMDH provides such improvements. In this endeavour, EGG classification based on GMDH will be researched for comprehensible classification without scarifying accuracy. GMDH is suggested to be used to optimally classify a given set of BCI’s EEG signals. The other areas related to BCI will also be addressed yet within the context of this purpose

A survey on modern trainable activation functions

In neural networks literature, there is a strong interest in identifying and defining activation functions which can improve neural network performance. In recent years there has been a renovated interest of the scientific community in investigating activation functions which can be trained during the learning process, usually referred to as "trainable", "learnable" or "adaptable" activation functions. They appear to lead to better network performance. Diverse and heterogeneous models of trainable activation function have been proposed in the literature. In this paper, we present a survey of these models. Starting from a discussion on the use of the term "activation function" in literature, we propose a taxonomy of trainable activation functions, highlight common and distinctive proprieties of recent and past models, and discuss main advantages and limitations of this type of approach. We show that many of the proposed approaches are equivalent to adding neuron layers which use fixed (non-trainable) activation functions and some simple local rule that constraints the corresponding weight layers.Comment: Published in "Neural Networks" journal (Elsevier

Metaheuristic design of feedforward neural networks: a review of two decades of research

Over the past two decades, the feedforward neural network (FNN) optimization has been a key interest among the researchers and practitioners of multiple disciplines. The FNN optimization is often viewed from the various perspectives: the optimization of weights, network architecture, activation nodes, learning parameters, learning environment, etc. Researchers adopted such different viewpoints mainly to improve the FNN's generalization ability. The gradient-descent algorithm such as backpropagation has been widely applied to optimize the FNNs. Its success is evident from the FNN's application to numerous real-world problems. However, due to the limitations of the gradient-based optimization methods, the metaheuristic algorithms including the evolutionary algorithms, swarm intelligence, etc., are still being widely explored by the researchers aiming to obtain generalized FNN for a given problem. This article attempts to summarize a broad spectrum of FNN optimization methodologies including conventional and metaheuristic approaches. This article also tries to connect various research directions emerged out of the FNN optimization practices, such as evolving neural network (NN), cooperative coevolution NN, complex-valued NN, deep learning, extreme learning machine, quantum NN, etc. Additionally, it provides interesting research challenges for future research to cope-up with the present information processing era