Enhancing Air Quality forecasting with functional neural networks: A case study of PM2.5 in Seoul

We introduce a new class of nonlinear models for functional data based on neural networks. Deep learning has been very successful in nonlinear modeling, but there has been little work done in the functional data setting. We propose two variations of our framework: a functional neural network with continuous hidden layers, called the Functional Direct Neural Network (FDNN), and a second version that uses basis expansions and continuous hidden layers, called the Functional Basis Neural Network (FBNN). Both are designed explicitly to exploit the structure inherent in functional data. To fit these models we derive a functional gradient based optimization algorithm. The effectiveness of the proposed methods in handling complex functional models is demonstrated by comprehensive simulation studies and real data examples. Supplementary materials for this article are available online.

A functional neural fuzzy network for classification applications

Three hardware oriented semistate descriptions for the functional artificial neural network (FANN) are introduced to pave the way for VLSI realization. The first one is current-mode based in order to use current mirrors, current multipliers and integrators/differentiators. Next we show a voltage-current mixed-mode one realizable with OTAs, and finally one with all voltage variables realizable through differential operational amplifiers, etc. The functional artificial neural network under consideration uses neurons which are functionals. The Fock space in which these neurons are represented by Volterra functionals is a reproducing kernel Hilbert space, with synaptic weights as functions themselves as introduced by de Figueiredo and his students. This functional neural network can capture the dynamics present in real-world (continuous-time-parameter) nonlinear systems, enabling it to model them, as well as simulate their behavior in a computer-based environment.

A functional neural network computing some eigenvalues and eigenvectors of a special real matrix

The VLSI implementation of a two-hidden layer discretized functional artificial neural network (FANN) has been demonstrated. A chip-set has been defined that implements the FANN, while it allows for expandability in the number of its inputs and outputs, as well as the number of neurons and connections in each hidden layer. Use of current-mode circuitry has resulted in compact multiplication circuitry and efficient manipulation of summation. The components (multiplier, exponential amplifier, analog memory cell) of the FANN have been implemented successfully, through MOSIS, using BiCMOS technology.

Alzheimer's disease (AD) is a prevalent neurodegenerative condition that can lead to severe cognitive and functional deterioration. Functional magnetic resonance imaging (fMRI) revealed abnormalities in AD in intrinsic synchronization between spatially separate regions in the so-called default mode network (DMN) of the brain. To understand the relationship between this disruption in large-scale synchrony and the cognitive impairment in AD, it is critical to determine whether and how the deficit in the low frequency hemodynamic fluctuations recorded by fMRI translates to much faster timescales of memory and other cognitive processes. The present study employed magnetoencephalography (MEG) and a Hidden Markov Model (HMM) approach to estimate spontaneous synchrony variations in the functional neural networks with high temporal resolution. In a group of cognitively healthy (CH) older adults, we found transient (mean duration of 150–250 ms) network activity states, which were visited in a rapid succession, and were characterized by spatially coordinated changes in the amplitude of source-localized electrophysiological oscillations. The inferred states were similar to those previously observed in younger participants using MEG, and the estimated cortical source distributions of the state-specific activity resembled the classic functional neural networks, such as the DMN. In patients with AD, inferred network states were different from those of the CH group in short-scale timing and oscillatory features. The state of increased oscillatory amplitudes in the regions overlapping the DMN was visited less often in AD and for shorter periods of time, suggesting that spontaneous synchronization in this network was less likely and less stable in the patients. During the visits to this state, in some DMN nodes, the amplitude change in the higher-frequency (8–30 Hz) oscillations was less robust in the AD than CH group. These findings highlight relevance of studying short-scale temporal evolution of spontaneous activity in functional neural networks to understanding the AD pathophysiology. Capacity of flexible intrinsic synchronization in the DMN may be crucial for memory and other higher cognitive functions. Our analysis yielded metrics that quantify distinct features of the neural synchrony disorder in AD and may offer sensitive indicators of the neural network health for future investigations.

Fuzzy Neural Networks consider one of the most important computational tools which are applied in many areas such as classification, pattern recognition and medical diagnosis. The learning process is very crucial for fuzzy neural network to be powerful in solving problems. In this study, a hybrid black stork foraging process based on particle swarm optimization (BSFP-PSO) is used to enhance the learning of new existing approach of fuzzy neural network called functional neural fuzzy network (FNFN). Classification problem have been adopted to assess the performance of the new proposed model black stork foraging process hybrid particle swarm optimization and functional neural fuzzy network. In conclusion, the experimental results have shown that the performance of the proposed model is better than the performance of standard particle swarm optimization with functional neural fuzzy network for solving Iris and Breast cancer classification in terms of error rate and classification accuracy.

In this article, single layer based functional basis neural network has been used for foreign exchange rate prediction. In general, foreign exchange rate problem is one of the most complex problems with high non linearity and data irregularity. From many studies it is found that foreign exchange rate prediction always fluctuates with economic growth, interest rate and influence rates and therefore it is very difficult for researcher to predict foreign exchange rate. Therefore, foreign exchange rate prediction becomes a challenging task for every researcher for both academic and industrial communities. In this article two type of single layer functional link artificial neural network Functional-link Artificial Neural Network (FLANN) and Laguerre Polynomial Equation ( LAPE) were applied to forecast foreign exchange data. With high data irregularity, FLANN and LAPE both the models provide extremely precise outcome for complex time series model. The single layered based functional basis neural network architectures results matched strongly with ARIMA with very less Mean Square Error (MSE). From the Simulation study, single layer based functional basis neural network models provide improved results compare to ARIMA model with less Root Mean Square Error (RMSE) and performs as universal approximator.

A recurrent functional link-based fuzzy neural network controller with improved particle swarm optimization is proposed to control the mover of a permanent-magnet synchronous motor (PMSM) servo drive to track periodic reference trajectories. First, a recurrent functional link-based fuzzy neural network is proposed to control the PMSM, and the connective weights of the recurrent functional link-base neural network, the mean value and standard deviation of Gaussian function are trained online by recurrent algorithm. Moreover, an improved particle swarm optimization (IPSO) is adopted in this study to adapt the learning rates to improve the learning capability and increase the speed of constringency. Finally, the control performance of the proposed method is verified by the simulated results.

Quick extraction of eigenpairs of a real symmetric matrix is very important in engineering. Using neural networks to complete this operation is in a parallel manner and can achieve high performance. So, this paper proposes a very concise functional neural network (FNN) to compute the largest (or smallest) eigenvalue and one its eigenvector. When the FNN is converted into a differential equation, the component analytic solution of this equation is obtained. Using the component solution, the convergence properties are fully analyzed. On the basis of this FNN, the method that can compute the largest (or smallest) eigenvalue and one its eigenvector whether the matrix is non-definite, positive definite or negative definite is designed. Finally, three examples show the validity of the method. Comparing with other neural networks designed for the same aim, the proposed FNN is very simple and concise, so it is very easy to be realized

Artificial intelligence (AI) is a thriving research field with many successful applications in areas such as computer vision and speech recognition. Machine learning methods, such as artificial neural networks (ANN), play a central role in modern AI technology. While ANN also holds great promise for human genetic research, the high-dimensional genetic data and complex genetic structure bring tremendous challenges. The vast majority of genetic variants on the genome have small or no effects on diseases, and fitting ANN on a large number of variants without considering the underlying genetic structure (e.g., linkage disequilibrium) could bring a serious overfitting issue. Furthermore, while a single disease phenotype is often studied in a classic genetic study, in emerging research fields (e.g., imaging genetics), researchers need to deal with different types of disease phenotypes. To address these challenges, we propose a functional neural networks (FNN) method. FNN uses a series of basis functions to model high-dimensional genetic data and a variety of phenotype data and further builds a multi-layer functional neural network to capture the complex relationships between genetic variants and disease phenotypes. Through simulations, we demonstrate the advantages of FNN for high-dimensional genetic data analysis in terms of robustness and accuracy. The real data applications also showed that FNN attained higher accuracy than the existing methods.

Rate of penetration (ROP) is defined as the amount of removed rock per unit area per unit time. It is affected by several factors which are inseparable. Current established models for determining the ROP include the basic mathematical and physics equations, as well as the use of empirical correlations. Given the complexity of the drilling process, the use of artificial intelligence (AI) has been a game changer because most of the unknown parameters can now be accounted for entirely at the modeling process. The objective of this paper is to evaluate the ability of the optimized adaptive neuro-fuzzy inference system (ANFIS), functional neural networks (FN), random forests (RF), and support vector machine (SVM) models to predict the ROP in real time from the drilling parameters in the S-shape well profile, for the first time, based on the drilling parameters of weight on bit (WOB), drillstring rotation (DSR), torque (T), pumping rate (GPM), and standpipe pressure (SPP). Data from two wells were used for training and testing (Well A and Well B with 4012 and 1717 data points, respectively), and one well for validation (Well C) with 2500 data points. Well A and Well B data were combined in the training-testing phase and were randomly divided into a 70:30 ratio for training/testing. The results showed that the ANFIS, FN, and RF models could effectively predict the ROP from the drilling parameters in the S-shape well profile, while the accuracy of the SVM model was very low. The ANFIS, FN, and RF models predicted the ROP for the training data with average absolute percentage errors (AAPEs) of 9.50%, 13.44%, and 3.25%, respectively. For the testing data, the ANFIS, FN, and RF models predicted the ROP with AAPEs of 9.57%, 11.20%, and 8.37%, respectively. The ANFIS, FN, and RF models overperformed the available empirical correlations for ROP prediction. The ANFIS model estimated the ROP for the validation data with an AAPE of 9.06%, whereas the FN model predicted the ROP with an AAPE of 10.48%, and the RF model predicted the ROP with an AAPE of 10.43%. The SVM model predicted the ROP for the validation data with a very high AAPE of 30.05% and all empirical correlations predicted the ROP with AAPEs greater than 25%.

To improve the measurement accuracy of coal ash content, this chapter proposes an intelligent soft-sensing method based on dual-energy γ-rays by using the functional link neural network. This method takes 241Am and 137Cs as the resources of low-energy and medium-energy γ-rays, respectively, and uses the γ count of the detector as auxiliary variable. The coal ash content is measured and verified after accomplishing the model of soft-sensing with the functional link neural network that is optimized by chaos algorithm. The result shows that the method of functional link neural network forecasting based on chaos optimization algorithm has higher accuracy and excellent extensive capability than conventional nuclear technology. The intelligent soft-sensing based on functional link neural network with optimized chaos algorithm forecasting model is of measurement accuracy, and the most error and mean error between the soft-sensing values and real values are 0.9 and 0.7 %.

A new approach to the identification of dynamical systems by means of evolved neural networks is presented. We implement two functional neural networks: polynomials and orthogonal basis functions. The functional neural networks contain four parameters that need to be optimized: the weights, training parameters, network topology and scaling factors. An approach to the solution of this combinatorial problem is to genetically evolve functional neural networks. This paper presents a preliminary analysis of the proposed method to automatically select network parameters. The networks are encoded as chromosomes that are evolved during the identification by means of genetic algorithms. Experimental results show that the method is effective for the identification of dynamical systems.

This paper presents a hybrid autoregressive moving average (ARMA) and a nonlinear functional link neural network for electricity price forecasting in an Energy market. The functional neural block helps to introduce nonlinearity by expanding the input space to higher dimensional space through a basis function without using any hidden layers like MLP structure. Unlike the conventional functional link artificial neural network (FLANN), the input layer comprises the inputs and tangent hyperbolic functions of the linear combination of the inputs known as the basis functions. The proposed hybrid neural network is trained by an unscented H-infinity filter to provide an accurate forecasting of day ahead electricity prices. The noise covariance parameters of the unscented H-infinity filter are further optimised with an adaptive differential evolution strategy. The studies on PJM, Spanish and Australian energy markets exhibit excellent forecasting results over different seasonal horizons for one day ahead of time.