Exploring artificial neural networks to model interatomic and intermolecular potential energy surfaces

We demonstrate how a back-propagation artificial neural network can be trained to represent a potential energy surface (PES) in a formless manner with limited data points and exploited to predict interaction energies for configurations not included in the training set. A similar exercise is undertaken for predicting the eigenvalues and eigenvectors of a model Hamiltonian matrix that delicately depends on parameters and exhibits crossing of eigen values.     

Combining rules for interatomic potential functions of Buckingham form

The geometric mean combining rule for the total interaction energy of two non-bonded atoms, the energy being described by the Buckingham type potential, is suggested. Some numerical examples are given to compare this rule with the combining rules for the exp-six potentials proposed by Mason and Rice.     

The Ne-Ne interatomic potential revisited

The neon-neon interaction has been re-examined in the light of new data, both theoretical and experimental. Because of recent interest in solids at very high pressures, a new accurate potential is presented with particular interest paid to its highly repulsive region. A potential in HFD-B form incorporating the most recent dispersion coefficients was fitted to accurate viscosity data and high-energy scattering beam data. The potential is able to predict a wide range of macroscopic (second virial coefficients, viscosity, thermal conductivity, diffusion and 0 K binding energy) and microscopic properties (spectroscopic differential and high-energy total cross sections). The potential is extended to very short range by extrapolating to united atom perturbation results.     

An accurate Ne—Ar interatomic potential

A combined analysis of experimental data on the Ne—Ar system, some from our laboratory and some from the literature, has been performed yielding an accurate interatomic potential. For this multi-property analysis a modified version of the Dunham expansion has been used as a potential model.     

Estimating probabilities of diabetes mellitus using neural networks

Classification problems are often encountered in medical diagnosis. This paper presents an introduction to classification theory and shows how artificial neural networks can be used for classification. We also map out a bootstrapped procedure for interval estimation of posterior probabilities. The entire procedure is illustrated using the diabetes mellitus data in Pima Indians.     

The general analytic expression for S4-symmetry-invariant potential functions of tetra-atomic homonuclear molecules

The potential energy of a homonuclear X₄ molecule is an invariant of the atom permutation group S₄ acting on the internal coordinates of X₄. It is shown by means of invariant theory that six algebraically independent invariants and five additional invariants are required to express the general invariant function for this group. Explicit expressions for these 11 invariants are given.     

Effective potential analytic continuation calculations of real time quantum correlation functions: asymmetric systems

We apply the effective potential analytic continuation (EPAC) method to one-dimensional asymmetric potential systems to obtain the real time quantum correlation functions at various temperatures. Comparing the EPAC results with the exact results, we find that for an asymmetric anharmonic oscillator the EPAC results are in very good agreement with the exact ones at low temperature, while this agreement becomes worse as the temperature increases. We also show that the EPAC calculation for a certain type of asymmetric potentials can be reduced to that for the corresponding symmetric potentials.     

Esters flash point prediction using artificial neural networks

In this article, an artificial neural network to predict the flash point of 95 esters was implemented. Four variables were used for its development. A neural network with 4‐5‐8‐5‐1 topology was encountered to gain the best agreement of the experimental results with those predicted (square correlation coefficient (R²) and root mean square error were 0.99 and 5.46 K for the training phase and 0.96 and 13.02 K for the testing set). © 2012 Wiley Periodicals, Inc.     

Modeling toxicity by using supervised kohonen neural networks

Counterprogation neural network is shown to be a powerful and suitable tool for the investigation of toxicity. This study mined a data set of 568 chemicals. Two hundred eighty-two objects were used as the training set and 286 as the test set. The final model developed presents high performances on the data set R(2) = 0.83 (R(2) = 0.97 on the training set, R(2) = 0.59 on the test set). This technique distinguishes itself also for the ability to give to the expert two-dimensional maps suitable for the study of the distribution/clustering of the data and the identification of outliers.     

Using neural networks to represent potential surfaces as sums of products

By using exponential activation functions with a neural network (NN) method we show that it is possible to fit potentials to a sum-of-products form. The sum-of-products form is desirable because it reduces the cost of doing the quadratures required for quantum dynamics calculations. It also greatly facilitates the use of the multiconfiguration time dependent Hartree method. Unlike potfit product representation algorithm, the new NN approach does not require using a grid of points. It also produces sum-of-products potentials with fewer terms. As the number of dimensions is increased, we expect the advantages of the exponential NN idea to become more significant.     

Hybrid neural modeling of bioprocesses using functional link networks

The objective of this work was to develop a model for an extractive ethanol fermentation in a simple and rapid way. This model must be sufficiently reliable to be used for posterior optimization and control studies. A hybrid neural model was developed, combining mass and energy balances with neural networks, which describe the process kinetics. To determine the best model, two structures of neural networks were compared: the functional link networks and the feedforward neural networks. The two structures are shown to describe well the process kinetics, and the advantages of using the functional link networks are discussed.     

Six-dimensional potential energy surface of the dissociative chemisorption of HCl on Au(111) using neural networks

We constructed a six-dimensional potential energy surface(PES)for the dissociative chemisorption of HCl on Au(111)using the neural networks method based on roughly 70000 energies obtained from extensive density functional theory(DFT)calculations.The resulting PES is accurate and smooth,based on the small fitting errors and good agreement between the fitted PES and the direct DFT calculations.Time-dependent wave packet calculations show that the potential energy surface is very well converged with respect to the number of DFT data points,as well as to the fitting process.The dissociation probabilities of HCl initially in the ground rovibrational state from six-dimensional quantum dynamical calculations are quite diferent from the four-dimensional fixed-site calculations,indicating it is essential to perform full-dimensional quantum dynamical studies for the title molecule-surface interaction system.     

QSAR modelling using combined simple competitive learning networks and RBF neural networks

The aim of this study was to propose a QSAR modelling approach based on the combination of simple competitive learning (SCL) networks with radial basis function (RBF) neural networks for predicting the biological activity of chemical compounds. The proposed QSAR method consisted of two phases. In the first phase, an SCL network was applied to determine the centres of an RBF neural network. In the second phase, the RBF neural network was used to predict the biological activity of various phenols and Rho kinase (ROCK) inhibitors. The predictive ability of the proposed QSAR models was evaluated and compared with other QSAR models using external validation. The results of this study showed that the proposed QSAR modelling approach leads to better performances than other models in predicting the biological activity of chemical compounds. This indicated the efficiency of simple competitive learning networks in determining the centres of RBF neural networks.     

Effective potential analytic continuation approach for real time quantum correlation functions involving nonlinear operators

We apply the effective potential analytic continuation (EPAC) method to the calculation of real time quantum correlation functions involving operators nonlinear in the position operator q. For a harmonic system the EPAC method provides the exact correlation function at all temperature ranges, while the other quantum dynamics methods, the centroid molecular dynamics and the ring polymer molecular dynamics, become worse at lower temperature. For an asymmetric anharmonic system, the EPAC correlation function is in very good agreement with the exact one at t = 0. When the time increases from zero, the EPAC method gives good coincidence with the exact result at lower temperature. Finally, we propose a simplified version of the EPAC method to reduce the computational cost required for the calculation of the standard effective potential.     

Identification of spectral lines of elements using artificial neural networks

Artificial neural networks (ANNs) are relatively new computational tools that have found extensive utilization in solving many complex real-world problems. This paper describes how an ANN can be used to identify the spectral lines of elements. The spectral lines of Cadmium (Cd), Calcium (Ca), Iron (Fe), Lithium (Li), Mercury (Hg), Potassium (K) and Strontium (Sr) in the visible range are chosen for the investigation. One of the unique features of this technique is that it uses the whole spectrum in the visible range instead of individual spectral lines. The spectrum of a sample taken with a spectrometer contains both original peaks and spurious peaks. It is a tedious task to identify these peaks to determine the elements present in the sample. ANNs capability of retrieving original data from noisy spectrum is also explored in this paper. The importance of the need of sufficient data for training ANNs to get accurate results is also emphasized. Two networks are examined: one trained in all spectral lines and other with the persistent lines only. The network trained in all spectral lines is found to be superior in analyzing the spectrum even in a noisy environment.     

Classification and identification of mosquito species using artificial neural networks

An artificial neural network method is presented for classification and identification of Anopheles mosquito species based on the internal transcribed spacer2 (ITS2) data of ribosomal DNA string. The method is implemented in two different multi-layered feed-forward neural network model forms, namely, multi-input single-output neural network (MISONN) and multi-input multi-output neural network (MIMONN). A number of data sequences in varying sizes of different Anopheline malarial vectors and their corresponding species coding are employed to develop the neural network models. The classification efficiency of the network models for untrained data sequences is evaluated in terms of quantitative performance criteria. The results demonstrate the efficiency of the neural network models to extract the genetic information in ITS2 sequences and to adapt to new data. The method of MISONN is found to exhibit superior performance over MIMONN in distinguishing and identification of the mosquito vectors.     

Predicting nucleic acid torsion angle values using artificial neural networks

By means of an error back-propagation artificial neural network, a new method to predict the torsion angles , and from torsion angles , , and for nucleic acid dinucleotides is introduced. To build a model, training sets and test sets of 163 and 81 dinucleotides, respectively, with known crystal structures, were assembled. With 7 hidden units in a three-layered network a model with good predictive ability is constructed. About 70 to 80% of the residuals for predicted torsion angles are smaller than 10 degrees. This means that such a model can be used to construct trial structures for conformational analysis that can be refined further. Moreover, when reasonable estimates for , , and are extracted from COSY experiments, this procedure can easily be extended to predict torsion angles for structures in solution.