Prediction of enthalpy of alkanes by the use of radial basis function neural networks

RbfDeSolver: A Software Tool to Approximate Differential Equations Using Radial Basis Functions

A new method for solving differential equations is presented in this work. The solution of the differential equations is done by adapting an artificial neural network, RBF, to the function under study. The adaptation of the parameters of the network is done with a hybrid genetic algorithm. In addition, this text presents in detail the software developed for the above method in ANSI C++. The user can code the underlying differential equation either in C++ or in Fortran format. The method was applied to a wide range of test functions of different types and the results are presented and analyzed in detail.

A Two-Phase Evolutionary Method to Train RBF Networks

This article proposes a two-phase hybrid method to train RBF neural networks for classification and regression problems. During the first phase, a range for the critical parameters of the RBF network is estimated and in the second phase a genetic algorithm is incorporated to locate the best RBF neural network for the underlying problem. The method is compared against other training methods of RBF neural networks on a wide series of classification and regression problems from the relevant literature and the results are reported.

Predicting equilibrium vapour pressure isotope effects by using artificial neural networks or multi-linear regression - A quantitative structure property relationship approach

We aim at predicting the effect of structure and isotopic substitutions on the equilibrium vapour pressure isotope effect of various organic compounds (alcohols, acids, alkanes, alkenes and aromatics) at intermediate temperatures. We attempt to explore quantitative structure property relationships by using artificial neural networks (ANN); the multi-layer perceptron (MLP) and compare the performances of it with multi-linear regression (MLR). These approaches are based on the relationship between the molecular structure (organic chain, polar functions, type of functions, type of isotope involved) of the organic compounds, and their equilibrium vapour pressure. A data set of 130 equilibrium vapour pressure isotope effects was used: 112 were used in the training set and the remaining 18 were used for the test/validation dataset. Two sets of descriptors were tested, a set with all the descriptors: number of(12)C, (13)C, (16)O, (18)O, (1)H, (2)H, OH functions, OD functions, CO functions, Connolly Solvent Accessible Surface Area (CSA) and temperature and a reduced set of descriptors. The dependent variable (the output) is the natural logarithm of the ratios of vapour pressures (ln R), expressed as light/heavy as in classical literature. Since the database is rather small, the leave-one-out procedure was used to validate both models. Considering higher determination coefficients and lower error values, it is concluded that the multi-layer perceptron provided better results compared to multi-linear regression. The stepwise regression procedure is a useful tool to reduce the number of descriptors. To our knowledge, a Quantitative Structure Property Relationship (QSPR) approach for isotopic studies is novel.

Random forests for feature selection in QSPR Models - an application for predicting standard enthalpy of formation of hydrocarbons

Background

One of the main topics in the development of quantitative structure-property relationship (QSPR) predictive models is the identification of the subset of variables that represent the structure of a molecule and which are predictors for a given property. There are several automated feature selection methods, ranging from backward, forward or stepwise procedures, to further elaborated methodologies such as evolutionary programming. The problem lies in selecting the minimum subset of descriptors that can predict a certain property with a good performance, computationally efficient and in a more robust way, since the presence of irrelevant or redundant features can cause poor generalization capacity. In this paper an alternative selection method, based on Random Forests to determine the variable importance is proposed in the context of QSPR regression problems, with an application to a manually curated dataset for predicting standard enthalpy of formation. The subsequent predictive models are trained with support vector machines introducing the variables sequentially from a ranked list based on the variable importance.

Results

The model generalizes well even with a high dimensional dataset and in the presence of highly correlated variables. The feature selection step was shown to yield lower prediction errors with RMSE values 23% lower than without feature selection, albeit using only 6% of the total number of variables (89 from the original 1485). The proposed approach further compared favourably with other feature selection methods and dimension reduction of the feature space. The predictive model was selected using a 10-fold cross validation procedure and, after selection, it was validated with an independent set to assess its performance when applied to new data and the results were similar to the ones obtained for the training set, supporting the robustness of the proposed approach.

Conclusions

The proposed methodology seemingly improves the prediction performance of standard enthalpy of formation of hydrocarbons using a limited set of molecular descriptors, providing faster and more cost-effective calculation of descriptors by reducing their numbers, and providing a better understanding of the underlying relationship between the molecular structure represented by descriptors and the property of interest.

Quantitative structure-retention relationships for organic pollutants in biopartitioning micellar chromatography

Quantitative structure-retention relationship (QSRR) models have been successfully developed for the prediction of the retention factor (log k) in the biopartitioning micellar chromatography (BMC) of 66 organic pollutants. Heuristic method (HM) and radial basis function neural networks (RBFNN) were utilized to construct the linear and non-linear QSRR models, respectively. The optimal QSRR model was developed based on a 6-17-1 radial basis function neural network architecture using molecular descriptors calculated from molecular structure alone. The RBFNN model gave a correlation coefficient (R2) of 0.8464 and root-mean-square error (RMSE) of 0.1925 for the test set. This paper provided a useful model for the predicting the log k of other organic compounds when experiment data are unknown.

Quantitative Structure-Property Relationship Study of the Solvent Polarity Using Wavelet Neural Networks

Quantitative structure-property relationship (QSPR) studies based on artificial neural network (ANN) and wavelet neural network (WNN) techniques were carried out for the prediction of solvent polarity. Experimental S' values for 69 solvents were assembled. This set included saturated and unsaturated hydrocarbons, solvents containing halogen, cyano, nitro, amide, sulfide, mercapto, sulfone, phosphate, ester, ether, etc. Semi-empirical quantum chemical calculations at AM1 level were used to find the optimum 3D geometry of the studied molecules and different quantum-chemical descriptors were calculated by the HyperChem software. A stepwise MLR method was used to select the best descriptors and the selected descriptors were used as input neurons in neural network models. The results obtained by the two methods were compared and it was shown that in WNN, the convergence speed was faster and the root mean square error of prediction set was also smaller than ANN. The average relative error in WNN was 7.9 and 6.8% for calibration and prediction set, respectively, and the results showed the ability of the WNN developed here to predict solvent polarity.

QSAR study on the Ah receptor-binding affinities of polyhalogenated dibenzo-p-dioxins using net atomic-charge descriptors and a radial basis neural network

A radial basis function neural network (RBFN) has been used to correlate Ah receptor-binding affinities of polychlorinated, polybrominated, and polychlorinated-brominated dibenzo-p-dioxins with molecular weight and eight net atomic charge descriptors. Support vector machine (SVM) and partial least square (PLS) regression models based on the same data set have also been built. Leave-one-out cross-validation was used to train the RBFN, SVM, and PLS models. For predicting Ah receptor-binding affinities, the RBFN model with a squared cross-validation correlation coefficient (q2) of 0.8818 outperforms the SVM and PLS models and also compares favorably with any other reported quantitative structure-activity relationship model based on the same activity data set. The significance of the RBFN model with net atomic charges as descriptors suggests that electrostatic and dispersion-type interactions play important roles in governing the Ah receptor binding of polychlorinated, polybrominated, and polychlorinated-brominated dibenzo-p-dioxins.

Development of migration models for acids in capillary electrophoresis using heuristic and radial basis function neural network methods

A quantitative structure-mobility relationship (QSMR) was developed for the absolute mobilities of a diverse set of 277 organic and inorganic acids in capillary electrophoresis based on the descriptors calculated from the structure alone. The heuristic method (HM) and the radial basis function neural networks (RBFNN) were utilized to construct the linear and nonlinear prediction models, respectively. The prediction results were in agreement with the experimental values. The HM model gave a root-mean-square (RMS) error of 3.66 electrophoretic mobility units for the training set, 4.67 for the test set, and 3.88 for the whole data set, while the RBFNN gave an RMS error of 2.49, 3.19, and 2.65, respectively. The heuristic linear model could give some insights into the factors that are likely to govern the mobilities of the compounds, however, the prediction results of the RBFNN model seem to be better than that of the HM.

Radial basis function neural network based QSPR for the prediction of critical pressures of substituted benzenes

The Quantitative Structure-Property Relationship (QSPR) method is used to develop the correlation between structures of a great number of substituted benzenes and their critical pressure. Molecular descriptors calculated from structure alone were used to represent molecular structures. A subset of the calculated descriptors selected using forward stepwise regression was used in the QSPR model development. Multiple Linear Regression and Radial Basis Function Neural Networks are utilized to construct the linear and non-linear prediction model, respectively. To obtain good prediction ability, both topological structure and training parameters of radial basis function neural networks are optimized. The prediction result agrees well with the experimental value of these properties.