Neural Network Methods for Data Analysis and Statistical Error Reduction

Abstract

The use of neural networks (NNs) to predict an outcome or the output results as a function of a set of input parameters has been gaining wider acceptance with the advance in computer technology as well as with an increased awareness of the potential of NNs. A neural network is first trained to learn the underlying functional relationship between the output and the input parameters by providing it with a large number of data points, where each data point corresponds to a set of output and input parameters. Sumpter and Noid demonstrated the use of NNs to map the vibrational motion derived from the vibrational spectra onto a PES with relatively high accuracy. In another application, Sumpter et al. trained an NN to learn the relation between the phase-space points along a trajectory and the mode energies for stretching, torsion, and bending vibrations of H2O2. Likewise, Nami et al. demonstrated the use of NNs to determine the TiO2 deposition rates in a chemical vapor deposition (CVD) process from the knowledge of a range of deposition conditions. In view of the success achieved in obtaining interpolated values of the PESs for multi-atomic systems using an NN trained by the ab initio energy values for a large number of configurations, it is reasonable to ask whether we can successfully compute the results of an MD trajectory for a chemical reaction using an NN trained by the data obtained by previous MD simulations. If this can be done successfully, it becomes possible to execute a small number of trajectories, M, and then utilize the results of these trajectories as a database to train an NN to predict the final results of a very large number of trajectories N, where N >> M, that can be used to increase the statistical accuracy of the MD calculations and to further explore the dependence of the trajectory results upon a wide variety of variables without actually having to perform any further numerical integrations. In effect, the NN replaces the computationally laborious numerical integrations.