Modified Energy Function Research Articles

Two regularizers for recursive least squared algorithms in feedforward multilayered neural networks

Recursive least squares (RLS)-based algorithms are a class of fast online training algorithms for feedforward multilayered neural networks (FMNNs). Though the standard RLS algorithm has an implicit weight decay term in its energy function, the weight decay effect decreases linearly as the number of learning epochs increases, thus rendering a diminishing weight decay effect as training progresses. In this paper, we derive two modified RLS algorithms to tackle this problem. In the first algorithm, namely, the true weight decay RLS (TWDRLS) algorithm, we consider a modified energy function whereby the weight decay effect remains constant, irrespective of the number of learning epochs. The second version, the input perturbation RLS (IPRLS) algorithm, is derived by requiring robustness in its prediction performance to input perturbations. Simulation results show that both algorithms improve the generalization capability of the trained network.

Atomistic modelling of nematic liquid crystals: a study of structure-property relationships in steroidal mesogen based liquid crystals

In this study we report molecular mechanics calculations designed to predict and interpret structure property relationships in nematic liquid crystals. A family of liquid crystals with steroidal mesogens were studied and the results were compared with available X-ray data. Low energy conformations of dimers were analysed to provide quantitative information about the local intermolecular interactions and their anisotropic nature. Important contributions to the molecular packing could be identified and the geometry of the dimers and the extent of their positional correlation was successfully related to their observed packing behaviour. By monitoring the relative orientation of the two molecules, a qualitative study of liquid crystalline phase stability was accomplished. Simulations were also carried out with a modified energy function which includes a nematic contribution representing the cumulative intermolecular interactions owing to long range orientational order present in liquid crystals. Along with providing a systematic study of the relative importance of the various competing forces (steric repulsion, attractive forces, long-range electrostatic interactions) in the formation of liquid crystalline phases, this method can also be expected to be useful in predicting mesophase behaviour.

On the calculation of first‐order properties: Expectation value versus energy derivative approach

AbstractThe definition of so‐called first‐order properties is, in general, not unique for approximate solutions of the Schrödinger equation. In the present work, the determination of molecular properties as the expectation value or energy derivative are compared for a wide class of electron correlation treatments that are based on the stationarity of certain modified energy functionals. The case in which all perturbation‐dependent parameters in the energy expression are optimized is taken as a reference point, to which the derivative and the expectation value approaches are related by a sequence of approximations. By analyzing the validity of these approximations, we are in a position to give general criteria for the choice of the method to be employed. The derivative approach is shown to be a special case of a general method to improve the calculation of molecular properties. Furthermore, this method is extended to give a correction to the energy itself. © 1992 John Wiley & Sons, Inc.