Simultaneous fitting of a potential-energy surface and its corresponding force fields using feedforward neural networks

Abstract

An improved neural network (NN) approach is presented for the simultaneous development of accurate potential-energy hypersurfaces and corresponding force fields that can be utilized to conduct ab initio molecular dynamics and Monte Carlo studies on gas-phase chemical reactions. The method is termed as combined function derivative approximation (CFDA). The novelty of the CFDA method lies in the fact that although the NN has only a single output neuron that represents potential energy, the network is trained in such a way that the derivatives of the NN output match the gradient of the potential-energy hypersurface. Accurate force fields can therefore be computed simply by differentiating the network. Both the computed energies and the gradients are then accurately interpolated using the NN. This approach is superior to having the gradients appear in the output layer of the NN because it greatly simplifies the required architecture of the network. The CFDA permits weighting of function fitting relative to gradient fitting. In every test that we have run on six different systems, CFDA training (without a validation set) has produced smaller out-of-sample testing error than early stopping (with a validation set) or Bayesian regularization (without a validation set). This indicates that CFDA training does a better job of preventing overfitting than the standard methods currently in use. The training data can be obtained using an empirical potential surface or any ab initio method. The accuracy and interpolation power of the method have been tested for the reaction dynamics of H+HBr using an analytical potential. The results show that the present NN training technique produces more accurate fits to both the potential-energy surface as well as the corresponding force fields than the previous methods. The fitting and interpolation accuracy is so high (rms error=1.2 cm(-1)) that trajectories computed on the NN potential exhibit point-by-point agreement with corresponding trajectories on the analytic surface.

Developing accurate molecular mechanics force fields for conjugated molecular systems

“…In these cases the various procedures used to fit the global ab initio PES are more appropriate and few examples are given by refs. [73][74][75] for systems with fewer degrees of freedom, sometime also based on force matching. It is not surprising that the most convenient strategy for FF optimization depends on the number of degrees of freedom of the chemical system and the physics that one needs to model within that a classical FF.…”

Stratified construction of neural network based interatomic models for multicomponent materials

“…The local information can be introduced in the form of the atomic forces but they do not define the lastlayer biases and are more prone to numerical noise. Both energy-and force-based fittings have been discussed and used in previous studies [35,61,63,72]. We have implemented analytical derivatives for each fitting type and rely on either Broyden-Fletcher-GoldfarbShanno (BFGS) or conjugate-gradient minimizer to drive the least squares optimization.…”

Generative Topographic Mapping of Conformational Space

“…Note that attempts to "machine-learn" an energy landscape have been already [21] reported, using neural networks, but only for small systems with very few degrees of freedom and often targeted to substitute the learned approximate model to much more time-consuming quantum Hamiltonians. Collapsing all degrees of freedom involved in peptide folding on a 2D map leaves little room for expectations of a physically useful approximate energy landscape (with an error of the order of k B T -which is actually not even achieved by the force field energy itself).…”