Size-independent neural networks based first-principles method for accurate prediction of heat of formation of fuels

Abstract

Neural network-based first-principles method for predicting heat of formation (HOF) was previously demonstrated to be able to achieve chemical accuracy in a broad spectrum of target molecules [L. H. Hu et al., J. Chem. Phys. 119, 11501 (2003)]. However, its accuracy deteriorates with the increase in molecular size. A closer inspection reveals a systematic correlation between the prediction error and the molecular size, which appears correctable by further statistical analysis, calling for a more sophisticated machine learning algorithm. Despite the apparent difference between simple and complex molecules, all the essential physical information is already present in a carefully selected set of small molecule representatives. A model that can capture the fundamental physics would be able to predict large and complex molecules from information extracted only from a small molecules database. To this end, a size-independent, multi-step multi-variable linear regression-neural network-B3LYP method is developed in this work, which successfully improves the overall prediction accuracy by training with smaller molecules only. And in particular, the calculation errors for larger molecules are drastically reduced to the same magnitudes as those of the smaller molecules. Specifically, the method is based on a 164-molecule database that consists of molecules made of hydrogen and carbon elements. 4 molecular descriptors were selected to encode molecule's characteristics, among which raw HOF calculated from B3LYP and the molecular size are also included. Upon the size-independent machine learning correction, the mean absolute deviation (MAD) of the B3LYP/6-311+G(3df,2p)-calculated HOF is reduced from 16.58 to 1.43 kcal/mol and from 17.33 to 1.69 kcal/mol for the training and testing sets (small molecules), respectively. Furthermore, the MAD of the testing set (large molecules) is reduced from 28.75 to 1.67 kcal/mol.

Toward Chemical Accuracy in Predicting Enthalpies of Formation with General-Purpose Data-Driven Methods

“…Obviously, in all these specialpurpose approaches, ML's role is relegated to only predicting or improving the prediction of enthalpy of formation for a given chemical structure, and some ML-based approaches have the further limitation that they were developed only for certain classes of compounds such as acyclic hydrocarbons, 33 cyclic hydrocarbons, 34 energetic materials, 8 or fuels. 39 Such specialpurpose ML approaches also rely on molecular structures and other descriptors derived from structures, which are provided to a ML model, with the consequence that the ML model itself can neither generate a new molecular geometry nor improve upon it. An alternative to both QM and special-purpose ML approaches comes from a parallel development of general-purpose, data-driven methods based on ML, which target accurate predictions of QM potential energies for a wide range of compounds and can be used as a drop-in replacement for QM or force-field methods in many simulations such as molecular dynamics and geometry optimizations.…”

Effective Molecular Descriptors for Chemical Accuracy at DFT Cost: Fragmentation, Error-Cancellation, and Machine Learning

“…Simultaneously, machine learning (ML) has been added to the quantum chemical toolbox, ,,,,− leading to a significant decrease in the computational cost and/or increase in the accuracy of the corresponding calculated properties. The success of a given ML model depends on its chosen set of molecular descriptors, as the representation must fully describe patterns in the desired output values.…”

Guest Editorial: Special Topic on Data-Enabled Theoretical Chemistry

“…Yang et al 30 introduce a size-independent NN model of heats of formation trained on small organic molecules that can be applied to large molecules. For these, the MAE from reference B3LYP numbers is reduced to 1.7 kcal/mol.…”