Machine learning the C 5 H 5 potential energy surface Yoona Yang 1 , Carles Martí Aliod 1 , Michael S. Eldred 2 , Judit Zádor 1 , Habib N. Najm 1 1 Combustion Research Facility, USA, 2 Optimization & UQ Department, USA Understanding the mechanism of molecular weight growth for hydrocarbons is a scientific puzzle with implications to combustion science and human health. Many of the key reactions during the initial stages happen over multiple interconnected wells and require the solution of the master equation. A plethora of these reactions have been studied, but there is no consensus on the key elementary steps, partially because of the complexity and number of the possible pathways. Part of the complexity that arises can be tackled with automated kinetics tools, such as KinBot. 1 However, these tools rely on expensive electronic structure calculations to evaluate the properties of the stationary points on the potential energy surfaces (PESs). To alleviate this problem, we are building a neural network (NN), with atomic environment vector (AEV) inputs, to represent the PES of the relevant class of heavy hydrocarbons to replace electronic structure calculations and accelerate discovery. Atomistic machine learning has found use in speeding up estimation of stable molecule energies, at DFT or better accuracy, with orders of magnitude lower cost. However, studying reactive process is a much more challenging task for NN fitting. Johansson et al. 2 postulated resonantly stabilized molecules to be key for molecular weight growth processes in flames, but rigorous proof for this hypothesis is lacking. We demonstrate our initial results on a C 5 H 5 PES, which corresponds to the products of the acetylene + propargyl reaction. Propargyl and several species on the C 5 H 5 PES, such as cyclopentadienyl, are resonantly stabilized molecules. We use KinBot to explore the reactions starting at the initial adduct of the propargyl + acetylene reactants at the B3LYP/6-31+G(d) level of theory. KinBot is able to find all known pathways and several new ones. We extract, organize, and curate the large number of structures that arise during the exploration, and create a diversified database of perturbed structures using normal mode sampling. To enhance the performance of our NN PES construction, we explore multiple strategies. We used an uncertainty- informed active learning query-by-committee strategy, employing an ensemble of NNs, to identify the optimal next batch of training data points. We enhanced our training using forces, which can be obtained almost for free and provide 30x more data for the C 5 H 5 system than energies alone. The model trained using both energy and force shows the same accuracy with 25 times less data points than the model trained using energy only. Lastly, we developed a range of multifidelity NN constructions, which we trained using data at different levels of theory. We found that a hybrid discrepancy-based architecture shows the best performance. Our NN PES exhibits ab initio accuracy (< 1 kcal/mol error), which allows the investigation of reaction rates, with well-matched results in comparison with ab initio rate computations. References 1. Van de Vijver, R.; Zádor, J., Kinbot: Automated Stationary Point Search on Potential Energy Surfaces. Comp. Phys. Comm. 2020, 248 , 106947. 2. Johansson, K. O.; Head-Gordon, M. P.; Schrader, P. E.; Wilson, K. R.; Michelsen, H. A., Resonance-Stabilized Hydrocarbon- Radical Chain Reactions May Explain Soot Inception and Growth. Science 2018, 361 (6406), 997-1000.
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