Neural network ensemble for computing cross sections for rotational transitions in H$_{2}$O + H$_{2}$O collisions

TL;DR

The paper tackles the computational bottleneck of obtaining rotationally inelastic cross sections for H$_2$O+H$_2$O collisions by developing a neural-network ensemble trained on MQCT data, covering 12 quantum-number inputs and both para/ortho symmetries. By transforming targets to $\log_{10}$ and carefully curating training data around the energy-gap $\Delta E$, the authors construct multiple NN models that interpolate state-to-state cross sections across collision energies. The approach achieves an average relative error around $4\times10^{-1}$ for cross sections (RMSE) and maintains thermally averaged cross sections accurate to roughly $13$–$14\%$ of MQCT values, while reducing computational costs by about a factor of 50. This enables rapid expansion of collision-rate databases for astrophysical modeling and is demonstrated to be robust enough to extend to other complex molecular systems and datasets.

Abstract

Water (H$_2$O) is one of the most abundant molecules in the universe and is found in a wide variety of astrophysical environments. Rotational transitions in H$_2$O + H$_2$O collisions are important in modeling environments rich in water molecules but they are computationally intractable using quantum mechanical methods. Here, we present a machine learning (ML) tool using an ensemble of neural networks (NNs) to predict cross sections to construct a database of rate coefficients for rotationally inelastic transitions in collisions of complex molecules such as water. The proposed methodology utilizes data computed with a mixed quantum-classical theory (MQCT). We illustrate that efficient ML models using NN can be built to accurately interpolate in the space of 12 quantum numbers for rotational transitions in two asymmetric top molecules, spanning both initial and final states. We examine various architectures of data corresponding to each collision energy, symmetry of water molecule, and excitation/de-excitation rotational transitions, and optimize the training/validation data sets. Using only about 10\% of the computed data for training, the NNs predict cross sections of state-to-state rotational transitions of H$_{2}$O + H$_{2}$O collision with average relative root mean square error of 0.409. Thermally averaged cross sections, computed using the predicted state-to-state cross sections ($\sim$90\%) and the data used for training and validation ($\sim$10\%) were compared against those obtained entirely from MQCT calculations. The agreement is found to be excellent with an average percent deviation of about $\sim$13.5\%. The methodology is robust, and thus, applicable to other complex molecular systems.

Figures (10)

• Figure 1: State-to-state cross sections for rotational transitions in H$_{2}$O + H$_{2}$O collisions as functions of the energy difference between initial and final rotational levels ($\Delta E$). Results for para-H$_{2}$O and ortho-H$_{2}$O targets are shown by open circles (red) and crosses (blue), respectively.
• Figure 2: Comparison of TACSs evaluated with all individual state-to-state cross sections from MQCT calculations with those computed by eliminating $\sigma<0.01~\mathrm{\AA}^{2}$. The dashed black line is the perfect agreement, while blue circles and red crosses correspond to the TACS for para and ortho-H$_{2}$ targets, respectively.
• Figure 3: A visual representation of the data used for training and validation as well as testing. The red circles denote the data for training and validation and the blue crosses denote the data for testing as given by eq. (\ref{['train_val_data']}).
• Figure 4: Architecture of the ML models comprised of four hidden layers with each having 128 neurons, thirteen features for the input layer, and one output neuron for the logarithm of the cross sections.
• Figure 5: The training and test data for all state-to-state transitions at the highest and lowest collision energies, based on Dataset 3, are presented as a function of $\Delta E$ for the para-H$_{2}$O molecule. The dataset for other collision energies and for ortho-H$_{2}$O is very similar.