Approaching Exact Quantum Chemistry through Data-Driven Multi-scale and Multi-fidelity Machine Learning Models

Bing Huang

Accuracy and efficiency are two challenging aspects to reconcile in quantum chemical computations. Even for small molecules, the computational cost for approaching or achieving exact solutions in quantum chemistry is prohibitively high. In recent years, the emergence of Machine Learning (ML) methods has provided a promising avenue to overcome this challenge[1-3], yet ML methods struggle to evade the curse imposed by scaling relationships[4]: obtaining more accurate results often requires adding more training samples (which significantly increases the cost of dataset construction and training). A more severe issue is that the precision of the training data for ML models determines the upper limit of prediction accuracy[5]. Therefore, to achieve absolute high precision (relative to experimental observations), a large amount of high-precision training data is needed, which is currently quite scarce. Herein, I would talk about a multi-level machine learning model[5,7] based on molecular fragments[6] and multi-fidelity molecular datasets, employing combinatorial mathematics and kernel methods, to approach exact solutions in quantum chemistry at minimal computational cost, thus fundamentally reconciling the contradiction between accuracy and efficiency. A distinctive feature of this model is the use of novel combination of datasets with different levels of precision: high-precision calculations (e.g., quantum Monte Carlo method) are performed only for the smallest molecular fragments, while larger molecular fragments are treated with increasingly more inexpensive methods (e.g., PBE/cc-pVTZ). Essentially, this model exploits the locality of atoms in molecules and the error cancellation mechanism widely exploited in quantum chemistry (as in composite methods like G2), which can be realized by combinatorial mathematics methods. Extensive numerical results demonstrate that this model can effectively approach exact solutions in quantum chemistry for medium-sized organic molecules (containing approximately nine or more non-hydrogen atoms). Once corresponding systematic big data can be established, this model is expected to achieve efficient and high-precision quantum chemical property predictions universally (i.e., for any compound system), thus greatly expanding the application scope of traditional quantum chemical computations and enabling direct correlation or comparison with experimental data.

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