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<p>Chemical modeling has traditionally been dominated by the exact framework of <i>ab initio</i> models based on the fundaments of quantum mechanics. However, recent advances in machine learning and data-driven approaches have intercepted the exact <i>ab initio</i> frameworks by using an <i>end-to-end</i> probabilistic model for the Schrödinger equation in the Born-Oppenheimer approximation—from raw nuclear configurations to quantum observables such as the energy. While probabilistic modeling offers promising advancements to speed up computational predictions, the internal representation and its connection to the underlying quantum data—the wave function or electron density—which they implicitly rely on for training, remains relatively poorly understood. This study seeks to make a first comparison of the internal representation from a probabilistic end-to-end models with those from pure <i>ab initio</i> frameworks such as density functional theory. We do this by comparing the internal atomwise representation of graph models, also called embeddings, to their most natural <i>ab initio</i> counterpart, electron occupancy values. Our findings show that the embedding representations can be employed to transfer learn atomic occupancy values whereas the reverse mapping appears to be less accurate. We discuss the assumption that the probabilistic model could infer the existence of an underlying electron density underpinning the computational <i>ab initio</i> data.</p>

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Occupancies vs embeddings: internal representations of Ab Initio and graph probabilistic models.

  • 期刊论文

  • 发表日期：

    2026年1月8日

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  • Incé Amina Husain,
  • Amer Marwan El-Samman,
  • Stijn De Baerdemacker

摘要

Chemical modeling has traditionally been dominated by the exact framework of ab initio models based on the fundaments of quantum mechanics. However, recent advances in machine learning and data-driven approaches have intercepted the exact ab initio frameworks by using an end-to-end probabilistic model for the Schrödinger equation in the Born-Oppenheimer approximation—from raw nuclear configurations to quantum observables such as the energy. While probabilistic modeling offers promising advancements to speed up computational predictions, the internal representation and its connection to the underlying quantum data—the wave function or electron density—which they implicitly rely on for training, remains relatively poorly understood. This study seeks to make a first comparison of the internal representation from a probabilistic end-to-end models with those from pure ab initio frameworks such as density functional theory. We do this by comparing the internal atomwise representation of graph models, also called embeddings, to their most natural ab initio counterpart, electron occupancy values. Our findings show that the embedding representations can be employed to transfer learn atomic occupancy values whereas the reverse mapping appears to be less accurate. We discuss the assumption that the probabilistic model could infer the existence of an underlying electron density underpinning the computational ab initio data.