Vinod Vivin, Zaspel Peter
School of Mathematics and Natural Sciences, University of Wuppertal, Wuppertal 42119 Germany.
J Chem Theory Comput. 2025 Mar 25;21(6):3077-3091. doi: 10.1021/acs.jctc.4c01491. Epub 2025 Mar 13.
Recent progress in machine learning (ML) has made high-accuracy quantum chemistry (QC) calculations more accessible. Of particular interest are multifidelity machine learning (MFML) methods, where training data from differing accuracies or fidelities are used. These methods usually employ a fixed scaling factor, γ, to relate the number of training samples across different fidelities, which reflects the cost and assumed sparsity of the data. This study investigates the impact of modifying γ on model efficiency and accuracy for the prediction of vertical excitation energies using the QeMFi benchmark data set. Further, this work introduces QC compute time-informed scaling factors, denoted as θ, that vary based on QC compute times at different fidelities. A novel error metric, error contours of MFML, is proposed to provide a comprehensive view of model error contributions from each fidelity. The results indicate that high model accuracy can be achieved with just 2 training samples at the target fidelity when a larger number of samples from lower fidelities are used. This is further illustrated through a novel concept, the Γ-curve, which compares model error against the time-cost of generating training samples, demonstrating that multifidelity models can achieve high accuracy while minimizing training data costs.
机器学习（ML）的最新进展使高精度量子化学（QC）计算变得更加容易实现。特别值得关注的是多保真度机器学习（MFML）方法，该方法使用来自不同精度或保真度的训练数据。这些方法通常采用固定的缩放因子γ来关联不同保真度下的训练样本数量，这反映了数据的成本和假设的稀疏性。本研究使用QeMFi基准数据集，研究修改γ对垂直激发能预测模型效率和准确性的影响。此外，这项工作引入了基于QC计算时间的缩放因子θ，该因子根据不同保真度下的QC计算时间而变化。提出了一种新的误差度量——MFML误差等高线，以全面了解每个保真度对模型误差的贡献。结果表明，当使用大量来自较低保真度的样本时，在目标保真度下仅用2个训练样本就能实现较高的模型精度。通过一个新颖的概念——Γ曲线进一步说明了这一点，该曲线将模型误差与生成训练样本的时间成本进行比较，表明多保真度模型可以在最小化训练数据成本的同时实现高精度。
