Multi-fidelity graph neural networks for predicting toluene/water partition coefficients

Accurate prediction of toluene/water partition coefficients of neutral species is crucial in drug discovery and separation processes; however, data-driven modeling of these coefficients remains challenging due to limited available experimental data. To address the limitation of available data, we apply multi-fidelity learning approaches leveraging a quantum chemical dataset (low fidelity) of approximately 9000 entries generated by COSMO-RS and an experimental dataset (high fidelity) of about 250 entries collected from the literature. We explore the transfer learning, feature-augmented learning, and multi-target learning approaches in combination with graph neural networks, validating them on two external datasets: one with molecules similar to training data (EXT-Zamora) and one with more challenging molecules (EXT-SAMPL9). Our results show that multi-target learning significantly improves predictive accuracy, achieving a root-mean-square error of 0.44 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>log</mml:mo> <mml:mi>P</mml:mi></mml:mrow> </mml:math> units for the EXT-Zamora, compared to a root-mean-square error of 0.63 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>log</mml:mo> <mml:mi>P</mml:mi></mml:mrow> </mml:math> units for single-task models. For the EXT-SAMPL9 dataset, multi-target learning achieves a root-mean-square error of 1.02 <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mo>log</mml:mo> <mml:mi>P</mml:mi></mml:mrow> </mml:math> units, indicating reasonable performance even for more complex molecular structures. These findings highlight the potential of multi-fidelity learning approaches that leverage quantum chemical data to improve toluene/water partition coefficient predictions and address challenges posed by limited experimental data. We expect the applicability of the methods used beyond just toluene/water partition coefficients.