Continuum models for ion transport through polyamide nanopores require solving partial differential equations (PDEs) through complex pore geometries. Resolving spatiotemporal features at this length and time-scale can make solving these equations computationally intractable. In addition, mechanistic models frequently require functional relationships between ion interaction parameters under nano-confinement, which are often too challenging to measure experimentally or know a priori. In this work, we develop the first physics-informed deep learning model to learn ion transport behaviour across polyamide nanopores. The proposed architecture leverages neural differential equations in conjunction with classical closure models as inductive biases directly encoded into the neural framework. The neural differential equations are pre-trained on simulated data from continuum models and fine-tuned on independent experimental data to learn ion rejection behaviour. Gaussian noise augmentations from experimental uncertainty estimates are also introduced into the measured data to improve model generalization. Our approach is compared to other physics-informed deep learning models and shows strong agreement with experimental measurements across all studied datasets.

翻译：通过聚酰胺纳米孔的离子输运连续介质模型需要求解复杂孔隙几何结构下的偏微分方程。在这种长度和时间尺度下解析时空特征可能导致求解过程在计算上变得难以处理。此外，机理模型通常需要纳米限域条件下离子相互作用参数之间的函数关系，而这些关系往往难以通过实验测量或先验获取。本研究首次开发了物理信息深度学习模型来学习聚酰胺纳米孔中的离子输运行为。所提出的架构将神经微分方程与经典闭合模型相结合，作为直接编码到神经框架中的归纳偏置。该神经微分方程首先在连续介质模型的模拟数据上进行预训练，随后利用独立实验数据进行微调以学习离子截留行为。通过引入基于实验不确定性估计的高斯噪声增强测量数据，提升了模型的泛化能力。与其他物理信息深度学习模型的对比表明，本方法在所有研究数据集上均与实验测量结果高度吻合。