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：通过聚酰胺纳米孔进行离子输运的连续介质模型需要求解复杂孔隙几何结构中的偏微分方程。解析该尺度下的时空特征可能导致求解这些方程的计算复杂度超出实际可行范围。此外，机理模型通常需要纳米约束条件下离子相互作用参数之间的函数关系，而这类参数要么难以通过实验测量，要么无法预先获知。本文首次开发了物理信息驱动的深度学习模型，用于学习聚酰胺纳米孔中的离子输运行为。所提出的架构结合神经微分方程与经典闭合模型，将归纳偏置直接编码至神经框架中。神经微分方程首先通过连续介质模型生成的模拟数据进行预训练，随后利用独立实验数据微调以学习离子截留行为。同时引入基于实验不确定性估计的高斯噪声增强技术处理测量数据，从而提升模型泛化能力。与其它物理信息驱动的深度学习模型相比，本方法在所有研究数据集上均与实验测量结果表现出高度一致性。