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:通过聚酰胺纳米粒子进行离子传输的连续性模型需要通过复杂的孔径地貌解决部分差异方程(PDEs) 。 以这种长度和时间尺度解决时空特征可以使这些方程的计算难以解决。 此外, 机械化模型经常需要纳米封闭下离子互动参数之间的功能关系, 这对于实验性或先验性测量来说往往过于困难。 在这项工作中, 我们开发了第一个物理知情的深层次学习模型, 以学习跨聚酰胺纳米粒子的离子传输行为。 拟议的建筑利用神经差异方程式与经典封闭方程模型相结合, 将感性偏向性偏向直接编码到神经框架。 神经差异方程式经过预先培训, 模拟数据来自连续模型,对独立实验数据进行微调,以学习电离子拒绝行为。 实验性不确定性估计产生的噪音增强值也被引入测量的数据中, 以改进模型的概括性。 我们的方法与其他物理学知情深度学习模型进行比较, 并显示所有研究数据集的实验性测量结果的强烈一致。</s>