用于学习多离子输运的物理约束神经微分方程
Physics-constrained neural differential equations for learning multi-ionic transport
AI总结：
针对聚酰胺纳米孔离子输运连续介质模型计算成本高、离子作用参数难获取的问题，提出融合经典闭合模型的物理约束神经微分方程模型，经模拟预训练、实验微调及噪声增强提升泛化性，在多数据集上与实验结果高度匹配。
摘要：
用于描述聚酰胺纳米孔中离子输运的连续介质模型需要在复杂孔道几何结构下求解偏微分方程（PDE）。在该长度与时间尺度下解析时空特征，会导致这类方程的求解在计算上难以实现。此外，机理模型通常需要纳米约束下离子相互作用参数之间的函数关系，而这类关系往往难以通过实验测量或先验获知。本研究开发了首个用于学习聚酰胺纳米孔中离子输运行为的物理启发深度学习模型。该架构将神经微分方程与经典闭合模型作为归纳偏置，直接编码到神经框架中。神经微分方程先在连续介质模型生成的模拟数据上预训练，再在独立实验数据上微调以学习离子截留行为。研究还将源自实验不确定性估计的高斯噪声增强引入测量数据，以提升模型泛化能力。该方法与其他物理启发深度学习模型进行了对比，在所有研究数据集上均与实验测量结果高度吻合。
英文摘要：
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.
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