Ionic thermoregulated osmotic energy conversion in nanochannels synergistically utilizes osmotic and thermal energy for power generation based on ionic selective transport in charged nano-membranes under salinity gradients and thermal regulations. Currently, no explicit general dimensionless formulas exist that reflect the relationship between impact factors and performance to guide performance designs. In this study, data-driven insight is presented to establish a framework for obtaining explicit and general relational expressions based on data augmentation using the similarity principle and deep learning. The original database is derived from a finite element simulation with 10,000 dimensional samples, then augmented to 30,000 dimensional samples via similarity principle-based data augmentation. Subsequently, a deep neural network model with decay algorithms is employed to expand the database to new 300,000 dimensional samples with a prediction accuracy exceeding 98 %, which are further converted to dimensionless forms for multiple linear regression. Three dimensionless and explicit formulas for the electrical potential, output power, and energy conversion efficiency are obtained, which indicate determination coefficients of 0.91, 0.93, and 0.92, respectively. Furthermore, considering actual experimental and application situations, the modified dimensionless formula of the output power predicts the experimental results with an average error of 7.80 %. This study efficiently alleviates experimental burden and facilitates engineering applications.

中文翻译：

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基于相似原理和深度学习的离子温控渗透能转换通用显式公式的数据驱动框架


纳米通道中的离子温控渗透能转换基于盐度梯度和热调节下带电纳米​​膜中的离子选择性传输，协同利用渗透能和热能进行发电。目前，尚不存在明确的通用无量纲公式来反映影响因子与绩效之间的关系来指导绩效设计。在本研究中，提出了数据驱动的洞察力，以使用相似性原理和深度学习建立基于数据增强的获取显式和通用关系表达式的框架。原始数据库是通过 10,000 维样本的有限元模拟得出的，然后通过基于相似性原理的数据增强扩展到 30,000 维样本。随后，采用具有衰减算法的深度神经网络模型将数据库扩展到新的30万维样本，预测精度超过98%，并进一步转换为无量纲形式进行多元线性回归。得到了电势、输出功率和能量转换效率的三个无量纲显式公式，其决定系数分别为0.91、0.93和0.92。此外，考虑到实际实验和应用情况，修正后的输出功率无量纲公式对实验结果的预测平均误差为7.80%。该研究有效减轻了实验负担，有利于工程应用。