Data-driven framework for general explicit formula of ionic thermoregulated osmotic energy conversion based on similarity principle and deep learning

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.