A Physical Information Neural Network (PINN)-Based Model for Soft Measurement of 3D Temperature Field in Aluminium Electrolysers

Aluminium electrolysers, as the core equipment for aluminium electrolysis, have an internal three-dimensional temperature distribution that directly reflects their working condition and impacts both production quality and safety. Traditional measurement methods and soft measurement techniques are inadequate, and research on high-dimensional data, such as 3D temperature fields, still needs enhancement. In this paper, we propose a PINN-based soft measurement model for the 3D temperature field of aluminium electrolysers. This model uses the operating current and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\boldsymbol{x},\ \boldsymbol{y},\ \boldsymbol{z}$</tex> coordinates as inputs to the PINN, and outputs the temperatures at the corresponding positions. The prediction error is less than 1%, and the prediction time is reduced by six orders of magnitude compared to finite element simulations, meeting the requirements for real-time online prediction in engineering applications.