MIMO system identification and uncertainty calibration with a limited amount of data using transfer learning

Multiple-input multiple-output (MIMO) systems are fundamental in numerous advanced engineering applications, from aerospace to telecommunications, where precise system identification is critical for optimal performance. However, the identification of such systems often faces significant hurdles due to data scarcity, with existing approaches typically requiring substantial amounts of data for effective training. Addressing this challenge, this paper introduces a novel transfer learning framework designed specifically for MIMO system identification under conditions of limited data and inherent uncertainties. The proposed framework is applied to two case studies: the first in metal additive manufacturing, specifically the laser-blown powder-directed energy deposition as the source domain and the laser hot wire-directed energy deposition as the target domain, and the second involving a nonlinear case study of a continuous stirred-tank reactor (CSTR) with a temperature-dependent reaction. The results underscore the framework's effectiveness in capturing the dynamics of the target systems, including the ability to effectively model nonlinear dynamics. Comparative analyses highlight the benefits of employing dimensionless numbers in dynamic system modelling, offering reduced dimensionality, more physical meaning, and increased model accuracy. Overall, the proposed framework presents a promising approach to enhance system identification in MIMO systems with limited data and uncertainties, with potential applications across diverse domains.