Sensor-driven modeling of complex systems using physics-informed supervised machine intelligence

Modeling the intricate dynamics of complex systems is crucial for addressing global challenges ranging from pandemics to the climate crisis. While conventional first-principles models often struggle, advanced nanosensors employed in arrays and networks provide the high-dimensional and real-time data needed to understand these systems empirically. These datasets are often noisy, incomplete, and manipulated by stochastic, systematic, and nonlinear physical effects, making modeling and prediction challenging. Supervised machine learning (SML) has emerged as a powerful framework to address these challenges by determining explicit input–output relationships, unveiling fundamental system dynamics, enabling accurate prediction, and providing decision support. This review critically examines supervised approaches, including support vector machines algorithms, for sensor-driven modeling of complex systems, with particular emphasis on physics-informed machine learning, where physical laws and domain knowledge are embedded to enhance interpretability, robustness, and generalization. It highlights essential preprocessing methods, including data cleaning, feature engineering, and data fusion, where classical formulations like Kalman filtering, Fourier transforms, and weighted variance minimization integrate sensor physics with computational methods. Further, it discusses core supervised approaches, including regression and classification models, along with their physics-informed variants that integrate conservation laws, stochastic noise models, and network dynamics into learning algorithms as constraints. Through representative case studies across environmental monitoring, biomedical sensing, and industrial diagnostics, their practical utility has been established. Finally, open challenges in scalability, generalization, and integration with physics-informed machine intelligence are outlined with alternate solutions and prospects. This interdisciplinary integration of sensor physics and physics-guided SML represents a powerful paradigm of sensor intelligence for data-driven modeling of complex physical and biological systems.