Characterization of Thermal Systems from Noisy and Low-resolution Measurements Using Dynamic Mode Decomposition

Abstract

Thermal monitoring in practical applications is often constrained by sparse sensing, measurement noise, and limited spatial resolution, which hinder the identification of heat transfer dynamics. In such settings, calibrating high-fidelity physical models is computationally demanding, motivating data-driven approaches. Dynamic Mode Decomposition (DMD) provides a framework for extracting spatiotemporal structures from measurement data, but its standard formulation is sensitive to noise and degraded observations. This chapter examines the use of DMD under these constraints, focusing on preprocessing and truncation strategies that affect stability and interpretability. Two cases are considered: forced convection with thermocouple data and transient heat conduction from degraded thermal images. The number of retained modes is treated as a modeling parameter that governs the trade-off between reconstruction fidelity and noise sensitivity. The results indicate that DMD recovers dominant thermal behavior from both sparse and degraded datasets when the truncation level is appropriately selected. Low-rank models provide stable but simplified descriptions, while higher-rank models improve spatial detail at the cost of increased noise sensitivity.