  Progress in automatic control of thermal processes and real-time estimation
of heat penetration into live tissue has long been limited by the difficulty of
obtaining high-fidelity thermodynamic models. Traditionally, in complex
thermodynamic systems, it is often infeasible to estimate the thermophysical
parameters of spatiotemporally varying processes, forcing the adoption of
model-free control architectures. This comes at the cost of losing any
robustness guarantees, and implies a need for extensive real-life testing. In
recent years, however, infrared cameras and other thermographic equipment have
become readily applicable to these processes, allowing for a real-time,
non-invasive means of sensing the thermal state of a process. In this work, we
present a novel physics-based approach to learning a thermal process's dynamics
directly from such real-time thermographic data, while focusing attention on
regions with high thermal activity. We call this process, which applies to any
higher-dimensional scalar field, attention-based noise robust averaging (ANRA).
Given a partial-differential equation model structure, we show that our
approach is robust against noise, and can be used to initialize optimization
routines to further refine parameter estimates. We demonstrate our method on
several simulation examples, as well as by applying it to electrosurgical
thermal response data on in vivo porcine skin tissue.
