Learning reaction-transport coupling from thermal waves

Although thermal waves are ubiquitous in nature and engineering, the development of diagnostic tools capable of elucidating the roles of reaction and transport remains an unmet need. This limits our comprehension of the physics and ability to predict wave dynamics. Here we demonstrate that thermal properties and chemical kinetics can be learned directly from observing thermal wave dynamics, using partial differential equation-constrained optimization. This enables the determination of unobserved reaction rates without the need for a comprehensive measurement of all state variables, given the model space constrained by governing equations. Examples include steady planar waves and unsteady pulsating waves of which dynamics are commonly observed in nature. We show successful learning of thermal properties and chemical kinetics and reconstruction of wave dynamics with the inferred properties, which enables the comprehension of the intricate reaction-transport coupling from thermal data.