# Indoor temperature field reconstruction

Indoor heating usually relies on one or a few fixed-point temperature readings, which miss the spatial variation around an occupant. A physics-informed neural network drops time as an explicit input and instead infers how the temperature field evolves from spatial coordinates plus a few sensor readings and their rates of change; across nine horizontal planes in three room-scale configurations it matched a validated COMSOL multiphysics simulation with a maximum relative error below 1.85%. Wired into occupant-centric heating control, it showed an average numerical error of about 0.67% against COMSOL-based offline control, with inference fast enough for real-time use.

Indoor heating usually relies on one or a few fixed-point temperature readings, which miss the spatial variation around an occupant. A physics-informed neural network drops time as an explicit input and instead infers how the temperature field evolves from spatial coordinates plus a few sensor readings and their rates of change; across nine horizontal planes in three room-scale configurations it matched a validated COMSOL multiphysics simulation with a maximum relative error below 1.85%. Wired into occupant-centric heating control, it showed an average numerical error of about 0.67% against COMSOL-based offline control, with inference fast enough for real-time use.