Learning the Differential Operator of the Transient Heat Conduction Equation with Physics-Informed Fourier Neural Operators

Abstract

In this work, Physics-Informed Neural Operators (PINOs) are used to approximate the differential operator of the one-dimensional transient heat conduction equation. Building on Fourier Neural Operators (FNOs, neural architectures with Fourier layers) PINOs incorporate the governing differential equations directly, thereby eliminating the need for labeled data. Once trained, the model can predict solutions at future times and for initial conditions not encountered during training. This approach advances the modeling of physical phenomena by enabling the development of surrogate or reduced-order models applicable to optimization tasks and multiscale problems in heat transfer.