Fast Fourier Convolutional GAN for 30 m Clear-Sky Land Surface Temperature Gap-Free Reconstruction

Satellite-derived Land Surface Temperature (LST) provides spatially comprehensive data that ground stations cannot match. However, its utility is frequently limited by severe data gaps due to the presence of clouds. As LST is essential for understanding land-atmosphere interactions, numerous methods have been proposed to address this challenge. Yet, the development of a scalable and adaptable pipeline for generating gap-free LST datasets and reconstructing cloud-contaminated pixels remains challenging. Moreover, the reconstruction of extensive missing regions in fine-spatial-resolution observations is particularly difficult. To address this challenge, we propose a Multimodal Fast Fourier Convolutional GAN for reconstructing cloud-contaminated pixels in fine-resolution (30 m) Landsat imagery to generate gap-free clear-sky LST products. The method leverages Fast Fourier Convolution to enable a global receptive field across the image, and is guided by a stack of data consisting of satellite observations and Synthetic Aperture Radar (SAR) data. Across all LST quantiles, the interquartile range of scene-averaged RMSE (computed over reconstructed pixels) is consistently between 0.8 K and 1.8 K. The proposed approach enables the recovery of extensive missing regions, including scenes with more than 70% cloud-induced gaps, while relying on auxiliary data that are readily available at a near-global scale.

A hybrid analytical-PINN model for subsurface simulation of geothermal heat exchangers in heterogeneous underground

In this paper, a parametric physics-informed neural network for solving the heterogeneous soil thermal problem with borehole heat exchangers (BHEs) as singular sources is developed. There are three novel features in the present framework; namely, (i) the singularity is naturally removed by using analytical line source models; (ii) using the explicit formulation for gradient thermal conductivity enables physics-informed learning of the parametrization featuring the conductivity; (iii) the learned correction is utilized as an efficient universal corrector via superposition principles. We first introduce the decomposition of the temperature change and transform the approximation of the entire heterogeneous response to the correction compensating the difference between the practical solution and idealized homogeneous approximation. In such a way, the delta function singularity is excluded and the bulk heat transfer is captured for the sake of facilitating the effective training of the neural network. The original problem is then reformulated as a governing correction diffusion or advection-diffusion equation subject to a homogeneous initial condition. The linearly varying thermal conductivity is used to model the soil heterogeneity. We propose a physics-informed neural network to approximate a universal corrector with respect to a single borehole with unit heat extraction rate. As a result, the network is trained by minimizing the physics-informed and data-anchored loss function that is evaluated for sampled conductivity parameters on adaptively selected training points. In addition, we include the location indicator function regarding the source as a feature input of network and find that it helps the network to process the local information. We perform numerical tests to exhibit the effectiveness of the proposed method based on three different analytical models.