PIML-SM: Physics-informed machine learning to estimate surface soil moisture from multi-sensor satellite images by leveraging swarm intelligence

We introduce a physics-informed machine learning (PIML) algorithm based on a feed-forward neural network (FFNN) to estimate surface soil moisture from limited in situ measurements and Sentinel-1/2 satellite images on the alluvial fan of the Kosi River by leveraging radar physics. We set up a learning bias PIML by modifying the loss function of the FFNN by using the improved integral equation model (I2EM). A particle swarm optimization (PSO) algorithm is used to optimize the tuning parameters of the PIML. The effectiveness of the proposed model is compared with ten benchmark algorithms. The performance of PIML model is superior among the benchmark algorithms, achieving a correlation coefficient (R) of 0.94, a root mean square error (RMSE = 0.019 m³/m³), and bias =−0.03 m³/m³. We conclude that the PIML model can accurately estimate soil moisture solely from satellite images, achieving higher spatial and temporal resolutions, even with limited in situ observations. The findings of this study can be applied in agriculture, hydrology, flood management, and drought monitoring, particularly in data-scarce regions.