The integration of big data, physical laws, and machine learning algorithms has shown potential to improve the estimation and understanding of complex real-world systems. However, effectively incorporating physical laws with uncertainties into machine learning algorithms remains understudied. In this work, we bridge this gap by developing the Partial Physics Informed Diffusion Model (PPIDM), a novel framework that integrates known physical principles through a physics operator while reducing the impact of unknown dynamics by minimizing related discrepancies. We showcase PPIDM’s capabilities using ocean surface chlorophyll concentration data, which are influenced by both physical and biological processes, while the latter is poorly constrained. Experimental results reveal that PPIDM achieves substantially improved prediction accuracy and stability, significantly outperforming baseline methods that either neglect physics entirely or impose incomplete physical constraints under the assumption of completeness.

Accurate remote estimation of chlorophyll-a (CHL) concentration for turbid inland waters is a challenging task due to their optical complexity. In situ spectra (n=666) measured with ASD and Ocean Optics spectrometers from three drinking water sources in Indiana, USA, were used to calibrate the partial least squares model (PLS), artificial neural network model (ANN), and the three-band model (TBM) for CHL estimates; model performances are validated with three independent datasets (n=360) from China. The PLS-ANN model resulted in accurate model calibration ( R2=0.94; Range=0.2-296.6 μg/l of CHL), outperforming the PLS (R2=0.87), ANN (R2=0.91), and TBM (R2=0.86). With an independent validation dataset, the PLS-ANN yielded relatively high accuracy (RMSE: 6.12 μg/l; rRMSE=42.12%; range=0.45-97.2 μg/l of CHL), while TBM yielded acceptable accuracy (RMSE: 8.85 μg/l; rRMSE=63.21%). With simulated ESA/MERIS and EO-1/Hyperion spectra, the PLS-ANN also (MERIS: R2=0.84; Hyperion: R2=0.88) outperforms the TBM (MERIS: R2=0.69; Hyperion: R2=0.76) for model calibration. For validation, the PLS-ANN achieves good performance with simulated spectra (MERIS: RMSE=7.83 μg/l, rRMSE=48.79%; Hyperion: RMSE=6.98 μg/l, rRMSE=45.57%) as compared to the TBM (MERIS: RMSE=10.39 μg/l, rRMSE=68.92%; Hyperion: RMSE=9.54 μg/l, rRMSE=65.35%). Nevertheless, considering the large and diverse datasets, the TBM is a robust semiempirical algorithm. Based on our observations, both the PLS-ANN and TBM are effective approaches for CHL estimation in turbid waters.

The paper proposes a method of collapsed buildings extraction from post-earthquake airborne images. Firstly, training and validation samples are selected, and feature extraction is conducted through morphological profiles and texture statistics based on gray-level co-occurrence matrix, and then support vector machine classifier is used to extract collapsed buildings. An initial experiment is carried out on images acquired after the 5.12 wenchuan earthquake. Results show that morphological features and texture features are complementary to each other in describing collapsed buildings; a reasonable extraction result is achieved based on these two kinds of features. However, due to the complexity of collapsed buildings in airborne images, more work is needed such as introducing more features and also a proper feature reduction method.