A Physics‐Informed Neural Network for Retrieving the Continuous Soil Particle Size Distribution From Vis– NIR Spectra

ABSTRACT Estimating the soil particle size distribution (PSD) from visible–near infrared (vis–NIR) reflectance spectra is conventionally limited to predicting discrete soil fractions (e.g., sand, silt, and clay). This approach presents significant challenges: it requires the harmonization of data from different classification systems and, by reducing the PSD to a few values, fails to reflect the entire variation in soil texture. To address these gaps, we present a novel physics‐informed neural network (PINN) for the direct estimation of the continuous PSD from vis–NIR reflectance measurements. The PINN learns a continuous, differentiable, and non‐parametric representation of the cumulative PSD by integrating both measurements and physical constraints imposed during training. This approach eliminates the need for harmonization and interpolation of measurements originating from different soil texture classification systems and allows the model to be trained on datasets with varying numbers of measurements per sample. Performance evaluation on 30% of the 2777 studied samples showed that the PINN achieved an RMSE of 6.77% and an R 2 of 0.97 in predicting the cumulative PSD fraction. For the texture fractions, the model achieved RMSE values of 4.72%, 3.06%, and 2.75% for sand, silt, and clay, respectively. A comparison with a physics‐agnostic (i.e., physics‐uninformed) version of the model revealed that both approaches performed similarly in terms of RMSE and R 2 . However, the physics‐agnostic model violated physical constraints even in data‐rich scenarios. In contrast, the PSD obtained from the PINN maintained its physical integrity even under data sparsity conditions and consistently produced non‐negative, monotonically increasing predictions that sum to 100% at the largest particle size.