The accurate description of the flow of water in porous media is of the greatest importance due to its numerous applications in several areas (groundwater, soil mechanics, etc.). The nonlinear Richards equation is often used as the governing equation that describes this phenomenon and a large number of research studies aimed to solve it numerically. However, due to the nonlinearity of the constitutive expressions for permeability, it remains a challenging modeling problem. In this paper, the stationary form of Richards’ equation used in saturated soils is solved by two numerical methods: generalized finite differences, an emerging method that has been successfully applied to the transient case, and a finite element method, for benchmarking. The nonlinearity of the solution in both cases is handled using a Newtonian iteration. The comparative results show that a generalized finite difference iteration yields satisfactory results in a standard test problem with a singularity at the boundary.

Background: Artificial intelligence (AI) models applied to diabetes mellitus research have grown in recent years, particularly in the field of medical imaging. However little work has been done exploring real-world data (RWD) sources such as electronic health records (EHR) mostly due to the lack of reliable public diabetes databases. However, with more than 500 million patients affected worldwide, complications of this condition have catastrophic consequences. In this manuscript we aim to first extract, clean and transform a novel diabetes research database, DiabetIA, and secondly train machine learning (ML) models to predict diabetic complications. Methods: In this study, we used observational retrospective data from the Mexican Institute for Social Security (IMSS) extracting and de-identifying EHR data for almost 2 million patients seen at primary care facilities. After applying eligibility criteria for this study, we constructed a diabetes complications database. Next, we trained naïve Bayesian models with various subsets of variables, including an expert-selected model. Results: The DiabetIA database is composed of 136,674 patients (414,770 records and 447 variables), with 33,314 presenting diabetes (24.3%). The most frequent diabetic complications were diabetic foot with 2,537 patients, nephropathy with 1,914 patients, retinopathy with 1,829 patients, and neuropathy with 786 patients. These complications were accurately predicted by the Gaussian naïve Bayessian models with an average area under the curve AUC of 0.86. Our expert-selected model, achieved an average AUC of 0.84 with 21 curated variables. Conclusion: Our study offers the largest longitudinal research database from EHR data in Latin America for research. The DiabetIA database provides a useful resource to estimate the burden of diabetic complications on healthcare systems. Machine learning models can provide accurate estimations of the total cases presented in medical units. For patients and their clinicians, it is imperative to have a way to calculate this risk and start clinical interventions to slow down or prevent the complications of this condition. Brief description: The study centers on establishing the DiabetIA database, a substantial repository encompassing de-identified electronic health records from 136,674 patients sourced from primary care facilities within the Mexican Institute for Social Security (IMSS). Our efforts involved curating, cleansing, and transforming this extensive dataset, and then employing machine learning models to predict diabetic complications with high accuracy.