The goal of this project is to develop integrated data-driven modeling capabilities with physics constraints. This project will advance methods for integrating data and models by using state-of-the-art physics-informed machine learning methods to improve the accuracy of model predictions through better model parameterization and uncertainty quantification. We will develop (1) physics-informed machine-learning (PIML) parameter estimation methods and (2) PIML surrogate models. In these models, the unknown parameter fields and state variables are modeled with deep neural networks (DNN) or conditional Karhunen-Loeve (KL) expansions. The main advantage of these methods is that they require a relatively small amount of data for training. This is because the physics constraints allow us to fill “gaps” in the data and make the surrogate models more accurate. We will focus on surrogate models where inputs are functions, rather than a finite number of parameters that could be an output of climate or socioeconomic models. Project deliverables include physics-informed machine-learning codes for parameter estimation and surrogate modeling that can be integrated with the existing USGS computational models. To date, we have delivered three machine-learning codes that differ in the way physics is enforced. These codes are described in the Product List section. They rely on MODFLOW to generate training data sets. The publication plan is to submit at least two papers, including one paper on parameter estimation and one paper on surrogate modeling. To date, we have submitted two papers and are preparing the third paper. These papers are listed in the Product List section.