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• Standard DNN methods might lead to highly uncertain and inaccurate predictions. • Multiphysics-informed neural network (MPINN) method is proposed. • Multiphisics constraints improve predictive ability of DNNs. • MPINN allows assimilating multiphysics data. • MPINN reduces data requirements for parameter estimation. Data assimilation for parameter and state estimation in subsurface transport problems remains a significant challenge because of the sparsity of measurements, the heterogeneity of porous media, and the high computational cost of forward numerical models. We present a multiphysics-informed deep neural network machine learning method for estimating space-dependent hydraulic conductivity, hydraulic head, and concentration fields from sparse measurements. In this approach, we employ individual deep neural networks (DNNs) to approximate the unknown parameters (e.g., hydraulic conductivity) and states (e.g., hydraulic head and concentration) of a physical system. Next, we jointly train these DNNs by minimizing the loss function that consists of the governing equations residuals in addition to the error with respect to measurement data. We apply this approach to assimilate conductivity, hydraulic head, and concentration measurements for the joint inversion of these parameter and states in a steady-state advection–dispersion problem. We study the accuracy of the proposed data assimilation approach with respect to the data size (i.e., the number of measured variables and the number of measurements of each variable), DNN size, and the complexity of the parameter field. We demonstrate that the physics-informed DNNs are significantly more accurate than the standard data-driven DNNs, especially when the training set consists of sparse data. We also show that the accuracy of parameter estimation increases as more different multiphysics variables are inverted jointly. [ABSTRACT FROM AUTHOR]

• This paper introduces the concept of Traveling Pilot Points (TRIPS) for solving the categorical inverse problem • The TRIPS methodology combined with subspace methods is used to identify channel structures in a categorical aquifer system while honoring calibration and prior constraints • Tests on a synthetic example suggest that the TRIPS methodology has promise and could be tested on more complicated problems Categorical parameter distributions are common-place in hydrogeological systems consisting of geologic facies/categories with distinct properties, e.g., high-permeability channels embedded in a low-permeability matrix. Parameter estimation is difficult in such systems because the discontinuities in the parameter space hinder the inverse problem. Previous research in this area has been focused on the use of stochastic methods. In this paper, we present a novel approach based on Traveling Pilot points (TRIPS) combined with subspace parameter estimation methods to generate realistic categorical parameter distributions that honor calibration constraints (e.g., - measured water levels). In traditional implementations, aquifer properties (e.g., hydraulic conductivity) are estimated at fixed pilot point locations. In the TRIPS implementation, both the properties associated with the pilot points and their locations are estimated. Tikhonov regularization constraints are incorporated in the parameter estimation process to produce realistic parameter depictions. For a synthetic aquifer system, we solved the categorical inverse problem by combining the TRIPS methodology with two subspace methods: Null Space Monte Carlo (NSMC) and Posterior Covariance (PC). A posterior ensemble developed with the rejection sampling (RS) method is compared against the TRIPS ensembles. The comparisons indicated similarities between the various ensembles and to the reference parameter distribution. Between the two subspace methods, the NSMC method produced an ensemble with more variability than the PC method. These preliminary results suggest that the TRIPS methodology has promise and could be tested on more complicated problems. [ABSTRACT FROM AUTHOR]