Deep-Learning-Based Adjoint State Method: Methodology and Preliminary Application to Inverse Modelling

We present an efficient adjoint model based on the deep-learning surrogate to address high-dimensional inversion problem with an application to subsurface transport. The proposed method provides a completely code non-intrusive and computationally feasible way to approximate the model derivatives, which subsequently can be used to derive gradients for inverse modelling. This conceptual deep-learning framework, i.e., an architecture of deep convolutional neural network through combining autoencoder and autoregressive structure, efficiently produces an analogously analytical adjoint with the help of auto-differentiation (AD) module in the popular deep-learning packages. This work has been submitted to Water Resources Research. The code will be updated based on the acceptation of submitted paper.