Latent-Space Inversion (LSI) for Subsurface Flow Model Calibration with Physics-Informed Autoencoding

Abstract:

Traditional model calibration is performed by formulating and solving a nonlinear inverse problem through repeated forward flow simulation runs in an iterative scheme. Parameterization methods are typically applied to reduce the dimensionality of spatially distributed flow properties (as unknowns) prior to solving the inverse problem, thereby decoupling parameterization from the inversion process. We present novel neural network architectures that offer the versatility to develop direct inverse mapping from data to model parameter space and allow for parameterization to be informed by the flow response data. Specifically, we present the Latent-Space Inversion (LSI) as a novel physics-informed parameterization and inversion method, where dimensionality reduction is tailored to the physics that governs the behavior of subsurface flow systems. We demonstrate LSI as a robust and effective approach for calibration of subsurface flow models over standard autoencoders where dimensionality reduction of model parameters is done independently of dynamic data integration. Parameterization with LSI provides a compact description of the parameters in a latent space that exploits the redundancy of large-scale geologic features and retains features that are sensitive to flow data. The LSI consists of a pair of deep convolutional autoencoders that are coupled as an architecture to extract spatial geologic features in subsurface models and temporal trends in flow data. The LSI model is trained to effectively represent the model and data and to learn the complex nonlinear inverse mapping between data and model simultaneously. Once field data becomes available, calibrated models can be rapidly obtained using the trained LSI architecture. We demonstrate the effectiveness of LSI using large-scale 3D subsurface flow models with both Gaussian and complex fluvial (non-Gaussian) spatial features. In addition to learning the inverse mapping directly from training data, LSI performs dimensionality reduction of the parameters by retaining the salient spatial (geologic) patterns in the training models, which is critical for geologic plausibility of the solutions, especially when the underlying patterns are complex (non-Gaussian).