rsyamil/latent-space-inversion-lsi

Joint parameterization and direct history-matching method for engineering systems. LSI simultaneously extracts salient spatial and temporal features for direct inversion. Exploration of meaningful latent spaces allows rapid generation of ensemble of relevant inversion solutions.

latent-space-inversion-lsi

This repository supplements H052-08 - Latent-Space Inversion (LSI) for Subsurface Flow Model Calibration with Physics-Informed Autoencoding as presented at the American Geophysical Union Fall Meeting 2020 (AGUFM2020) and Latent-Space Inversion (LSI): A Deep Learning Framework for Inverse Mapping of Subsurface Flow Data (COMG).

latent-space-inversion 
│
└─── mnist
│   
└─── 2d-fluvial

Demos based on the MNIST dataset and a 2D fluvial field dataset (see folder structure) are archived in this repository.

The AGUFM2020 video presentation can be viewed below:

Workflow

LSI performs simultaneous dimensionality reduction (by extracting salient spatial features from M and temporal features from D) and inverse mapping (by mapping the salient features in D to M, i.e. latent spaces z_d and z_m). The architecture is composed of dual autoencoders connected with a regression model as shown below and is trained jointly. Since the latent spaces z_d and z_m correspond to meaningful spatial and temporal variations in D and M respectively, they can be explored to obtain an ensemble of relevant inversion solutions. The sampled points in the data latent space can be inversely mapped to the model latent space and the model decoder can be used to decode the sampled points around z_m to obtain the ensemble of relevant inversion solutions.

In practical applications, observed d can be noisy and LSI helps us to quickly obtain the ensemble of relevant inversion solutions that can be accepted within the noise level, as well as understand the variations of spatial features within the ensemble to improve the predictive power of the inversion solutions.

latent-space-inversion-lsi's Issues

Unable to connect trained layers VAE in autoencoderdual.py for loaded h5 model

LSI architecture can also utilize VAEs, see autoencoderdual.py. When LSI is trained and the computation graphs are active, we can get m2zm and d2zd but when model is loaded, and m2zm/d2zd need to be assembled from the loaded h5 models. An error associated with the sampling (lambda) layer is thrown.

Run qc-demo.ipynb to replicate the error, use LSI.train_autoencoder_dual_var() and set load=False.

architecture for 2d-fluvial example can be improved

remove dense layers and replace with conv, train for longer epoch