Parameter inversion with sequential neural density estimators: an enhanced machine learning-based inversion
Abstract
Estimating hydrological properties and quantifying their uncertainty from observed measurements is critical for sustainable groundwater management and decision-making processes. One recent development in this parameter inversion problem is called the machine learning-based inversion: we first use machine learning methods to find the unknown non-linear projection from data to hydrological model variables, then we use additional density estimators such as kernel density estimators to estimate the joint distribution of the projected lower-dimensional data and model variables.
In this work, we improve the ML-based inversion method and learn the posterior density directly using neural density estimators without two separate steps. The specific neural density estimator we used is masked autoregressive flow (MAF). MAF represents the posterior distribution p(m|d) through a series of bijective autoregressive functions. Those autoregressive functions are functions of data d and Gaussian random variables z. Hidden neural network layers in autoregressive functions learn the non-linear projection in the ML-based inversion. After many bijective transformations on Gaussian distributions, we can learn any posterior density through masked autoregressive flow by maximizing the total probability of Monte Carlo ensembles. To better constrain our posterior distributions with observed data, we also sequentially train the neural density estimators. One advantage of using neural posterior density estimators is likelihood-free, which means we do not need additional definitions and/or assumptions of the likelihood function. We test the effectiveness of neural density estimators on one synthetic pumping test with uncertain geostatistical parameters and on a real floodplain at the Slate River, Colorado. We derive the posterior distributions of hydrological parameters in the layered floodplain structure to understand the uncertainty of water exchanges due to beaver-induced inundation.- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2022
- Bibcode:
- 2022AGUFMNG35B0464W