# Variational encoder geostatistical analysis (VEGAS) with an application to large scale riverine bathymetry

arXiv: https://arxiv.org/abs/2111.11719 · HTML: https://mlsanity.com/paper/2111.11719/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 58 references that are in the map.
- First posted on arXiv 23 Nov 2021.

## Builds on (most cited first, 6 of 6)

- [An Introduction to Variational Autoencoders](https://mlsanity.com/paper/1906.02691/) (2019)
- [Exploring Generalization in Deep Learning](https://mlsanity.com/paper/1706.08947/) (2017)
- [Why and When Can Deep -- but Not Shallow -- Networks Avoid the Curse of Dimensionality: a Review](https://mlsanity.com/paper/1611.00740/) (2016)
- [A Comprehensive Review of Deep Learning Applications in Hydrology and Water Resources](https://mlsanity.com/paper/2007.12269/) (2020)
- [Application of deep learning to large scale riverine flow velocity estimation](https://mlsanity.com/paper/2012.02620/) (2020)
- [Tangent: Automatic Differentiation Using Source Code Transformation in Python](https://mlsanity.com/paper/1711.02712/) (2017)

## Built on by (most cited first, 3 of 3)

- [Differentiable modeling to unify machine learning and physical models and advance Geosciences](https://mlsanity.com/paper/2301.04027/) (2023)
- [Function-Space Decoupled Diffusion for Forward and Inverse Modeling in Carbon Capture and Storage](https://mlsanity.com/paper/2602.12274/) (2026)
- [Subsurface Characterization using Ensemble-based Approaches with Deep Generative Models](https://mlsanity.com/paper/2310.00839/) (2023)

## Abstract (arXiv)

Estimation of riverbed profiles, also known as bathymetry, plays a vital role in many applications, such as safe and efficient inland navigation, prediction of bank erosion, land subsidence, and flood risk management. The high cost and complex logistics of direct bathymetry surveys, i.e., depth imaging, have encouraged the use of indirect measurements such as surface flow velocities. However, estimating high-resolution bathymetry from indirect measurements is an inverse problem that can be computationally challenging. Here, we propose a reduced-order model (ROM) based approach that utilizes a variational autoencoder (VAE), a type of deep neural network with a narrow layer in the middle, to compress bathymetry and flow velocity information and accelerate bathymetry inverse problems from flow velocity measurements. In our application, the shallow-water equations (SWE) with appropriate boundary conditions (BCs), e.g., the discharge and/or the free surface elevation, constitute the forward problem, to predict flow velocity. Then, ROMs of the SWEs are constructed on a nonlinear manifold of low dimensionality through a variational encoder. Estimation with uncertainty quantification (UQ) is performed on the low-dimensional latent space in a Bayesian setting. We have tested our inversion approach on a one-mile reach of the Savannah River, GA, USA. Once the neural network is trained (offline stage), the proposed technique can perform the inversion operation orders of magnitude faster than traditional inversion methods that are commonly based on linear projections, such as principal component analysis (PCA), or the principal component geostatistical approach (PCGA). Furthermore, tests show that the algorithm can estimate the bathymetry with good accuracy even with sparse flow velocity measurements.