# Inferring Underwater Topography with FINN

arXiv: https://arxiv.org/abs/2408.10649 · HTML: https://mlsanity.com/paper/2408.10649/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 22 references that are in the map.
- First posted on arXiv 20 Aug 2024.

## Builds on (most cited first, 8 of 8)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [Disentangling Physical Dynamics from Unknown Factors for Unsupervised Video Prediction](https://mlsanity.com/paper/2003.01460/) (2020)
- [Composing Partial Differential Equations with Physics-Aware Neural Networks](https://mlsanity.com/paper/2111.11798/) (2021)
- [Finite Volume Neural Network: Modeling Subsurface Contaminant Transport](https://mlsanity.com/paper/2104.06010/) (2021)
- [A Distributed Neural Network Architecture for Robust Non-Linear Spatio-Temporal Prediction](https://mlsanity.com/paper/1912.11141/) (2019)
- [Active Tuning](https://mlsanity.com/paper/2010.03958/) (2020)

## Abstract (arXiv)

Spatiotemporal partial differential equations (PDEs) find extensive application across various scientific and engineering fields. While numerous models have emerged from both physics and machine learning (ML) communities, there is a growing trend towards integrating these approaches to develop hybrid architectures known as physics-aware machine learning models. Among these, the finite volume neural network (FINN) has emerged as a recent addition. FINN has proven to be particularly efficient in uncovering latent structures in data. In this study, we explore the capabilities of FINN in tackling the shallow-water equations, which simulates wave dynamics in coastal regions. Specifically, we investigate FINN's efficacy to reconstruct underwater topography based on these particular wave equations. Our findings reveal that FINN exhibits a remarkable capacity to infer topography solely from wave dynamics, distinguishing itself from both conventional ML and physics-aware ML models. Our results underscore the potential of FINN in advancing our understanding of spatiotemporal phenomena and enhancing parametrization capabilities in related domains.