# Towards Optimally Weighted Physics-Informed Neural Networks in Ocean Modelling

arXiv: https://arxiv.org/abs/2106.08747 · HTML: https://mlsanity.com/paper/2106.08747/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 38 references that are in the map.
- First posted on arXiv 16 Jun 2021.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DGM: A deep learning algorithm for solving partial differential equations](https://mlsanity.com/paper/1708.07469/) (2017)
- [Augmented Neural ODEs](https://mlsanity.com/paper/1904.01681/) (2019)
- [Physics-informed neural networks for myocardial perfusion MRI quantification](https://mlsanity.com/paper/2011.12844/) (2020)
- [Optimal Function Approximation with Relu Neural Networks](https://mlsanity.com/paper/1909.03731/) (2019)
- [PCE-PINNs: Physics-Informed Neural Networks for Uncertainty Propagation in Ocean Modeling](https://mlsanity.com/paper/2105.02939/) (2021)

## Built on by (most cited first, 1 of 1)

- [One-Shot Transfer Learning of Physics-Informed Neural Networks](https://mlsanity.com/paper/2110.11286/) (2021)

## Abstract (arXiv)

The carbon pump of the world's ocean plays a vital role in the biosphere and climate of the earth, urging improved understanding of the functions and influences of the ocean for climate change analyses. State-of-the-art techniques are required to develop models that can capture the complexity of ocean currents and temperature flows. This work explores the benefits of using physics-informed neural networks (PINNs) for solving partial differential equations related to ocean modeling; such as the Burgers, wave, and advection-diffusion equations. We explore the trade-offs of using data vs. physical models in PINNs for solving partial differential equations. PINNs account for the deviation from physical laws in order to improve learning and generalization. We observed how the relative weight between the data and physical model in the loss function influence training results, where small data sets benefit more from the added physics information.