# Physics-Informed Localized Learning for Advection-Diffusion-Reaction Systems

arXiv: https://arxiv.org/abs/2305.03774 · HTML: https://mlsanity.com/paper/2305.03774/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 20 references that are in the map.
- First posted on arXiv 5 May 2023.

## Builds on (most cited first, 10 of 10)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Neural Operator: Graph Kernel Network for Partial Differential Equations](https://mlsanity.com/paper/2003.03485/) (2020)
- [Neural Operator: Learning Maps Between Function Spaces](https://mlsanity.com/paper/2108.08481/) (2021)
- [Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2006.09535/) (2020)
- [Embed to Control: A Locally Linear Latent Dynamics Model for Control from Raw Images](https://mlsanity.com/paper/1506.07365/) (2015)
- [Model Reduction and Neural Networks for Parametric PDEs](https://mlsanity.com/paper/2005.03180/) (2020)
- [Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification](https://mlsanity.com/paper/1801.06879/) (2018)

## Built on by (most cited first, 2 of 2)

- [Transfer learning-based physics-informed convolutional neural network for simulating flow in porous media with time-varying controls](https://mlsanity.com/paper/2310.06319/) (2023)
- [A Fourier Neural Operator Approach for Modelling Exciton-Polariton Condensate Systems](https://mlsanity.com/paper/2309.15593/) (2023)

## Abstract (arXiv)

The global push to advance Carbon Capture and Sequestration initiatives and green energy solutions, such as geothermal, have thrust new demands upon the current state-of-the-art subsurface fluid simulators. The requirement to be able to simulate a large order of reservoir states simultaneously, in a short period of time, has opened the door of opportunity for the application of machine learning techniques for surrogate modelling. We propose a novel physics-informed and boundary condition-aware Localized Learning method which extends the Embed-to-Control (E2C) and Embed-to-Control and Observe (E2CO) models to learn local representations of global state variables in an Advection-Diffusion Reaction system. Trained on reservoir simulation data, we show that our model is able to predict future states of the system, for a given set of controls, to a great deal of accuracy with only a fraction of the available information. It hence reduces training times significantly compared to the original E2C and E2CO models, lending to its benefit in application to optimal control problems.