# Uncovering solutions from data corrupted by systematic errors: A physics-constrained convolutional neural network approach

arXiv: https://arxiv.org/abs/2306.04600 · HTML: https://mlsanity.com/paper/2306.04600/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 37 references that are in the map.
- First posted on arXiv 7 Jun 2023.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Machine learning accelerated computational fluid dynamics](https://mlsanity.com/paper/2102.01010/) (2021)
- [Recent Advances in Convolutional Neural Networks](https://mlsanity.com/paper/1512.07108/) (2015)
- [Universality of Deep Convolutional Neural Networks](https://mlsanity.com/paper/1805.10769/) (2018)
- [Real-time thermoacoustic data assimilation](https://mlsanity.com/paper/2106.06409/) (2021)
- [Modelling spatiotemporal turbulent dynamics with the convolutional autoencoder echo state network](https://mlsanity.com/paper/2211.11379/) (2022)

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

- [Physics-constrained convolutional neural networks for inverse problems in spatiotemporal partial differential equations](https://mlsanity.com/paper/2401.10306/) (2024)

## Abstract (arXiv)

Information on natural phenomena and engineering systems is typically contained in data. Data can be corrupted by systematic errors in models and experiments. In this paper, we propose a tool to uncover the spatiotemporal solution of the underlying physical system by removing the systematic errors from data. The tool is the physics-constrained convolutional neural network (PC-CNN), which combines information from both the systems governing equations and data. We focus on fundamental phenomena that are modelled by partial differential equations, such as linear convection, Burgers equation, and two-dimensional turbulence. First, we formulate the problem, describe the physics-constrained convolutional neural network, and parameterise the systematic error. Second, we uncover the solutions from data corrupted by large multimodal systematic errors. Third, we perform a parametric study for different systematic errors. We show that the method is robust. Fourth, we analyse the physical properties of the uncovered solutions. We show that the solutions inferred from the PC-CNN are physical, in contrast to the data corrupted by systematic errors that does not fulfil the governing equations. This work opens opportunities for removing epistemic errors from models, and systematic errors from measurements.