# Can Physics Informed Neural Operators Self Improve?

arXiv: https://arxiv.org/abs/2311.13885 · HTML: https://mlsanity.com/paper/2311.13885/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 18 references that are in the map.
- First posted on arXiv 23 Nov 2023.

## Builds on (most cited first, 12 of 12)

- [wav2vec 2.0: A Framework for Self-Supervised Learning of Speech Representations](https://mlsanity.com/paper/2006.11477/) (2020)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [FourCastNet: A Global Data-driven High-resolution Weather Model using Adaptive Fourier Neural Operators](https://mlsanity.com/paper/2202.11214/) (2022)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Multiwavelet-based Operator Learning for Differential Equations](https://mlsanity.com/paper/2109.13459/) (2021)
- [MIST: Multiple Instance Self-Training Framework for Video Anomaly Detection](https://mlsanity.com/paper/2104.01633/) (2021)
- [Wavelet neural operator: a neural operator for parametric partial differential equations](https://mlsanity.com/paper/2205.02191/) (2022)
- [Learning Deep Implicit Fourier Neural Operators (IFNOs) with Applications to Heterogeneous Material Modeling](https://mlsanity.com/paper/2203.08205/) (2022)
- [Unsupervised Self-Training for Sentiment Analysis of Code-Switched Data](https://mlsanity.com/paper/2103.14797/) (2021)
- [ST-PINN: A Self-Training Physics-Informed Neural Network for Partial Differential Equations](https://mlsanity.com/paper/2306.09389/) (2023)
- [Joint Speech Transcription and Translation: Pseudo-Labeling with Out-of-Distribution Data](https://mlsanity.com/paper/2212.09982/) (2022)
- [How important are specialized transforms in Neural Operators?](https://mlsanity.com/paper/2308.09293/) (2023)

## Abstract (arXiv)

Self-training techniques have shown remarkable value across many deep learning models and tasks. However, such techniques remain largely unexplored when considered in the context of learning fast solvers for systems of partial differential equations (Eg: Neural Operators). In this work, we explore the use of self-training for Fourier Neural Operators (FNO). Neural Operators emerged as a data driven technique, however, data from experiments or traditional solvers is not always readily available. Physics Informed Neural Operators (PINO) overcome this constraint by utilizing a physics loss for the training, however the accuracy of PINO trained without data does not match the performance obtained by training with data. In this work we show that self-training can be used to close this gap in performance. We examine canonical examples, namely the 1D-Burgers and 2D-Darcy PDEs, to showcase the efficacy of self-training. Specifically, FNOs, when trained exclusively with physics loss through self-training, approach 1.07x for Burgers and 1.02x for Darcy, compared to FNOs trained with both data and physics loss. Furthermore, we discover that pseudo-labels can be used for self-training without necessarily training to convergence in each iteration. A consequence of this is that we are able to discover self-training schedules that improve upon the baseline performance of PINO in terms of accuracy as well as time.