# Pseudo-Physics-Informed Neural Operators: Enhancing Operator Learning from Limited Data

arXiv: https://arxiv.org/abs/2502.02682 · HTML: https://mlsanity.com/paper/2502.02682/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 39 references that are in the map.
- First posted on arXiv 4 Feb 2025.

## Builds on (most cited first, 20 of 20)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [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)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Conditional Image Generation with PixelCNN Decoders](https://mlsanity.com/paper/1606.05328/) (2016)
- [Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets](https://mlsanity.com/paper/2103.10974/) (2021)
- [Physics-Informed Neural Operator for Learning Partial Differential Equations](https://mlsanity.com/paper/2111.03794/) (2021)
- [Multipole Graph Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2006.09535/) (2020)
- [Choose a Transformer: Fourier or Galerkin](https://mlsanity.com/paper/2105.14995/) (2021)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [Transformer for Partial Differential Equations' Operator Learning](https://mlsanity.com/paper/2205.13671/) (2022)
- [Multiwavelet-based Operator Learning for Differential Equations](https://mlsanity.com/paper/2109.13459/) (2021)
- [Convolutional Neural Operators for robust and accurate learning of PDEs](https://mlsanity.com/paper/2302.01178/) (2023)
- [Physics-informed learning of governing equations from scarce data](https://mlsanity.com/paper/2005.03448/) (2020)
- [Applications of physics informed neural operators](https://mlsanity.com/paper/2203.12634/) (2022)
- [Bayesian Spline Learning for Equation Discovery of Nonlinear Dynamics with Quantified Uncertainty](https://mlsanity.com/paper/2210.08095/) (2022)
- [opPINN: Physics-Informed Neural Network with operator learning to approximate solutions to the Fokker-Planck-Landau equation](https://mlsanity.com/paper/2207.01765/) (2022)
- [Adaptive physics-informed neural operator for coarse-grained non-equilibrium flows](https://mlsanity.com/paper/2210.15799/) (2022)
- [Equation Discovery with Bayesian Spike-and-Slab Priors and Efficient Kernels](https://mlsanity.com/paper/2310.05387/) (2023)

## Abstract (arXiv)

Neural operators have shown great potential in surrogate modeling. However, training a well-performing neural operator typically requires a substantial amount of data, which can pose a major challenge in complex applications. In such scenarios, detailed physical knowledge can be unavailable or difficult to obtain, and collecting extensive data is often prohibitively expensive. To mitigate this challenge, we propose the Pseudo Physics-Informed Neural Operator (PPI-NO) framework. PPI-NO constructs a surrogate physics system for the target system using partial differential equations (PDEs) derived from simple, rudimentary physics principles, such as basic differential operators. This surrogate system is coupled with a neural operator model, using an alternating update and learning process to iteratively enhance the model's predictive power. While the physics derived via PPI-NO may not mirror the ground-truth underlying physical laws -- hence the term ``pseudo physics'' -- this approach significantly improves the accuracy of standard operator learning models in data-scarce scenarios, which is evidenced by extensive evaluations across five benchmark tasks and a fatigue modeling application.