# SPINN: An Optimal Self-Supervised Physics-Informed Neural Network Framework

arXiv: https://arxiv.org/abs/2509.05886 · HTML: https://mlsanity.com/paper/2509.05886/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 22 references that are in the map.
- First posted on arXiv 7 Sep 2025.

## Builds on (most cited first, 4 of 4)

- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [Convolutional-network models to predict wall-bounded turbulence from wall quantities](https://mlsanity.com/paper/2006.12483/) (2020)
- [Finite volume method network for acceleration of unsteady computational fluid dynamics: non-reacting and reacting flows](https://mlsanity.com/paper/2105.03332/) (2021)
- [Predictions of Reynolds and Nusselt numbers in turbulent convection using machine-learning models](https://mlsanity.com/paper/2201.03200/) (2022)

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

- [Physics-Informed Neural Networks with Learnable Loss Balancing and Transfer Learning](https://mlsanity.com/paper/2605.05217/) (2026)

## Abstract (arXiv)

A surrogate model is developed to predict the convective heat transfer coefficient of liquid sodium (Na) flow within rectangular miniature heat sinks. Initially, kernel-based machine learning techniques and shallow neural network are applied to a dataset with 87 Nusselt numbers for liquid sodium in rectangular miniature heat sinks. Subsequently, a self-supervised physics-informed neural network and transfer learning approach are used to increase the estimation performance. In the self-supervised physics-informed neural network, an additional layer determines the weight the of physics in the loss function to balance data and physics based on their uncertainty for a better estimation. For transfer learning, a shallow neural network trained on water is adapted for use with Na. Validation results show that the self-supervised physics-informed neural network successfully estimate the heat transfer rates of Na with an error margin of approximately +8%. Using only physics for regression, the error remains between 5% to 10%. Other machine learning methods specify the prediction mostly within +8%. High-fidelity modeling of turbulent forced convection of liquid metals using computational fluid dynamics (CFD) is both time-consuming and computationally expensive. Therefore, machine learning based models offer a powerful alternative tool for the design and optimization of liquid-metal-cooled miniature heat sinks.