# Physics-Informed Neural Networks with Learnable Loss Balancing and Transfer Learning

arXiv: https://arxiv.org/abs/2605.05217 · HTML: https://mlsanity.com/paper/2605.05217/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 8 of its 24 references that are in the map.
- First posted on arXiv 17 Apr 2026.

## Builds on (most cited first, 8 of 8)

- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data](https://mlsanity.com/paper/2003.06097/) (2020)
- [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)
- [SPINN: An Optimal Self-Supervised Physics-Informed Neural Network Framework](https://mlsanity.com/paper/2509.05886/) (2025)
- [Explainable AI-Enhanced Supervisory Control for Robust Multi-Agent Robotic Systems](https://mlsanity.com/paper/2509.15491/) (2025)

## Abstract (arXiv)

We propose a self-supervised physics-informed neural network (PINN) framework that adaptively balances physics-based and data-driven supervision for scientific machine learning under data scarcity. Unlike prior PINNs that rely on fixed or heuristic weighting of physics residuals and data loss, our approach introduces a learnable blending neuron that dynamically adjusts the relative contribution of each term based on their uncertainties. This mechanism enables stable training and improved generalization without manual tuning. To further enhance efficiency, we integrate a transfer learning strategy that reuses representations from related domains and adapts them to new physical systems with limited data. We validate the framework for the prediction of heat transfer in liquid-metal miniature heat sinks using only 87 CFD datapoints, where the adaptive PINN achieves an error <8%, outperforming shallow neural networks, kernel methods, and physics-only baselines. Our framework provides a general recipe for embedding physics adaptively into neural networks, offering a robust and reproducible approach for data-scarce problems across various scientific domains, including fluid dynamics and material modeling.