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

TL;DR

This paper introduces a self-supervised physics-informed neural network framework that adaptively balances physics and data supervision, incorporating transfer learning to improve predictions in data-scarce scientific problems.

Contribution

It presents a learnable blending mechanism for PINNs and a transfer learning strategy, enabling stable training and better generalization with limited data.

Findings

Achieved less than 8% error in heat transfer prediction with only 87 CFD data points.

Outperformed shallow neural networks, kernel methods, and physics-only models.

Demonstrated robustness and reproducibility across scientific domains.

Abstract

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.