Federated Physics-informed Learning : with Burgers’ Equation

Sammanfattning

This thesis investigates Federated Physics-Informed Learning, a framework that integrates physical laws into federated machine learning to improve model performance across decentralized datasets. In federated learning, multiple clients collaboratively train a model without sharing raw data. Incorporating physics into this setting offers a promising solution by enforcing constraints derived from known physical principles. The central research question addressed is: how can physics-informed modeling enhance learning in a federated setup? This problem is both timely and relevant for engineering applications, as federated approaches reduce the need for expensive or centralized data collection while maintaining privacy. Despite growing interest in physics-informed machine learning and federated learning separately, combining these approaches remains a relatively unexplored area, particularly for systems governed by partial differential equations. To address this, a series of experiments were conducted using a combination of centralized, federated, and ensemble neural network architectures. The models were trained on distributed datasets with varying overlap, and performance was evaluated in terms of accuracy, stability, and adherence to physical laws. Special attention was given to the enforcement of physical constraints, such as initial and boundary conditions as well as the overall residual. The results indicate that explicitly enforcing initial and boundary conditions over the partial differential equation residual significantly improves performance compared to alternative strategies. This approach enhances both predictive accuracy and physical consistency across decentralized clients, demonstrating the potential of federated physics-informed learning for practical engineering applications. These findings provide a foundation for future research into scalable, privacy-preserving, and physically consistent machine learning systems, offering a new approach to addressing complex problems where data is distributed and costly to acquire.