Bayesian Reasoning for Physics-Informed Neural Networks

We are pleased to inform that a paper by Krzysztof M. Graczyk and Kornel Witkowski, titled Bayesian Reasoning for Physics-Informed Neural Networks, has been published in Physical Review E.

The authors propose a new approach to training physics-informed neural networks (PINNs), machine-learning models that incorporate knowledge of physical laws into the learning process. Such methods are used to solve equations describing physical systems, including heat flow, waves, and fluid dynamics. One of the key challenges in applying these networks is how to balance different sources of information, such as the governing equation, boundary conditions, and measurement data.

The paper introduces a Bayesian framework that automatically determines the weights assigned to these different components and provides uncertainty estimates for the resulting solution. This makes the training process more systematic, interpretable, and less dependent on trial-and-error choices.

The proposed method may help improve the reliability of machine-learning techniques used in computational physics and scientific modelling.

Publication: K. M. Graczyk, K. Witkowski, Bayesian Reasoning for Physics-Informed Neural Networks, Physical Review E113, 055307.