Periodically activated physics-informed neural networks for assimilation tasks for three-dimensional Rayleigh–Bénard convection

• Published in: Computers & fluids 2024-10, Vol.283, p.106419, Article 106419
• Main Authors: Mommert, Michael, Barta, Robin, Bauer, Christian, Volk, Marie-Christine, Wagner, Claus
• Format: Article
• Language: English
• Subjects: Activation functions; Assimilation; Machine learning; Physics-informed neural networks; Rayleigh–Bénard convection
• ISSN: 0045-7930
• DOI: 10.1016/j.compfluid.2024.106419

We apply physics-informed neural networks to three-dimensional Rayleigh–Bénard convection in a cubic cell with a Rayleigh number of Ra=106 and a Prandtl number of Pr=0.7 to assimilate the velocity vector field from given temperature fields and vice versa. With the respective ground truth data provided by a direct numerical simulation, we are able to evaluate the performance of the different activation functions applied (sine, hyperbolic tangent and exponential linear unit) and different numbers of neurons (32, 64, 128, 256) for each of the five hidden layers of the multi-layer perceptron. The main result is that the use of a periodic activation function (sine) typically benefits the assimilation performance in terms of the analyzed metrics, correlation with the ground truth and mean average error. The higher quality of results from sine-activated physics-informed neural networks is also manifested in the probability density function and power spectra of the inferred velocity or temperature fields. Regarding the two assimilation directions, the assimilation of temperature fields based on velocities appears to be more challenging in the sense that it exhibits a sharper limit on the number of neurons below which viable assimilation results cannot be achieved. [Display omitted] •Investigations of 3D turbulent Rayleigh–Benard convection at Ra=106,Pr=0.7.•PINNs are used to assimilate temperature fields from velocity fields and vice versa.•Best results are achieved with sine activation in comparison with to tanh and ELU.•Prerequisite of PINN’s sufficient expressiveness investigated by varying layer width.•Provision of suitable loss component weights for each assimilation direction.