Constructing a reynolds stress model of decaying homogeneous isotropic turbulence using physics informed neural network

This study develops a neural network (NN) model to predict the decay of homogeneous isotropic turbulence (HIT). A series of decay cases was simulated using a GPU-accelerated pseudo-spectral solver over a low range of Taylor-scale Reynolds numbers, and the resulting time-resolved fields were converted to dimensionless form and used as training and validation data. A central contribution of this work is a fully dimensionless and Reynolds-number–consistent formulation of the HIT decay equations, which allows the decay coefficient to be identified directly from data. Traditional decay models often combine available experimental or numerical data with asymptotic descriptions of turbulence behavior in the limits Re$_λ$ → 0 and Re$_λ$ → ∞; however, such asymptotic guidance may rely on mathematically inconsistent relationships. By pairing the consistent nondimensional formulation with reliable DNS data, we obtain a data-driven decay function Z that reflects the governing dynamics across the simulated Reynolds-number range. A physics-informed neural network (PINN) is then trained to model the evolution of the normalized velocity and dissipation fields. ... mehrHeld-out cases demonstrate accurate prediction of key turbulence quantities together with an explicit, data-inferred closure for turbulence decay.