Bayesian inference-based physics-informed neural network for performance study of hybrid nanofluids

Accurate prediction of thermophysical properties of hybrid nanofluids (HNFs) is a major challenge in thermodynamic applications. This research provides a computational framework to solve the complexity of heat transfer and flow physics in Al 2 O 3 –Cu/water HNFs. A reconstruction of the statistical microstructure of the fluid is constructed by the Karhunen–Loève expansion. The physical processes are modeled with a system of partial differential equations that model the interactions between the base fluid and dispersed nanoparticles. In the context of flow variables and entropy generation with sharp gradients, a Bayesian inference extension of the physics-informed neural network (PINN) is developed to improve prediction accuracy. Bayesian inference PINN (BIPINN) is the extension that infers posterior distributions of hidden thermal flow states, conditioned on prior physical laws. The framework is validated through many physical problems such as convective flow, thermal conduction, and fluctuation control. BIPINN shows improved accuracy over the finite element method while also showing improved generalization under sparse data while illustrating robustness of the framework while modeling complex thermal-fluid systems.