Design of a unified physics-informed neural network using interior point algorithm to study the bioconvection nanofluid flow via stretching surface

Numerical simulation of fluids is crucial in modeling physical phenomena in various fields, including engineering, physics, and environmental science. Fluids are typically described by the Navier-Stokes equations, but solving these coupled equations for complex models with computational fluid dynamics (CFD) tools remains challenging due to the high computational cost and time required to address the minute interpolation errors. In this article, we have introduced a novel physics-informed machine learning technique that does not rely on any reference dataset to study bioconvection nanofluid flow across an inclined stretching surface. More specifically, a structured physics-informed neural network (PINN) architecture is devised to enforce the initial and boundary conditions. The governing partial differential equations are transformed into third-order nonlinear ordinary differential equations (ODEs). The transformed ODEs are incorporated into the loss of the PINN to drive the training. The weights of PINN are trained with the interior point algorithm (IPA). The effects of the thermophoresis parameter and the Brownian motion parameter on the velocity, temperature, nanoparticle concentration, and microorganisms’ density profiles have been graphically presented and analysed by creating two different PINNs in an unsupervised way. The proposed results are compared with traditional finite element solutions, and they show satisfactory agreement with a precision of 2–4 decimal places. Statistical analysis for a large number of independent executions validates the convergence and worth of the proposed approach. The research offers continuous solutions over the whole trained interval with comparable accuracy and paves the way for the application of physics-informed machine learning to complex fluid mechanics and heat transfer problems.