An innovative end-to-end PINN-based solution for rapidly simulating homogeneous heat flow problems: An adaptive universal physics-guided auto-solver

In contemporary heat flow computations, the widespread application of deep learning, specifically Physical Informed Neural Networks (PINN), has been noted. However, existing PINN methods often exhibit limited applicability to specific operational conditions and are hindered by prolonged training times, rendering them unsuitable for engineering scenarios requiring frequent changes in operational parameters. This study addresses the imperative of enhancing the computational efficiency of conventional PINN methodologies and introduces an innovative end-to-end PINN-based solution—Adaptive Universal Physics-Guided Auto-Solver (AUPgAS) for swift simulation of homogeneous heat flow problems. AUPgAS introduces the operational condition as a variable within the neural network, thereby enhancing the model's versatility in addressing homogeneous problems. Simultaneously, AUPgAS refines training accuracy through the incorporation of adaptive sampling methods. The efficacy of this method is demonstrated through validations on two application cases of laminar incompressible flow with viscosity, namely the flow around a cylinder and the flow around two cylinders. After training, the model demonstrates the capability to predict pressure and velocity fields of the flow around a single cylinder in different locations in case Ⅰ, as well as simulate the flow field when the distance between two cylinders rapidly changes in case Ⅱ. Comparative analyses with traditional computational fluid dynamics methods show that the AUPgAS greatly reduces the solution time, the average time taken by the trained AUPgAS to solve for each problem is 3.4 s, which is a significant improvement in efficiency compared to the average time taken by the traditional fluid dynamics methods, which is 910 s. Furthermore, the agreement of the results obtained by AUPgAS with the reference solution is commendable, with a minimum average error of 13.55%. This end-to-end approach presents an innovative and efficient solution for the rapid simulation of homogeneous heat flow problems, offering promising advancements in the realm of engineering computational efficiency.