An-improved-PINNs-with-the-adaptive-weight-sampling-and-DE-algorithm

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An-improved-PINNs-with-the-adaptive-weight-sampling-and-DE-algorithm

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An improved and generic PINNs for fluid dynamic analysis is proposed. This approach incorporates three key improvements: residual-based adaptive sampling, which automatically samples points in areas with larger residuals; adaptive loss weights, which balance the loss terms effectively; and the utilization of the DE optimization algorithm

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# An-improved-PINNs-with-the-adaptive-weight-sampling-and-DE-algorithm
An improved and generic PINNs for fluid dynamic analysis  is proposed. This approach incorporates three key improvements: residual-based adaptive sampling, which automatically samples points in areas with larger residuals; adaptive loss weights, which balance the loss terms effectively; and the utilization of the DE optimization algorithm

Physics-informed neural networks (PINNs)-based flow modeling is emerging as a potential AI technique for solving fluid dynamics problems. However, conventional PINNs encounter inherent limitations when simulating the incompressible fluids, such as difficulties in selecting the sampling points, balancing the loss items, and optimizing the hyperparameters. These limitations often lead to non-convergence of PINNs.

To overcome these issues, an improved and generic PINNs for fluid dynamic analysis  is proposed. This approach incorporates three key improvements: residual-based adaptive sampling, which automatically samples points in areas with larger residuals; adaptive loss weights, which balance the loss terms effectively; and the utilization of the differential evolution (DE) optimization algorithm. In the present study, three case studies, Kovasznay flow, vortex shedding past a cylinder, and Beltrami flow are employed to validate proposed PINNs. The contribution of each improvement to the final simulation result is investigated and quantified. The simulation results demonstrate good agreement with both analytical solutions and benchmarked CFD calculation results, showcasing the efficiency and validity of the proposed method. The proposed PINNs have the potential to reduce the reliance on CFD simulations for solving fluid dynamics problems.

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