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<p>Physics-informed neural networks (PINNs) offer a promising mesh-free alternative to conventional computational fluid dynamics (CFD), but their practical use is limited by high training cost and poor generalization across different geometric configurations. This work proposes a geometry-conditioned hypernetwork PINN (GCH-PINN) framework that combines a convolutional neural network (CNN) HyperNet with a PINN MainNet to predict steady, incompressible laminar flow around two-dimensional obstacles over a family of shapes and locations. The HyperNet processes a signed distance function (SDF) map of the obstacle to extract spatial features and dynamically generates the weights and biases of the MainNet’s first hidden layer, enabling the solver to adapt its internal representation to each geometry without retraining. The MainNet, implemented as a multilayer perceptron, is trained using a hybrid loss that enforces the continuity and Navier–Stokes equations via automatic differentiation while leveraging full-field CFD solutions as supervision. The GCH-PINN is evaluated on two scenarios: single-factor variation (fixed location, varying shape) and two-factor variation (varying both shape and location) in a square domain. Across both settings, the network achieves Mean Absolute Errors (MAE) on the order of 10<sup>-6</sup>–10<sup>-4</sup> and mean relative L₂ errors 3.86—8.02% for single-factor and 7.14—15.90% for two-factor cases based on predicted velocity (<i>u,v</i>) and pressure (<i>p</i>) fields among unseen cases, with errors localized near obstacle surfaces and wake shear layers. Results demonstrate that the proposed GCH-PINN can serve as an efficient surrogate for CFD, providing fast, physics-consistent predictions over diverse obstacle configurations and indicating a path toward generalized, geometry-conditioned PINN solvers.</p>

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Physics-informed hypernetworks for generalized obstacle-flow prediction with varying shapes and locations

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月27日

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  • Chin-Cheng Shih,
  • Po-Ting Lin,
  • Dariga Shektybayeva,
  • Ulisses Braga-Neto,
  • Bruce L. Tai

摘要

Physics-informed neural networks (PINNs) offer a promising mesh-free alternative to conventional computational fluid dynamics (CFD), but their practical use is limited by high training cost and poor generalization across different geometric configurations. This work proposes a geometry-conditioned hypernetwork PINN (GCH-PINN) framework that combines a convolutional neural network (CNN) HyperNet with a PINN MainNet to predict steady, incompressible laminar flow around two-dimensional obstacles over a family of shapes and locations. The HyperNet processes a signed distance function (SDF) map of the obstacle to extract spatial features and dynamically generates the weights and biases of the MainNet’s first hidden layer, enabling the solver to adapt its internal representation to each geometry without retraining. The MainNet, implemented as a multilayer perceptron, is trained using a hybrid loss that enforces the continuity and Navier–Stokes equations via automatic differentiation while leveraging full-field CFD solutions as supervision. The GCH-PINN is evaluated on two scenarios: single-factor variation (fixed location, varying shape) and two-factor variation (varying both shape and location) in a square domain. Across both settings, the network achieves Mean Absolute Errors (MAE) on the order of 10-6–10-4 and mean relative L₂ errors 3.86—8.02% for single-factor and 7.14—15.90% for two-factor cases based on predicted velocity (u,v) and pressure (p) fields among unseen cases, with errors localized near obstacle surfaces and wake shear layers. Results demonstrate that the proposed GCH-PINN can serve as an efficient surrogate for CFD, providing fast, physics-consistent predictions over diverse obstacle configurations and indicating a path toward generalized, geometry-conditioned PINN solvers.