A geometry-adaptive physics-informed operator framework generalized for arbitrary geometries

초록

Physics-informed neural operators are a promising framework for solving partial differential equations (PDEs) by integrating physical laws into neural network architectures. However, existing methods such as physics-informed DeepONet (PI-DeepONet) struggle to generalize under complex geometric variations because they encode spatial coordinates independently of the geometry. In this study, we propose a geometry-adaptive physics-informed DeepONet (GAPI-DeepONet) that effectively captures geometry-dependent nonlinearities by integrating a generalized geometry representation into the branch network and modulating the trunk network through a geometry-adaptive conditioning network. Unlike naïve PI-DeepONet or existing embedding approaches, the proposed method is designed to more efficiently capture geometry-dependent nonlinear behaviors by directly modulating the geometry-sensitive features of the trunk network through trainable geometry-adaptive parameters. By applying layer-wise modulation to the trunk features, this architecture can effectively handle a wider range of geometric configurations while maintaining training efficiency. We evaluate the performance of the proposed model on three representative problems, including flow around a cylinder, NACA (National Advisory Committee for Aeronautics) airfoil flow, and a three-dimensional heat sink, with conventional PI-DeepONet, Fourier Neural Operator (FNO), and ResUNet-based DeepONet. The proposed GAPI-DeepONet consistently outperforms comparative models both for accuracy and robustness, achieving up to a 90% reduction in the L2 relative error and demonstrating its capability to resolve fine-scale variations under varying geometric conditions. These results highlight its potential for real-time simulation and further optimization tasks in many engineering problems involving complex geometric variations.

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