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This paper presents a Sobolev-adapted Bayesian Neural Network (BNN) framework for aerodynamic shape optimization (ASO) within a Bayesian Optimization (BO) context. By integrating gradient information through Sobolev training, the proposed Gradient-Enhanced BNN (GEBNN) efficiently leverages first-order information to enhance data efficiency and adaptability in non-stationary design spaces. Benchmark tests illustrate the GEBNN’s effectiveness in ASO scenarios, demonstrating its potential as a flexible and robust surrogate model for complex, constrained, nonlinear optimization problems.

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Sobolev Learning for Bayesian Neural Network Assisted Aerodynamic Shape Optimization

  • 会议论文

  • 发表日期：

    2026年

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  • Jan Rottmayer,
  • Long Chen,
  • Nicolas R. Gauger

摘要

This paper presents a Sobolev-adapted Bayesian Neural Network (BNN) framework for aerodynamic shape optimization (ASO) within a Bayesian Optimization (BO) context. By integrating gradient information through Sobolev training, the proposed Gradient-Enhanced BNN (GEBNN) efficiently leverages first-order information to enhance data efficiency and adaptability in non-stationary design spaces. Benchmark tests illustrate the GEBNN’s effectiveness in ASO scenarios, demonstrating its potential as a flexible and robust surrogate model for complex, constrained, nonlinear optimization problems.