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arXiv 2605.04474cs.LG
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面向几何的神经优化器用于形状优化与反演

Geometry-Aware Neural Optimizer for Shape Optimization and Inversion

Guoze Sun, Tianya Miao, Haoyang Huang, Huaguan Chen, Han Wan, Rui Zhang, Hao Sun

AI总结:

本文提出GANO框架,通过统一几何表示、场级预测和自动优化/反演,在单个潜在空间循环中实现端到端可微处理,提升几何处理的稳定性和可控性。

摘要:

几何对于由偏微分方程主导的系统至关重要,推动了形状优化与反演。经典流程进行几何处理的昂贵正向模拟,需要大量专家努力。神经替代品加速正向分析,但无法闭环,因为从目标到几何的梯度通常不可用。现有可微方法要么依赖于限制性的参数化,要么由标量目标驱动的不稳定潜在优化,限制了可解释性和部分控制。为了解决这些挑战,我们提出了Geometry-Aware Neural Optimizer(GANO),一个端到端可微框架,统一了几何表示、场级预测和自动优化/反演在一个潜在空间循环中。GANO通过自动解码器编码形状,并通过去噪机制稳定潜在更新,并且一个几何指导的替代品为几何更新提供可靠的梯度路径。此外,GANO通过空域投影支持部分控制,并利用无重新网格化投影加速几何处理。我们进一步证明去噪诱导了隐含的雅可比正则化,减少了解码器的敏感性,从而产生受控变形。在三个基准测试上,涵盖2D亥姆霍兹、2D机翼和3D车辆,实验表明了最先进的精度和稳定的、可控的更新,实现了机翼升阻比提高达+55.9%和车辆阻力降低约7%。

英文摘要:

Geometry is central to PDE-governed systems, motivating shape optimization and inversion. Classical pipelines conduct costly forward simulation with geometry processing, requiring substantial expert effort. Neural surrogates accelerate forward analysis but do not close the loop because gradients from objectives to geometry are often unavailable. Existing differentiable methods either rely on restrictive parameterizations or unstable latent optimization driven by scalar objectives, limiting interpretability and part-wise control. To address these challenges, we propose Geometry-Aware Neural Optimizer (\textbf{\textsc{GANO}}), an end-to-end differentiable framework that unifies geometry representation, field-level prediction, and automated optimization/inversion in a single latent-space loop. \textsc{GANO} encodes shapes with an auto-decoder and stabilizes latent updates via a denoising mechanism, and a geometry-informed surrogate provides a reliable gradient pathway for geometry updates. Moreover, \textsc{GANO} supports part-wise control through null-space projection and uses remeshing-free projection to accelerate geometry processing. We further prove that denoising induces an implicit Jacobian regularization that reduces decoder sensitivity, yielding controlled deformations. Experiments on three benchmarks spanning 2D Helmholtz, 2D airfoil, and 3D vehicles show state-of-the-art accuracy and stable, controllable updates, achieving up to +55.9% lift-to-drag improvement for airfoils and ~7% drag reduction for vehicles.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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