For numerical design, the development of efficient and accurate surrogate models is paramount. They allow us to approximate complex physical phenomena, thereby reducing the computational burden of direct numerical simulations. We propose INFINITY, a deep learning model that utilizes implicit neural representations (INRs) to address this challenge. Our framework encodes geometric information and physical fields into compact representations and learns a mapping between them to infer the physical fields. We use an airfoil design optimization problem as an example task and we evaluate our approach on the challenging AirfRANS dataset, which closely resembles real-world industrial use-cases. The experimental results demonstrate that our framework achieves state-of-the-art performance by accurately inferring physical fields throughout the volume and surface. Additionally we demonstrate its applicability in contexts such as design exploration and shape optimization: our model can correctly predict drag and lift coefficients while adhering to the equations.

翻译：在数值设计中，开发高效且精确的代理模型至关重要。此类模型能够近似描述复杂的物理现象，从而降低直接数值模拟的计算负担。我们提出INFINITY——一种利用隐式神经表示（INR）应对这一挑战的深度学习模型。该框架将几何信息与物理场编码为紧凑表示，并学习两者之间的映射关系以推断物理场。我们以翼型设计优化问题作为示例任务，并在高度接近真实工业应用场景的AirfRANS数据集上评估该方法。实验结果表明，我们的框架通过准确推断体域与表面的物理场，达到了最先进的性能。此外，我们展示了其在设计探索与形状优化等场景中的应用性：该模型能够正确预测阻力和升力系数，同时遵循方程约束。