HCC: Small: Neural Network-based Solvers for Integral Equations in Light Transport

神经网络通常与人工智能中的应用程序相关联，例如计算机视觉、自然语言处理或机器人技术。它们对这些应用很有吸引力，因为它们可以模拟高度复杂的关系，例如图像中数百万个单独像素的颜色如何与图像的高级描述相关，包括所示对象的类型等。然而，该项目将利用神经网络的能力来解决数值模拟问题，重点是光传输作为应用领域。将开发新的技术来模拟3D虚拟环境和相应的照片级图像之间的复杂关系。这项工作将使许多创新的计算机图形应用程序成为可能，例如在增强和虚拟现实领域。这些新技术将产生广泛的影响，因为它们可以适应和应用于广泛的相关科学模拟问题。项目成果的好处包括提高可实现的精度，并能够解决比目前可能的更大规模和更复杂的几何问题。该项目将开发基于神经网络的函数表示的新的数值技术，以解决光传输问题的积分方程组。该方法将使用神经网络表示连续解，并利用基于梯度的数值解技术来最小化残差的适当范数，此后将开发和评估改进基线方法的性能和精度的先进技术，包括适用于有效表示多维函数的新型神经网络结构，例如求解光和辐射传递方程所需的空间角辐射场，以及数值问题中剩余范数的高效蒙特卡罗采样和课程学习策略，以便能够以较低的计算成本进行稳健的梯度估计。最后，将研究新的、不太可能的学习技术，以进一步加速融合。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Neural networks are commonly associated with applications in artificial intelligence such as computer vision, natural language processing, or robotics. They are attractive for these applications because they can model highly complex relationships, such as how colors of millions of individual pixels in an image are related to a high-level description of the image, including the types of objects that are shown etc. This project, however, will leverage the capacity of neural networks to solve numerical simulation problems, with a focus on light transport as the application domain. Novel techniques will be developed to model the complex relationship between 3D virtual environments and corresponding photo-realistic images. This work will enable numerous innovative computer graphics applications, for example in augmented and virtual reality. The new techniques will have broad impact, because they can be adapted and applied to a vast range of related scientific simulation problems. The benefits of the project outcomes include improving the achievable accuracy and enabling the solution of problems at a larger scale and with more complex geometries than is currently possible.This project will develop novel numerical techniques for neural network-based function representations to solve integral equations for light transport problems. The approach will represent continuous solutions using neural networks, and leverage gradient-based numerical solution techniques that minimize appropriate norms of the residuals, after which advanced techniques that improve the performance and accuracy of the baseline approach will be developed and evaluated, including novel neural network architectures that are suitable to effectively represent multi-dimensional functions such as the spatio-angular radiance fields required to solve light and radiative transfer equations, and efficient Monte Carlo sampling and curriculum learning strategies for the residual norms in the numerical problems to allow robust estimation of gradients at lower computational cost. Finally, novel few-shot learning techniques to further accelerate convergence will be investigated.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.