Neural Radiance Fields (NeRF) have achieved great success in the task of
synthesizing novel views that preserve the same resolution as the training
views. However, it is challenging for NeRF to synthesize high-quality
high-resolution novel views with low-resolution training data. To solve this
problem, we propose a zero-shot super-resolution training framework for NeRF.
This framework aims to guide the NeRF model to synthesize high-resolution novel
views via single-scene internal learning rather than requiring any external
high-resolution training data. Our approach consists of two stages. First, we
learn a scene-specific degradation mapping by performing internal learning on a
pretrained low-resolution coarse NeRF. Second, we optimize a super-resolution
fine NeRF by conducting inverse rendering with our mapping function so as to
backpropagate the gradients from low-resolution 2D space into the
super-resolution 3D sampling space. Then, we further introduce a temporal
ensemble strategy in the inference phase to compensate for the scene estimation
errors. Our method is featured on two points: (1) it does not consume
high-resolution views or additional scene data to train super-resolution NeRF;
(2) it can speed up the training process by adopting a coarse-to-fine strategy.
By conducting extensive experiments on public datasets, we have qualitatively
and quantitatively demonstrated the effectiveness of our method.

我们提出了一种 NeRF 的零样本超分辨率训练框架，通过单场景内部学习指导 NeRF 模型合成高分辨率的新颖视角，而无需外部高分辨率训练数据。我们的方法采用两个阶段，首先通过内部学习在预训练的低分辨率粗糙 NeRF 上学习场景特定的退化映射，然后通过反向渲染使用映射函数优化超分辨率细致 NeRF，并通过推理阶段引入时间集成策略来补偿场景估计错误。通过在公共数据集上进行大量实验，我们定性和定量地验证了我们方法的有效性。

ZS-SRT：神经辐射场的高效零样本超分辨率训练方法

ZS-SRT: An Efficient Zero-Shot Super-Resolution Training Method for  Neural Radiance Fields

The classical development of neural networks has primarily focused on
learning mappings between finite-dimensional Euclidean spaces. Recently, this
has been generalized to neural operators that learn mappings between function
spaces. For partial differential equations (PDEs), neural operators directly
learn the mapping from any functional parametric dependence to the solution.
Thus, they learn an entire family of PDEs, in contrast to classical methods
which solve one instance of the equation. In this work, we formulate a new
neural operator by parameterizing the integral kernel directly in Fourier
space, allowing for an expressive and efficient architecture. We perform
experiments on Burgers' equation, Darcy flow, and Navier-Stokes equation. The
Fourier neural operator is the first ML-based method to successfully model
turbulent flows with zero-shot super-resolution. It is up to three orders of
magnitude faster compared to traditional PDE solvers. Additionally, it achieves
superior accuracy compared to previous learning-based solvers under fixed
resolution.

该论文提出了一种新的神经算子，通过直接在傅里叶空间中参数化积分核，实现了对偏微分方程的求解，并在 Burgers' equation、Darcy 流和 Navier-Stokes 方程等测试中展现了高准确率和比传统方法高三个数量级的速度。