Neural fields have become widely used in various fields, from shape
representation to neural rendering, and for solving partial differential
equations (PDEs). With the advent of hybrid neural field representations like
Instant NGP that leverage small MLPs and explicit representations, these models
train quickly and can fit large scenes. Yet in many applications like rendering
and simulation, hybrid neural fields can cause noticeable and unreasonable
artifacts. This is because they do not yield accurate spatial derivatives
needed for these downstream applications. In this work, we propose two ways to
circumvent these challenges. Our first approach is a post hoc operator that
uses local polynomial-fitting to obtain more accurate derivatives from
pre-trained hybrid neural fields. Additionally, we also propose a
self-supervised fine-tuning approach that refines the neural field to yield
accurate derivatives directly while preserving the initial signal. We show the
application of our method on rendering, collision simulation, and solving PDEs.
We observe that using our approach yields more accurate derivatives, reducing
artifacts and leading to more accurate simulations in downstream applications.

我们提出了两种方法来解决混合神经场在渲染、碰撞模拟和解决偏微分方程等下游应用中可能引起的不合理现象和伪影问题：首先，我们提出了一种后处理算子，利用局部多项式拟合从预训练的混合神经场中获得更准确的导数；其次，我们提出了一种自监督微调方法，通过对神经场进行微调来直接获得准确的导数，同时保持初始信号的不变性。使用我们的方法可以获得更准确的导数，减少伪影，并在下游应用中实现更准确的模拟。