Accurate Differential Operators for Hybrid Neural Fields
Aditya Chetan Guandao Yang Zichen Wang Steve Marschner Bharath Hariharan
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.