🤖 AI Summary
Hybrid neural fields (e.g., Instant NGP) suffer from inaccurate spatial derivative estimation, introducing severe artifacts in neural rendering, physics simulation, and PDE solving. To address this, we propose the first high-fidelity derivative correction framework tailored for hybrid neural fields. Our method employs plug-and-play post-processing via local polynomial fitting to enhance derivatives, coupled with a lightweight, self-supervised gradient consistency loss for fine-tuning the hash grid + MLP architecture. Crucially, it operates without retraining pre-trained models, preserving original signal fidelity while substantially improving derivative accuracy. Experiments demonstrate that our approach eliminates high-frequency rendering artifacts, enhances stability in contact force computation for rigid-body collision simulation, and significantly reduces gradient errors in PDE solving. By delivering geometrically and physically consistent derivatives, our framework enables robust downstream applications in graphics, simulation, and scientific computing.
📝 Abstract
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 hybrid neural field to yield accurate derivatives directly while preserving the initial signal. We show applications of our method to 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.
