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.

翻译：神经场已在多个领域广泛应用，从形状表示到神经渲染，以及用于求解偏微分方程（PDE）。随着如Instant NGP等利用小型MLP和显式表示的混合神经场表示的出现，这些模型训练快速且能适配大规模场景。然而在渲染和模拟等应用中，混合神经场可能会产生明显且不合理的伪影，这是因为它们无法为这些下游应用提供所需的空间导数精确值。在本文中，我们提出两种规避这些挑战的方法。第一种方法是事后算子，利用局部多项式拟合从预训练的混合神经场中获取更精确的导数。此外，我们还提出了一种自监督微调方法，在保留初始信号的同时直接优化神经场以生成精确导数。我们展示了该方法在渲染、碰撞模拟和PDE求解中的应用。结果表明，采用我们的方法可获得更精确的导数，从而减少伪影并提升下游应用的模拟准确性。