We delve into the physics-informed neural reconstruction of smoke and obstacles through sparse-view RGB videos, tackling challenges arising from limited observation of complex dynamics. Existing physics-informed neural networks often emphasize short-term physics constraints, leaving the proper preservation of long-term conservation less explored. We introduce Neural Characteristic Trajectory Fields, a novel representation utilizing Eulerian neural fields to implicitly model Lagrangian fluid trajectories. This topology-free, auto-differentiable representation facilitates efficient flow map calculations between arbitrary frames as well as efficient velocity extraction via auto-differentiation. Consequently, it enables end-to-end supervision covering long-term conservation and short-term physics priors. Building on the representation, we propose physics-informed trajectory learning and integration into NeRF-based scene reconstruction. We enable advanced obstacle handling through self-supervised scene decomposition and seamless integrated boundary constraints. Our results showcase the ability to overcome challenges like occlusion uncertainty, density-color ambiguity, and static-dynamic entanglements. Code and sample tests are at \url{https://github.com/19reborn/PICT_smoke}.

翻译：本文深入研究了通过稀疏视角RGB视频进行基于物理信息的烟雾与障碍物神经重建，旨在解决复杂动态系统观测受限所带来的挑战。现有基于物理信息的神经网络通常侧重于短期物理约束，而对长期守恒特性的恰当保持则探索不足。我们提出了神经特征轨迹场，这是一种利用欧拉神经场隐式建模拉格朗日流体轨迹的新型表征方法。这种无拓扑结构、可自动微分的表征，不仅支持任意帧间流场映射的高效计算，还能通过自动微分实现速度场的高效提取。因此，它实现了覆盖长期守恒特性与短期物理先验的端到端监督。基于该表征，我们提出了物理信息轨迹学习框架，并将其集成到基于NeRF的场景重建中。通过自监督场景分解与无缝集成的边界约束，我们实现了先进的障碍物处理能力。实验结果表明，该方法能够有效克服遮挡不确定性、密度-颜色歧义性以及静态-动态纠缠等挑战。代码与测试样例发布于\url{https://github.com/19reborn/PICT_smoke}。