用物理规律约束神经网络，实现无需标注的高精度粒子轨迹追踪。
Physics-Informed Tracking (PIT)
- 通过可微分物理模块约束轨迹满足已知动力学
- 在噪声和干净条件下均达亚像素级追踪精度
- 适合无标签数据的粒子运动分析与仿真验证
我们提出物理信息追踪（PIT），一种基于视频的单粒子追踪框架。神经网络自编码器将粒子定位为热图峰值（地标），嵌入自编码器中的可微分物理模块约束多个地标随时间满足已知动力学。新颖的物理信息地标损失（PILL）将预测轨迹与地标对比，强制物理一致性，无需标签。其监督变体（PILLS）则对比预测位置、速度和碰撞结果与仿真真值，支持端到端反向传播。为支持监督与无监督学习，采用具有分裂瓶颈的自编码器，将追踪相关结构（通过地标热图表示）与背景噪声及图像重建分离。我们评估了26因子设计（n = 4重复，64配置），结果显示PILLS在双线性与物理优化解码器输出下，无论在干净或噪声条件下均持续实现亚像素级追踪精度。
原文摘要 · Abstract (English)
We propose Physics-Informed Tracking (PIT), a video-based framework for tracking a single particle from video, where a neural network autoencoder localizes a particle as a heatmap peak (landmark) and a differentiable physics module embedded in the autoencoder constrains several landmarks over time (a trajectory) to satisfy known dynamics. The novel Physics-Informed Landmark Loss (PILL) compares this predicted trajectory back against the landmarks, enforcing physical consistency without labels. Its supervised variant (PILLS) instead compares the prediction against ground-truth position, velocity, and bounce from simulation, enabling end-to-end backpropagation. To support supervised and unsupervised learning, we use an autoencoder with a split bottleneck that separates A) tracking-related structure via landmark heatmaps from B) background noise and subsequent image reconstruction. We evaluate a replicated 26 factorial design (n = 4 replicates, 64 configurations), showing that PILLS consistently achieves sub-pixel tracking accuracy for the bilinear and physics-refined decoder outputs under both clean and noisy conditions.
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