融合物理方程与神经网络，用少量数据精准预测各类球体轨迹。
A Universal Model Combining Differential Equations and Neural Networks for Ball Trajectory Prediction
- 用通用物理公式结合神经网络推断轨迹参数。
- 仅需几十个样本即可实现高精度预测，且泛化能力强。
- 适合需要快速、准确轨迹建模的体育分析与机器人场景。
本文提出一种融合物理方程与神经网络的数据驱动通用球体轨迹预测方法。现有方法多针对特定球类，难以泛化。主要挑战来自三方面：第一，学习模型依赖大规模数据，但在未见场景中精度下降；第二，物理模型依赖复杂公式和精确输入（如旋转状态），但实际获取困难；第三，如何将物理原理与神经网络结合以实现高精度、实时推理和强泛化仍具挑战。为此，我们推导出三个通用物理公式，利用神经网络与观测轨迹点联合推断部分参数并拟合剩余参数。该方法仅需数十个训练样本即可实现高精度轨迹预测。大量实验表明，该方法在泛化性、实时性能和准确性上均优于现有方法。
原文摘要 · Abstract (English)
This paper presents a data driven universal ball trajectory prediction method integrated with physics equations. Existing methods are designed for specific ball types and struggle to generalize. This challenge arises from three key factors. First, learning-based models require large datasets but suffer from accuracy drops in unseen scenarios. Second, physics-based models rely on complex formulas and detailed inputs, yet accurately obtaining ball states, such as spin, is often impractical. Third, integrating physical principles with neural networks to achieve high accuracy, fast inference, and strong generalization remains difficult. To address these issues, we propose an innovative approach that incorporates physics-based equations and neural networks. We first derive three generalized physical formulas. Then, using a neural network and observed trajectory points, we infer certain parameters while fitting the remaining ones. These formulas enable precise trajectory prediction with minimal training data: only a few dozen samples. Extensive experiments demonstrate our method superiority in generalization, real-time performance, and accuracy.
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