This study investigates the application of deep residual networks for predicting the dynamics of interacting three-dimensional rigid bodies. We present a framework combining a 3D physics simulator implemented in C++ with a deep learning model constructed using PyTorch. The simulator generates training data encompassing linear and angular motion, elastic collisions, fluid friction, gravitational effects, and damping. Our deep residual network, consisting of an input layer, multiple residual blocks, and an output layer, is designed to handle the complexities of 3D dynamics. We evaluate the network's performance using a datasetof 10,000 simulated scenarios, each involving 3-5 interacting rigid bodies. The model achieves a mean squared error of 0.015 for position predictions and 0.022 for orientation predictions, representing a 25% improvement over baseline methods. Our results demonstrate the network's ability to capture intricate physical interactions, with particular success in predicting elastic collisions and rotational dynamics. This work significantly contributes to physics-informed machine learning by showcasing the immense potential of deep residual networks in modeling complex 3D physical systems. We discuss our approach's limitations and propose future directions for improving generalization to more diverse object shapes and materials.

翻译：本研究探讨了深度残差网络在预测相互作用的三维刚体动力学中的应用。我们提出了一个将C++实现的三维物理模拟器与PyTorch构建的深度学习模型相结合的框架。该模拟器生成的训练数据涵盖线性与角运动、弹性碰撞、流体摩擦、重力效应及阻尼作用。我们设计的深度残差网络包含输入层、多个残差块和输出层，旨在处理三维动力学的复杂性。我们在包含10,000个模拟场景的数据集上评估网络性能，每个场景涉及3-5个相互作用的刚体。该模型在位置预测上达到0.015的均方误差，在姿态预测上达到0.022的均方误差，较基线方法提升25%。实验结果表明该网络能够捕捉复杂的物理相互作用，尤其在预测弹性碰撞和旋转动力学方面表现突出。本研究通过展示深度残差网络在复杂三维物理系统建模中的巨大潜力，为物理信息机器学习领域作出重要贡献。我们讨论了当前方法的局限性，并提出了未来改进方向，以提升模型对不同物体形状和材料的泛化能力。