论文标题
通过明确的约束来简化哈密顿和拉格朗日神经网络
Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit Constraints
论文作者
论文摘要
关于物理世界的推理需要具有正确的归纳偏见的模型，以学习基本动力学。最近的工作通过学习系统的哈密顿或拉格朗日式而不是直接的微分方程来改善预测轨迹的概括。尽管这些方法使用广义坐标编码系统的约束，但我们表明，将系统嵌入到笛卡尔坐标中，并用Lagrange乘数显式地执行约束，从而极大地简化了学习问题。我们介绍了一系列具有挑战性的混乱和扩展系统，包括具有N-铅，弹簧耦合，磁场，刚性转子和陀螺仪的系统，以推动当前方法的极限。我们的实验表明，具有明确限制的笛卡尔坐标可提高准确性和数据效率。
Reasoning about the physical world requires models that are endowed with the right inductive biases to learn the underlying dynamics. Recent works improve generalization for predicting trajectories by learning the Hamiltonian or Lagrangian of a system rather than the differential equations directly. While these methods encode the constraints of the systems using generalized coordinates, we show that embedding the system into Cartesian coordinates and enforcing the constraints explicitly with Lagrange multipliers dramatically simplifies the learning problem. We introduce a series of challenging chaotic and extended-body systems, including systems with N-pendulums, spring coupling, magnetic fields, rigid rotors, and gyroscopes, to push the limits of current approaches. Our experiments show that Cartesian coordinates with explicit constraints lead to a 100x improvement in accuracy and data efficiency.
