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.

通过将系统嵌入笛卡尔坐标并使用拉格朗日乘子显式地强制执行约束，本文证明了相较于使用广义坐标来编码系统约束的方法，使用笛卡尔坐标可以在准确度和数据效率方面提高 100 倍。

通过显式约束简化 Hamiltonian 和 Lagrangian 神经网络

Simplifying Hamiltonian and Lagrangian Neural Networks via Explicit  Constraints

Automating molecular design using deep reinforcement learning (RL) holds the
promise of accelerating the discovery of new chemical compounds. Existing
approaches work with molecular graphs and thus ignore the location of atoms in
space, which restricts them to 1) generating single organic molecules and 2)
heuristic reward functions. To address this, we present a novel RL formulation
for molecular design in Cartesian coordinates, thereby extending the class of
molecules that can be built. Our reward function is directly based on
fundamental physical properties such as the energy, which we approximate via
fast quantum-chemical methods. To enable progress towards de-novo molecular
design, we introduce MolGym, an RL environment comprising several challenging
molecular design tasks along with baselines. In our experiments, we show that
our agent can efficiently learn to solve these tasks from scratch by working in
a translation and rotation invariant state-action space.

本文提出了一种新颖的基于强化学习的分子设计方式，使用笛卡尔坐标系来扩展分子结构类型，并利用快速量子化学方法对基本物理性质（如能量）进行直接奖励函数的构建。同时，引入了名为 MolGym 的强化学习环境，在该环境中针对多种具有挑战性的分子设计任务成功展开实验，并在此基础上，构建出一种翻译及旋转不变的状态空间，实现了从零开始的高效学习。