In physics, there is a scalar function called the action which behaves like a cost function. When minimized, it yields the "path of least action" which represents the path a physical system will take through space and time. This function is crucial in theoretical physics and is usually minimized analytically to obtain equations of motion for various problems. In this paper, we propose a different approach: instead of minimizing the action analytically, we discretize it and then minimize it directly with gradient descent. We use this approach to obtain dynamics for six different physical systems and show that they are nearly identical to ground-truth dynamics. We discuss failure modes such as the unconstrained energy effect and show how to address them. Finally, we use the discretized action to construct a simple but novel quantum simulation.

翻译：在物理学中，存在一个被称为“作用量”的标量函数，其性质类似于代价函数。当作用量被最小化时，会产生“最小作用量路径”，即物理系统在时空中的演化轨迹。该函数在理论物理学中至关重要，通常通过解析方法最小化以推导各类问题的运动方程。本文提出了一种不同方法：不再通过解析方式最小化作用量，而是将其离散化后直接使用梯度下降进行优化。我们利用该方法获得了六个不同物理系统的动力学行为，并证明其结果与真实动力学几乎一致。同时，我们讨论了无约束能量效应等失效模式，并展示了相应的解决方案。最后，通过离散化作用量构建了一种简单但新颖的量子模拟方案。