自然的代价函数：通过最小化作用来模拟物理学
Nature's Cost Function: Simulating Physics by Minimizing the Action
摘要：
在物理学中，有一个标量函数称为动作，它的行为类似于成本函数。当最小化时，它产生“最小作用路径”，表示物理系统在空间和时间中的路径。该函数在理论物理中至关重要，通常通过解析最小化来获得各种问题的运动方程。在本文中，我们提出了一种不同的方法：而不是最小化的行动分析，我们离散化，然后直接最小化梯度下降。我们使用这种方法来获得六个不同的物理系统的动力学，并表明它们几乎是相同的地面实况动态。我们讨论了故障模式，如无约束能量效应，并说明如何解决这些问题。最后，我们利用离散化的作用量构造了一个简单而新颖的量子模拟。
英文摘要：
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.
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