深度守恒：物理守恒定律精确满足的潜在动力学模型
Deep Conservation: A latent-dynamics model for exact satisfaction of physical conservation laws
摘要：
这项工作提出了一种潜在的动态学习的方法，完全执行物理守恒定律。该方法包括两个步骤。首先，该方法使用深度卷积自编码器计算高维动态系统状态的低维嵌入。这就定义了一个低维非线性流形，在这个流形上，状态随后被强制演化。其次，该方法定义了一个潜在的动态模型，与约束优化问题的解决方案。在这里，目标函数被定义为在有限体积离散化的问题的控制体积的守恒律违反的平方和;非线性等式约束明确地强制执行守恒在规定的子域的问题。在适当的条件下，所得到的动力学模型保证了时间演化的潜状态完全满足守恒律在规定的子域。
英文摘要：
This work proposes an approach for latent-dynamics learning that exactly enforces physical conservation laws. The method comprises two steps. First, the method computes a low-dimensional embedding of the high-dimensional dynamical-system state using deep convolutional autoencoders. This defines a low-dimensional nonlinear manifold on which the state is subsequently enforced to evolve. Second, the method defines a latent-dynamics model that associates with the solution to a constrained optimization problem. Here, the objective function is defined as the sum of squares of conservation-law violations over control volumes within a finite-volume discretization of the problem; nonlinear equality constraints explicitly enforce conservation over prescribed subdomains of the problem. Under modest conditions, the resulting dynamics model guarantees that the time-evolution of the latent state exactly satisfies conservation laws over the prescribed subdomains.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
