用神经网络解束求解微分方程
Solving Differential Equations Using Neural Network Solution Bundles
摘要：
动力系统的时间演化经常由常微分方程（ODE）描述，必须在给定的初始条件下求解。大多数标准的方法数值积分常微分方程产生一个单一的解决方案，其值是在离散时间计算。当需要许多不同的解决方案与不同的初始条件的常微分方程，计算成本可能会变得显着。我们建议使用一个神经网络作为一个解决方案束，一个集合的解决方案，以各种初始状态和系统参数的常微分方程。神经网络解决方案束是用不需要所寻求的解决方案的任何先验知识的无监督损失来训练的，并且所得对象在初始条件和系统参数中是可微的。该解决方案束具有快速，并行化的系统状态评估，方便使用贝叶斯推理的参数估计在真实的动态系统。
英文摘要：
The time evolution of dynamical systems is frequently described by ordinary differential equations (ODEs), which must be solved for given initial conditions. Most standard approaches numerically integrate ODEs producing a single solution whose values are computed at discrete times. When many varied solutions with different initial conditions to the ODE are required, the computational cost can become significant. We propose that a neural network be used as a solution bundle, a collection of solutions to an ODE for various initial states and system parameters. The neural network solution bundle is trained with an unsupervised loss that does not require any prior knowledge of the sought solutions, and the resulting object is differentiable in initial conditions and system parameters. The solution bundle exhibits fast, parallelizable evaluation of the system state, facilitating the use of Bayesian inference for parameter estimation in real dynamical systems.
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。
