论文标题
Fenrir：针对初始价值问题的物理增强回归
Fenrir: Physics-Enhanced Regression for Initial Value Problems
论文作者
论文摘要
我们展示了如何使用概率数字将初始值问题转换为高斯 - 马尔科夫的过程，该过程由初始值问题的动力学参数化。因此，在普通微分方程中，参数估计的常常困难问题降低为高斯 - 马尔科夫回归中的高参数估计，这往往要容易得多。与经典的数值集成和梯度匹配方法相比，该方法的关系和好处是阐明的。特别是，与梯度匹配相比，该方法可以处理部分观察结果，并且具有某些逃避本地Optima的途径，而不是经典的数值集成。实验结果表明，该方法比竞争方法要好或适度的方法。
We show how probabilistic numerics can be used to convert an initial value problem into a Gauss--Markov process parametrised by the dynamics of the initial value problem. Consequently, the often difficult problem of parameter estimation in ordinary differential equations is reduced to hyperparameter estimation in Gauss--Markov regression, which tends to be considerably easier. The method's relation and benefits in comparison to classical numerical integration and gradient matching approaches is elucidated. In particular, the method can, in contrast to gradient matching, handle partial observations, and has certain routes for escaping local optima not available to classical numerical integration. Experimental results demonstrate that the method is on par or moderately better than competing approaches.
