AReS和MaRS --用于偏微分方程的对抗性和MMD最小化回归
AReS and MaRS - Adversarial and MMD-Minimizing Regression for SDEs
摘要：
随机微分方程是许多学科中一个重要的建模类。因此，存在许多依赖于各种离散化和数值积分方案的方法。在本文中，我们提出了一种新的，概率模型估计的漂移和扩散噪声观测的基础随机系统。使用最先进的对抗和矩匹配推理技术，我们避免了经典方法的离散化方案。这导致了随机初始猜测的参数精度和鲁棒性的显着改善。在四个已建立的基准系统，我们比较我们的算法的性能，最先进的解决方案的基础上扩展卡尔曼滤波和高斯过程。
英文摘要：
Stochastic differential equations are an important modeling class in many disciplines. Consequently, there exist many methods relying on various discretization and numerical integration schemes. In this paper, we propose a novel, probabilistic model for estimating the drift and diffusion given noisy observations of the underlying stochastic system. Using state-of-the-art adversarial and moment matching inference techniques, we avoid the discretization schemes of classical approaches. This leads to significant improvements in parameter accuracy and robustness given random initial guesses. On four established benchmark systems, we compare the performance of our algorithms to state-of-the-art solutions based on extended Kalman filtering and Gaussian processes.
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。
