Training Neural Networks to Discover Stochastic Differential Equation Based Models

训练神经网络以发现基于随机微分方程的模型

• 批准号: 2277653
• 金额: --
• 依托单位: University of Edinburgh
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2019
• 资助国家: 英国
• 起止时间: 2019 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2277653
• 关键词: Training; Neural; Networks; Discover; Stochastic

Differential equations are probably the most important tool on a mathematical modeller's workbench. The enormous variety of phenomena which have been successfully modelled using these types of equations is quite astounding - many of the fundamental laws of physics and chemistry are formulated as differential equations. Many complex systems in biology and economics too are modelled this way. In recent times, neural networks have become an increasingly powerful and popular method for creating models directly from data, without requiring the user to have an understanding of the underlying processes involved to build a powerful predictive model. These two modelling methods are now being researched together - the idea is to train neural networks to discover good differential equation-based models from data. However, differential equations have their limitations in what types of dynamics they can effectively model. Phenomenon such as financial markets and many biological processes are not well modelled using this technique as they display many sharp changes due to random perturbations which differential equations cannot express. A typical family of methods for modelling these phenomena, closely related to the differential equations discussed above, are stochastic differential equations. In the same way that neural networks can be trained on data to produce differential equation models, similarly, these stochastic models can be discovered by neural networks. However, some of the tricks that are used to make training these neural networks efficient for differential equations are not easy to transfer to the case of stochastic differential equations. In this project, we will be exploring what the most efficient and robust methods for training neural networks to discover stochastic differential equation-based models from data are. This has many applications including modelling financial markets and biological processes.

微分方程可能是数学建模器工作台上最重要的工具。成功使用这些类型的方程式成功建模的各种现象非常令人震惊 - 许多物理和化学的基本定律被表述为微分方程。以这种方式建模了许多生物学和经济学中的复杂系统。近来，神经网络已成为一种直接从数据创建模型的越来越强大且流行的方法，而无需用户了解涉及的基础过程以构建强大的预测模型。现在正在研究这两种建模方法 - 想法是训练神经网络，从数据中发现基于微分方程的良好方程模型。但是，微分方程在他们可以有效建模的哪种动力学类型上存在局限性。像金融市场和许多生物过程之类的现象无法使用此技术对它们进行建模，因为它们由于差分方程无法表达的随机扰动而显示出许多急剧变化。与上面讨论的微分方程密切相关的这些现象建模的典型方法家族是随机微分方程。就像可以在数据中培训神经网络以产生微分方程模型的方式一样，这些随机模型也可以通过神经网络发现。但是，用于训练这些神经网络有效地用于微分方程的某些技巧并不容易转移到随机微分方程的情况下。在这个项目中，我们将探讨从数据中发现基于随机微分方程的模型的神经网络最有效，最强大的方法。这有许多应用程序，包括建模金融市场和生物流程。