We present a data-driven modeling strategy to overcome improperly modeled dynamics for systems exhibiting complex spatio-temporal behaviors. We propose a Deep Learning framework to resolve the differences between the true dynamics of the system and the dynamics given by a model of the system that is either inaccurately or inadequately described. Our machine learning strategy leverages data generated from the improper system model and observational data from the actual system to create a neural network to model the dynamics of the actual system. We evaluate the proposed framework using numerical solutions obtained from three increasingly complex dynamical systems. Our results show that our system is capable of learning a data-driven model that provides accurate estimates of the system states both in previously unobserved regions as well as for future states. Our results show the power of state-of-the-art machine learning frameworks in estimating an accurate prior of the system’s true dynamics that can be used for prediction up to a finite horizon.

我们提出了一种数据驱动的建模策略，以克服表现出复杂时空行为的系统的建模不当动力学问题。我们提出了深度学习框架，以解决系统的真实动态与系统模型所给出的动态之间的差异，该动态模型描述得不正确或不充分。我们的机器学习策略利用不正确的系统模型生成的数据和实际系统的观测数据来创建神经网络，以对实际系统的动力学进行建模。我们使用从三个日益复杂的动力学系统获得的数值解来评估所提出的框架。我们的结果表明，我们的系统能够学习数据驱动的模型，该模型可提供对先前未观察到的区域以及未来状态的系统状态的准确估计。我们的结果显示了最新的机器学习框架在估计系统真实动态的准确先验的能力，该先验可用于有限范围的预测。