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首页> 外文期刊>Journal of Computational Physics >Deep learning of dynamics and signal-noise decomposition with time-stepping constraints
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Deep learning of dynamics and signal-noise decomposition with time-stepping constraints

机译：与时刻限制的动态和信号噪声分解的深度学习

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摘要

A critical challenge in the data-driven modeling of dynamical systems is producing methods robust to measurement error, particularly when data is limited. Many leading methods either rely on denoising prior to learning or on access to large volumes of data to average over the effect of noise. We propose a novel paradigm for data-driven modeling that simultaneously learns the dynamics and estimates the measurement noise at each observation. By constraining our learning algorithm, our method explicitly accounts for measurement error in the map between observations, treating both the measurement error and the dynamics as unknowns to be identified, rather than assuming idealized noiseless trajectories. We model the unknown vector field using a deep neural network, imposing a Runge-Kutta integrator structure to isolate this vector field, even when the data has a non-uniform timestep, thus constraining and focusing the modeling effort. We demonstrate the ability of this framework to form predictive models on a variety of canonical test problems of increasing complexity and show that it is robust to substantial amounts of measurement error. We also discuss issues with the generalizability of neural network models for dynamical systems and provide open-source code for all examples. (C) 2019 Elsevier Inc. All rights reserved.
机译：动态系统数据驱动建模中的一个关键挑战是生成对测量误差具有鲁棒性的方法，尤其是在数据有限的情况下。许多领先的方法要么依赖于学习前的去噪，要么依赖于访问大量数据来平均噪声的影响。我们提出了一种新的数据驱动建模范式，它可以同时学习动态并估计每次观测时的测量噪声。通过约束我们的学习算法，我们的方法明确说明了观测值之间映射中的测量误差，将测量误差和动力学视为待识别的未知量，而不是假设理想的无噪声轨迹。我们使用深度神经网络对未知向量场进行建模，采用龙格-库塔积分器结构隔离该向量场，即使数据的时间步长不一致，也会限制和集中建模工作。我们展示了该框架对各种日益复杂的规范测试问题形成预测模型的能力，并表明它对大量测量误差具有鲁棒性。我们还讨论了动态系统的神经网络模型的可推广性问题，并为所有示例提供了开放源代码。（C） 2019爱思唯尔公司版权所有。

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