摘要翻译：
随着大规模观测和模拟数据集的不断增加，数据驱动表示作为动力系统的有效和相关的计算表示出现在广泛的应用中，其中基于常微分方程的模型驱动模型仍然是最先进的方法。在这项工作中，我们研究神经网络(NN)作为物理声音数据驱动的这类系统的表示。将Runge-Kutta方法重新解释为图形模型，我们考虑了残差神经网络结构，并引入双线性层来嵌入非线性，这是动力系统的固有特征。通过对经典动力系统的数值实验，我们证明了所提出的基于神经网络的体系结构在预测性能和模型辨识方面的相关性。
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英文标题：
《Bilinear residual Neural Network for the identification and forecasting
  of dynamical systems》
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作者：
Ronan Fablet, Said Ouala, Cedric Herzet
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最新提交年份：
2017
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分类信息：

一级分类：Computer Science        计算机科学
二级分类：Machine Learning        机器学习
分类描述：Papers on all aspects of machine learning research (supervised, unsupervised, reinforcement learning, bandit problems, and so on) including also robustness, explanation, fairness, and methodology. cs.LG is also an appropriate primary category for applications of machine learning methods.
关于机器学习研究的所有方面的论文（有监督的，无监督的，强化学习，强盗问题，等等），包括健壮性，解释性，公平性和方法论。对于机器学习方法的应用，CS.LG也是一个合适的主要类别。
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一级分类：Electrical Engineering and Systems Science        电气工程与系统科学
二级分类：Signal Processing        信号处理
分类描述：Theory, algorithms, performance analysis and applications of signal and data analysis, including physical modeling, processing, detection and parameter estimation, learning, mining, retrieval, and information extraction. The term "signal" includes speech, audio, sonar, radar, geophysical, physiological, (bio-) medical, image, video, and multimodal natural and man-made signals, including communication signals and data. Topics of interest include: statistical signal processing, spectral estimation and system identification; filter design, adaptive filtering / stochastic learning; (compressive) sampling, sensing, and transform-domain methods including fast algorithms; signal processing for machine learning and machine learning for signal processing applications; in-network and graph signal processing; convex and nonconvex optimization methods for signal processing applications; radar, sonar, and sensor array beamforming and direction finding; communications signal processing; low power, multi-core and system-on-chip signal processing; sensing, communication, analysis and optimization for cyber-physical systems such as power grids and the Internet of Things.
信号和数据分析的理论、算法、性能分析和应用，包括物理建模、处理、检测和参数估计、学习、挖掘、检索和信息提取。“信号”一词包括语音、音频、声纳、雷达、地球物理、生理、（生物）医学、图像、视频和多模态自然和人为信号，包括通信信号和数据。感兴趣的主题包括：统计信号处理、谱估计和系统辨识；滤波器设计；自适应滤波/随机学习；（压缩）采样、传感和变换域方法，包括快速算法；用于机器学习的信号处理和用于信号处理应用的机器学习；网络与图形信号处理；信号处理中的凸和非凸优化方法；雷达、声纳和传感器阵列波束形成和测向；通信信号处理；低功耗、多核、片上系统信号处理；信息物理系统的传感、通信、分析和优化，如电网和物联网。
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一级分类：Physics        物理学
二级分类：Data Analysis, Statistics and Probability        数据分析、统计与概率
分类描述：Methods, software and hardware for physics data analysis: data processing and storage; measurement methodology; statistical and mathematical aspects such as parametrization and uncertainties.
物理数据分析的方法、软硬件：数据处理与存储；测量方法；统计和数学方面，如参数化和不确定性。
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英文摘要：
  Due to the increasing availability of large-scale observation and simulation datasets, data-driven representations arise as efficient and relevant computation representations of dynamical systems for a wide range of applications, where model-driven models based on ordinary differential equation remain the state-of-the-art approaches. In this work, we investigate neural networks (NN) as physically-sound data-driven representations of such systems. Reinterpreting Runge-Kutta methods as graphical models, we consider a residual NN architecture and introduce bilinear layers to embed non-linearities which are intrinsic features of dynamical systems. From numerical experiments for classic dynamical systems, we demonstrate the relevance of the proposed NN-based architecture both in terms of forecasting performance and model identification.
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PDF链接：
https://arxiv.org/pdf/1712.07003