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Exploiting the information content of noise in complex systems: Bayesian inference of nonlinear stochastic models and applications to human blood flow

利用复杂系统中噪声的信息内容：非线性随机模型的贝叶斯推理及其在人体血流中的应用

基本信息

批准号：
EP/D000610/1
负责人：
Peter Vaughan Elsmere McClintock
金额：
$ 44.34万
依托单位：
Lancaster University
依托单位国家：
英国
项目类别：
Research Grant
财政年份：
2006
资助国家：
英国
起止时间：
2006 至无数据
项目状态：
已结题

来源：
https://gtr.ukri.org/projects?ref=EP%2FD000610%2F1
关键词：
Exploiting information content noise complex

项目摘要

An enduring problem in many branches of science and engineering is that of identifying and characterising a nonlinear stochastic system from the signals it produces. Often, the system itself is inaccessible (e.g. remanent quantum vortex loops in superfluid helium or the inversion population in a semiconductor laser), or difficult to measure directly (e.g. the cardiovascular system, where measurements must usually be non-invasive). Furthermore, in addition to any dynamical fluctuations in the system itself (dynamical noise), the results will always be to some extent corrupted by external noise (measurement noise). Examples also arise in ecology, and in other scientific areas as diverse as molecular motors and coupled matter-radiation systems in astrophysics. The chief difficulty stems from the fact that, in a great number of important problems, it is not possible to derive a suitable model from first principles, and one is therefore faced with a rather broad range of possible parametric models to consider. Furthermore, experimental data can often be highly skewed, so that important hidden features of a model (e.g. coupling parameters) can be very difficult to extract due to the intricate interplay between noise and nonlinearity. There is still no reliable method of analysis, despite intensive effort by many scientists.A solution to this problem is sorely is needed, not only to gain physical insight into the complex dynamics of the system under consideration, but also to facilitate the development of realistic models and thus to improve the reliability and accuracy with which the future can be predicted.We now propose to solve the problem. Although it has been one of the most challenging in statistical physics, we can now tackle it - with a high expectation of success - by developing a full theory of Bayesian inference for stochastic nonlinear dynamical systems. It will exploit the information content of dynamical noise and will be robust in the face of measurement noise. The proposed approach is based on novel ideas developed in our collaboration with Dr. V.N. Smelyanskiy. The technique involves path-integral calculations of the likelihood of dynamical events, and it is applicable to complex stochastic nonlinear systems quite generally. As well as developing the fundamental ideas, we propose to apply them to a particular example of a complex system that is in practice inaccessible: the human cardiovascular system (CVS). Here, the measured time series data (a sequence of measurements equally spaced in time) are attributable to physiological processes occurring deep within the body.Enough initial work has already been completed between Lancaster and the NASA/Ames Research Center to demonstrate the feasibility of the research. Exploiting the huge amount of information about the originating system that is contained within the seemingly random fluctuations themselves, and following a number of innovations, we have succeeded in reconstructing stochastic nonlinear models from measurements of time series data.Our exemplary application to the CVS will not only provide the practical experience needed for iterative improvement in the basic technique, but the enterprise will also be intrinsically extremely useful. Suitable CVS data are currently being recorded as part of a separate research project in collaboration with the Royal Lancaster Infirmary. If a good stochastic nonlinear model of the CVS can be reconstructed, there are potentially important implications for medicine because we anticipate that it will prove possible to relate parameter values in the model to the state of the system. There potential for both early diagnosis of cardiovascular disease and for quantitative assessment of the effect of treatment. We emphasize that the range of applicability of our new inference method is potentially very broad, encompassing the wide range of problems mentioned above and many others.

在科学和工程的许多分支中，一个持久的问题是从它产生的信号中识别和表征非线性随机系统。通常，系统本身是不可接近的（例如，超流氦中的Reflux量子涡旋环或半导体激光器中的反转粒子数），或难以直接测量（例如，心血管系统，测量通常必须是非侵入性的）。此外，除了系统本身的任何动态波动（动态噪声）之外，结果总是在某种程度上被外部噪声（测量噪声）破坏。在生态学和其他科学领域，如天体物理学中的分子发动机和耦合物质辐射系统，也出现了这样的例子。主要的困难来自于这样一个事实，即在大量的重要问题中，不可能从第一原理导出一个合适的模型，因此人们面临着相当广泛的可能的参数模型来考虑。此外，实验数据通常可能是高度偏斜的，因此由于噪声和非线性之间的复杂相互作用，模型的重要隐藏特征（例如耦合参数）可能非常难以提取。尽管许多科学家付出了巨大的努力，但仍然没有可靠的分析方法。迫切需要解决这个问题，不仅要从物理上深入了解所考虑的系统的复杂动力学，而且要促进现实模型的发展，从而提高预测未来的可靠性和准确性。虽然它一直是统计物理学中最具挑战性的问题之一，但我们现在可以通过为随机非线性动力系统开发一个完整的贝叶斯推理理论来解决这个问题，并对成功抱有很高的期望。它将利用动态噪声的信息内容，并且在面对测量噪声时具有鲁棒性。所提出的方法是基于我们与V.N.博士合作开发的新想法。斯梅良斯基该技术涉及路径积分计算的动力学事件的可能性，它是适用于复杂的随机非线性系统相当普遍。以及发展的基本思想，我们建议将其应用到一个复杂的系统，在实践中是不可访问的一个特定的例子：人体心血管系统（CVS）。这里，所测量的时间序列数据（在时间上等间隔的测量序列）可归因于发生在身体深处的生理过程。兰开斯特和NASA/艾姆斯研究中心之间已经完成了足够的初步工作，以证明研究的可行性。利用包含在看似随机的波动本身中的关于原始系统的大量信息，并遵循一些创新，我们已经成功地从时间序列数据的测量中重建随机非线性模型。我们对CVS的示例性应用不仅将为基本技术的迭代改进提供所需的实践经验，但企业本身也将非常有用。合适的CVS数据目前正在记录作为一个单独的研究项目的一部分，与皇家兰开斯特医院合作。如果一个很好的随机非线性模型的CVS可以重建，有潜在的重要意义的医学，因为我们预计，它将证明有可能在模型中的参数值的系统的状态。这对心血管疾病的早期诊断和治疗效果的定量评估都有潜力。我们强调，我们的新的推理方法的适用范围可能是非常广泛的，包括上述和许多其他问题的广泛范围。