Extracting Theory from Data: Magnets, High Tc Superconductors, and Sloppy Models

从数据中提取理论：磁铁、高温超导体和草率模型

• 批准号: 1005479
• 负责人: James Sethna
• 金额: $ 18.4万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2010
• 资助国家: 美国
• 起止时间: 2010-10-01 至 2012-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1005479&HistoricalAwards=false
• 关键词: Extracting; Theory; Data; Magnets; Tc

TECHNICAL SUMMARYThis award supports theoretical research and education that will use insights into the fundamental structures of theoretical models to develop sophisticated new methods for extracting information from experiments and simulations. The PI will focus on three different topics: fitting nonlinear models to data, extracting universal scaling laws from critical systems, and identifying order parameter interactions in high temperature superconductors. (1) Fitting models to data. Systems biologists, climate modelers, economists, and most experimentalists fit their data to models. The PI has discovered that these multiparameter models all have a common, fascinating underlying structure. They are sloppy, with only a few parameter combinations that determine the fit to the data; the model predictions form a multidimensional hyper-ribbon in data space; methods for finding best fits move along geodesics on this hyper-ribbon. The PI will use these insights to develop new algorithms for finding optimal fits to data, which promise to be both faster and much more reliable than existing methods. (2) Extracting universal scaling laws. The PI is developing SloppyScaling, a flexible, expressive software environment for exploring universality and scaling underlying continuous transitions, avalanches, and other fractal, self-similar behavior. They use it to dramatically extend the scope of these theories, systematically extracting universal scaling forms for systems with multiple control variables, corrections to scaling, and crossovers between different universality classes. (3) Order parameters in high temperature superconductors. The PI is extracting the multiple competing order parameter fields in high temperature superconductors directly from experimental scanning-probe data. By studying how they respond to one another and to dirt and disorder, they will learn how they couple together and help piece together the puzzle of the underlying mechanism.This research project may have broad impact on other disciplines. It may improve the way we extract predictions from models and model information from data. The PI has a track record of excellent, successful women students, and the projects will provide interdisciplinary training for the graduate students involved.NONTECHNICAL SUMMARYThis award supports theoretical research and education that is aimed at improving the methods scientists use to compare theory and experiment. The PI will do so in three contexts. (1) Magnets. A piece of iron in a magnetic field of increasing strength, will magnetize in a series of "avalanches." This is why magnets hold on to the refrigerator: they magnetize the metal wall of the refrigerator in the right direction so as to attract it. The PI will study the magnetic crackling noise as magnetic regions with the magnetic order oriented in different directions rearrange into another magnet. In principle theory can explain all properties about these avalanches and crackling noise - the kinds of shapes the avalanches make in space and time, for example. The PI is developing a software package to aid experimentalists and simulators in making full use of these theories. (2) High temperature superconductors. The high-temperature superconductors are amazingly complicated: lots of different kinds of order seem to be competing, and it is a theoretical challenge to disentangle which features are most important for determining the superconducting properties. At sufficiently low temperatures, superconductors have an unusal kind of order that results in an electronic state of matter that can conduct electricity without losses. Sophisticated experiments on a high temperature superconductor reveal high-resolution images of the surface of one superconductor, and has found elaborate, complex patterns closely related to the superconductivity. The PI has been developing tools for extracting the competing fields out of his data, and will use them to gain quantitative understanding of how they work together.(3) Fitting models to data. A theoretical model does not usually directly predict the behavior of an experiment - one needs to give it some information about the experimental system. Thus the theory of fluids demands that we measure the viscosity and density of the air, the air speed, and the wing geometry, before it will make predictions about the drag on an airplane. Sometimes these parameters can not be determined separately, but are used to fit the data - climate models used to study global warming, econometric models used to predict how our economy works, and models of how cells work include lots of constants that are hard or impossible to directly measure. The PI has discovered that most multiparameter models share many common features; for example, they are sloppy, with many parameter combinations being very poorly determined by the data they are fit to. By using sophisticated mathematics normally used to study general relativity, the PI is using these common features to improve the way theoretical models are fit to experimental data. This research project may have broad impact on other disciplines. It may improve the way we extract predictions from models and model information from data. The PI has a track record of excellent, successful women students, and the projects will provide interdisciplinary training for the graduate students involved.

该奖项支持理论研究和教育，这些研究和教育将利用对理论模型基本结构的见解，开发从实验和模拟中提取信息的复杂新方法。PI将专注于三个不同的主题：将非线性模型拟合到数据，从临界系统中提取通用标度律，以及识别高温超导体中的序参量相互作用。(1)将模型拟合到数据。系统生物学家、气候建模者、经济学家和大多数实验学家都将他们的数据与模型相匹配。PI发现，这些多参数模型都有一个共同的，迷人的底层结构。它们是草率的，只有几个参数组合决定了数据的拟合;模型预测在数据空间中形成了一个多维的超带状;寻找最佳拟合的方法在这个超带状上沿着测地线移动。PI将利用这些见解来开发新的算法，以找到最佳的数据拟合，这有望比现有的方法更快，更可靠。(2)提取普遍的标度律。PI正在开发SloppyScaling，这是一个灵活的，富有表现力的软件环境，用于探索连续过渡，雪崩和其他分形，自相似行为的普遍性和缩放。他们用它来极大地扩展这些理论的范围，系统地提取具有多个控制变量的系统的通用标度形式，对标度的校正，以及不同普适性类之间的交叉。(3)高温超导体中的序参量。PI直接从实验扫描探针数据中提取高温超导体中的多个竞争序参量场。通过研究它们如何相互反应，以及对污垢和无序的反应，他们将了解它们是如何结合在一起的，并帮助拼凑出潜在机制的谜团。它可以改善我们从模型中提取预测和从数据中提取模型信息的方式。PI拥有优秀、成功的女学生的记录，项目将为参与的研究生提供跨学科的培训。非技术性总结该奖项支持理论研究和教育，旨在改善科学家用于比较理论和实验的方法。PI将在三种情况下这样做。(1)磁铁。一块铁在磁场强度增加，将磁化在一系列的“雪崩”。“这就是为什么磁铁会吸附在冰箱上的原因：它们会沿着正确的方向磁化冰箱的金属壁，从而吸引它。PI将研究磁有序方向不同的磁性区域重新排列成另一个磁铁时的磁噼啪声。原则上，理论可以解释这些雪崩和噼啪声的所有性质--例如，雪崩在空间和时间中形成的各种形状。 PI正在开发一个软件包，以帮助实验人员和模拟器充分利用这些理论。(2)高温超导体。高温超导体是惊人的复杂：许多不同种类的秩序似乎是竞争，这是一个理论上的挑战，以解开哪些功能是最重要的决定超导性能。在足够低的温度下，超导体具有一种特殊的秩序，导致物质的电子状态，可以无损耗地导电。 在高温超导体上进行的复杂实验揭示了一个超导体表面的高分辨率图像，并发现了与超导性密切相关的复杂图案。 PI一直在开发工具，从他的数据中提取竞争领域，并将使用它们来定量了解它们如何协同工作。(3)将模型拟合到数据。理论模型通常不能直接预测实验的行为--需要给它一些关于实验系统的信息。因此，流体理论要求我们测量空气的粘度和密度、空气速度和机翼几何形状，然后才能预测飞机的阻力。有时这些参数无法单独确定，但用于拟合数据-用于研究全球变暖的气候模型，用于预测我们的经济如何运作的计量经济学模型，以及细胞如何工作的模型包括许多难以或不可能直接测量的常数。PI发现，大多数多参数模型都有许多共同的特征;例如，它们都很草率，许多参数组合都很难由它们所拟合的数据确定。通过使用通常用于研究广义相对论的复杂数学，PI正在使用这些共同特征来改进理论模型与实验数据的拟合方式。这个研究项目可能会对其他学科产生广泛的影响。它可以改善我们从模型中提取预测和从数据中提取模型信息的方式。PI有优秀、成功的女学生的记录，这些项目将为所涉研究生提供跨学科培训。