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

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，开发复杂的新方法，从实验和模拟中提取信息。PI将专注于三个不同的主题：拟合非线性模型到数据，从关键系统中提取通用标度定律，以及识别高温超导体中的有序参数相互作用。(1)模型拟合数据。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，只有几个参数组合来决定与数据的拟合；模型预测在数据空间中形成多维的超带；寻找最佳匹配的方法沿着这个超带的测地线移动。PI将利用这些见解开发新的算法来寻找数据的最佳拟合，这些算法有望比现有方法更快、更可靠。(2)提取通用标度定律。PI正在开发SloppyScaling，这是一个灵活、富有表现力的软件环境，用于探索连续转换、雪崩和其他分形、自相似行为的普遍性和缩放性。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，对标度的修正，以及不同通用性类之间的交叉。(3)高温超导体的序参量。PI是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阶参数场。通过研究它们如何相互反应，如何对污垢和混乱做出反应，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。这个研究项目可能对其他学科产生广泛的影响。它可以改进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，这些项目将为参与的研究生提供跨学科的培训。该奖项支持旨在改进科学家用来比较理论和实验的方法的理论研究和教育。PI将在三种情况下这样做。(1)磁铁。一块铁在不断增强的磁场中，就会产生一系列的“雪崩”。这就是磁铁能抓住冰箱的原因：它们使冰箱的金属壁朝着正确的方向磁化，从而吸引冰箱。PI将研究不同方向磁序的磁区重新排列到另一个磁体中的磁裂纹噪声。理论上，理论可以解释这些雪崩和噼啪声的所有特性——例如，雪崩在空间和时间上形成的各种形状。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。高温超导体异常复杂：许多不同种类的秩序似乎相互竞争，要弄清哪些特征对决定超导性质最重要是一个理论上的挑战。在足够低的温度下，超导体有一种不寻常的秩序，导致物质的电子状态，可以导电而不损失。在高温超导体上进行的复杂实验揭示了一种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，并将利用它们来定量了解它们如何协同工作。(3)模型拟合数据。理论模型通常不能直接预测实验的行为——人们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、空气速度和机翼的几何形状，然后才能预测飞机的阻力。有时，这些参数不能单独确定，而是用来拟合数据——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，以及细胞如何运作的模型，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，它们很草率，许多参数组合很难由它们所适合的数据决定。通过使用通常用于研究广义相对论的复杂数学，PI正在利用这些共同特征来改进理论模型与实验数据的拟合方式。这个研究项目可能对其他学科产生广泛的影响。它可以改进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，这些项目将为参与的研究生提供跨学科的培训。

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.