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Physical systems are characterized by inherent symmetries, one of which is encapsulated in theunits of their parameters and system states. These symmetries enable a lossless order-reduction, e.g.,via dimensional analysis based on the Buckingham theorem. Despite the latter's benefits, machinelearning (ML) strategies for the discovery of constitutive laws seldom subject experimental and/ornumerical data to dimensional analysis. We demonstrate the potential of dimensional analysis to significantlyenhance the interpretability and generalizability of ML-discovered secondary laws. Ournumerical experiments with creeping fluid flow past solid ellipsoids show how dimensional analysisenables both deep neural networks and sparse regression to reproduce old results, e.g., Stokes law fora sphere, and generate new ones, e.g., an expression for an ellipsoid misaligned with the flow direction.Our results suggest the need to incorporate other physics-based symmetries and invariancesinto ML-based techniques for equation discovery.
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Methods for Analyzing Physics Student Retention and Physics Curricula
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Quantitative reasoning is an essential learning objective of physics instruction. The Physics Inventory for Quantitative Literacy (PIQL) is a published assessment tool that has been developed for calculus-based physics courses to help instructors evaluate whether their students learn to reason this way. However, the PIQL is not appropriate for the large population of students taking physics who are not enrolled in, or have not completed, calculus. To address this need, we have developed the General Equation-based Reasoning inventory of QuaNtity (GERQN). The GERQN is an of the PIQL and is appropriate for most physics students; the only requirement is that students have taken algebra, so they are familiar with the use of variables, negative quantities, and linear functions. In this paper, we present the development and validation of the GERQN, and a short discussion on how the GERQN can be used by instructors to help their students learn.more » « less
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In this paper, we use case study analysis of interviews with twelve white physics faculty to claim that physics expertise functions as white property, drawing on Harris’ definition of property as “every thing to which a [person] may attach a value and have a right” (Madison, 1906, as cited in Harris 1993, p. 1726). In particular, we use quotes from interviews to illustrate that physics expertise confers benefits to its holders, is jealously guarded, and is structurally protected. Faculty treat expertise as a marker of epistemic superiority in a discipline that is rooted in ideals of objectivity and neutrality, and they enforce contingencies around who can become a physicist, drawing on narratives that rely on those ideals. This argument has implications for a more just physics—one that divests from the property interest in physics expertise and invests in what Harris has called distributive justice, which centers a right to inclusion over a right to exclude.more » « less
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