In the United States, citizens and policymakers heavily rely upon Environmental Protection Agency mandated regulatory networks to monitor air pollution; increasingly they also depend on low-cost sensor networks to supplement spatial gaps in regulatory monitor networks coverage. Although these regulatory and low-cost networks in tandem provide enhanced spatiotemporal coverage in urban areas, low-cost sensors are located often in higher income, predominantly White areas. Such disparity in coverage may exacerbate existing inequalities and impact the ability of different communities to respond to the threat of air pollution. Here we present a study using cost-constrained multiresolution dynamic mode decomposition (mrDMDcc) to identify the optimal and equitable placement of fine particulate matter (PM2.5) sensors in four U.S. cities with histories of racial or income segregation: St. Louis, Houston, Boston, and Buffalo. This novel approach incorporates the variation of PM2.5 on timescales ranging from 1 day to over a decade to capture air pollution variability. We also introduce a cost function into the sensor placement optimization that represents the balance between our objectives of capturing PM2.5 extremes and increasing pollution monitoring in low-income and nonwhite areas. We find that the mrDMDcc algorithm places a greater number of sensors in historically low-income and nonwhite neighborhoods with known environmental pollution problems compared to networks using PM2.5 information alone. Our work provides a roadmap for the creation of equitable sensor networks in U.S. cities and offers a guide for democratizing air pollution data through increasing spatial coverage of low-cost sensors in less privileged communities.

Dynamic mode decomposition has emerged asa leading technique to identify spatiotemporal coherent structuresfrom high-dimensional data, benefiting from a strong connection to nonlinear dynamical systems via the Koopman operator. In this work, two recent innovations that extend dynamic mode decomposition to systems with actuation and systems with heavily subsampled measurements are integrated and unified. When combined, these methods yield a novel framework for compressive system identification. It is possible to identify a low-order model from limited input–output data and reconstruct the associated full-state dynamic modes with compressed sensing, adding interpretability to the state of the reduced-order model. Moreover, when full-state data are available, it is possible to dramatically accelerate downstream computations by first compressing the data. This unified framework is demonstrated on two model systems, investigating the effects of sensor noise, different types of measurements (e.g., point sensors, Gaussian random projections, etc.), compression ratios, and different choices of actuation (e.g., localized, broadband, etc.). In the first example, this architecture is explored on a test system with known low-rank dynamics and an artificially inflated state dimension. The second example consists of a real-world engineering application given by the fluid flow past a pitching airfoil at low Reynolds number. This example provides a challenging and realistic test case for the proposed method, and results demonstrate that the dominant coherent structures are well characterized despite actuation and heavily subsampled data.

This volume provides a snapshot of the current and future trends in turbulence research across a range of disciplines.