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Sensor placement is critical for efficient monitoring, control, and decision-making in modern engineering systems. Sensors play a crucial role in characterizing spatio-temporal dynamics in high-dimensional, non-linear systems such as fluid flows [@erichson2020shallow], manufacturing [@manohar2018predicting], geophysical [@alonso2010novel] and nuclear systems [@karnik2024constrained]. Optimal sensor placement ensures accurate, real-time tracking of key system variables with minimal hardware and enables cost-effective, real-time system analysis and control. In general, sensor placement optimization is NP-hard and cannot be solved in polynomial time. There are ${n \choose p} = n!/((n-p)!p!)$ possible combinations of choosing $p$ sensors from an $n$-dimensional state.
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Common approaches to optimizing sensor placement include maximizing the information criteria [@krause2008near], Bayesian Optimal Experimental Design [@alexanderian2021optimal], compressed sensing [@donoho2006compressed], and heuristic methods. Many sensor placement methods have submodular objective form, which sets guarantees on how close an efficient greedy placement can be to the unknown true optimum [@summers2015submodularity]. Sub-modular objectives can be efficiently optimized for hundreds or thousands of candidate locations using convex [joshi2008sensor] or greedy optimization approaches [@summers2015submodularity] .
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`PySensors` is a Python package [@de2021pysensors] dedicated to solving the complex challenge of optimal sensor placement in data-driven systems. It implements advanced sparse optimization algorithms that use dimensionality reduction techniques to identify the most informative measurement locations with remarkable efficiency [@manohar2018data;@brunton2016sparse;@clark2020multi]. It helps users identify the best locations for sensors when working with complex high dimensional data, focusing on both reconstruction [@manohar2018data] and classification [@brunton2016sparse] tasks. The package follows `scikit-learn` conventions for user-friendly access while offering advanced customization options for experienced users. Designed with researchers and practitioners in mind, `PySensors` provides open-source, accessible tools that support model discovery across various scientific applications.
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 and over-sampling cases (p > r)scenarios , select TPGR optimizer. In noisy environments enable uncertainty quantification for robust results.")
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 and over-sampling cases (p > r)scenarios , select TPGR optimizer. In noisy environments enable uncertainty quantification for robust results.")
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