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docs/JOSS2/paper.md

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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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![An overview image of capabilities of Pysensors](../Fig1.jpeg "PySensors 2.0 expands its capabilities by introducing custom basis functions, optimizers, constraints, solvers, and uncertainty quantification, enabling constrained sensing, over- and under-sampling, and uncertainty quantification in the presence of noisy sensor measurements.")
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![An overview image of capabilities of Pysensors](/Fig1.jpeg "PySensors 2.0 expands its capabilities by introducing custom basis functions, optimizers, constraints, solvers, and uncertainty quantification, enabling constrained sensing, over- and under-sampling, and uncertainty quantification in the presence of noisy sensor measurements.")
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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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\mathbf{K}=\boldsymbol{\Psi}_r \mathbf{B} \mathbf{B}^T \boldsymbol{\Psi}_r^T;\quad \mathbf{B}=\eta \mathbf{A}. \label{eqn:K}
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\end{align}
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![A flowchart to suggest which method to use](../Fig2.jpeg "When selecting a sensing method in PySensors, consider your primary objective: For field reconstruction in standard settings, use QR with Identity or SVD basis. For classification tasks, leverage SVD basis with SSPOC optimizer. When facing spatial constraints, choose GQR optimizer. For under-sampling (p < r) and over-sampling cases (p > r)scenarios , select TPGR optimizer. In noisy environments enable uncertainty quantification for robust results.")
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![A flowchart to suggest which method to use](/Fig2.jpeg "When selecting a sensing method in PySensors, consider your primary objective: For field reconstruction in standard settings, use QR with Identity or SVD basis. For classification tasks, leverage SVD basis with SSPOC optimizer. When facing spatial constraints, choose GQR optimizer. For under-sampling (p < r) and over-sampling cases (p > r)scenarios , select TPGR optimizer. In noisy environments enable uncertainty quantification for robust results.")
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# Acknowledgments

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