<ul><li>A new method for joint dimension reduction of input and output spaces of a function is introduced.</li><li>Conventional methods focus on reducing either the input or output space, while this coupled approach supports simultaneous reduction of both.</li><li>The method is suitable for goal-oriented dimension reduction, where input or output quantities of interest are prescribed.</li><li>Applications include goal-oriented sensor placement and goal-oriented sensitivity analysis, solving combinatorial optimization problems by optimizing gradient-based bounds.</li></ul>

Coupled Input-Output Dimension Reduction: Application to Goal-oriented Bayesian Experimental Design and Global Sensitivity Analysis

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