practical applications where the gas contains multiple components that vary in concentration . In the case of MOF-based gas sensors, interfering gas species, in addition to the analyte species, adsorb onto the MOF and contribute to the response (i.e. the total adsorbed mass of gas). As a consequence, the inverse problem of inferring the concentration of the analyte from a single-sensor response is underdetermined . To address the problem of cross-sensitivity, one might propose to design a MOF with a very high adsorptive selectivity for the analyte. However, this strategy may be difficult or impossible, and it requires a different MOF highly tailored to each sensing task. Gas sensor arrays tackle the issue of crosssensitivity by monitoring the response of a diverse set of (likely, cross-sensitive) MOFs , analogous to mammalian olfactory receptors . Each response of a crosssensitive MOF, though having contributions from the analyte and interferents, places one Figure : Illustrating a gas composition change to which a non-injective, gravimetric, MOFbased gas sensor is unresponsive. A single QCM-HKUST-1 sensor is immersed in a gas mixture of two different compositions: on the left, a predominantly CH 4 /C 2 H 6 mixture; on the right, a predominantly CH 4 /CO 2 mixture. The response of the sensor to the two distinct gas compositions is identical; hence, the sensor cannot be used to distinguish between these two compositions. The total mass of gas adsorbed in the HKUST-1 film remains the same upon changing from the CH 4 /C 2 H 6 to CH 4 /CO 2 mixture because the desorption of C 2 H 6 balances [in mass] the adsorption of CO 2 , while the adsorption of CH 4 remains approximately constant. constraint on the gas composition. As a whole, the response vector of the gas sensor array may provide sufficient information to uniquely determine the gas composition. Typically, a machine learning algorithm is used to parse the high-dimensional response of a sensor array . A few MOF-based gas sensor arrays have been experimentally demonstrated . Still, even gas sensor arrays are susceptible to cross-sensitivity; the inverse problem (determine the gas composition from the sensor array response vector) could still be underdetermined-particularly, if the number of MOFs comprising the array is less than the number of degrees of freedom in the gas composition. This circumstance can arise (i) in an environment with highly complex gas mixtures and/or (ii) a sensor array is calibrated for gas mixtures with a specific set of components, but an unexpected, interfering component is introduced.