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An adaptive interrogation technique that employs integrated semiconductor micro-ring resonators (MRR) for fast-response sensing applications is proposed and numerically studied. The basic sensing scheme consists of two MRRs in an add/drop signal configuration; the first MRR plays the role of the measuring sensor, while the second one acts as a reference optical filter that converts any frequency shift induced in the spectral characteristics of the measuring sensor into optical power variations. The proposed photonic sensor has the potential to adjust its transfer function dynamically, due to the varying response of the MMRs to different operating conditions, exhibiting either an ultra-low resolution operation capable of detecting extremely small refractive index changes, or an operation with a wide dynamic range. Finally, we propose a more sophisticated approach for simultaneous interrogation that incorporates multiple MRR sensors, based on thermal heaters that modulate the response of each MRR sensor with different modulation frequencies. In contrast to the conventional interrogation techniques, the proposed configurations enable ultra-high sampling rates crucial for studying fast biochemical reactions, such as enzyme kinetics.