Characterizing soft materials at high strain rates (i.e., > 10^3 s^−1) is critical for engineering, energy sciences, and biomechanical applications. Cavitation-based methods, e.g., the Inertial Microcavitation Rheometry (IMR) technique [1], achieve these strain rates by generating a microbubble in a soft material and measuring its evolution with high speed imaging. The IMR technique finds material properties by comparing laser-induced cavitation (LIC) radius–time data against Rayleigh-Plesset-type equations. To close the theoretical model requires stipulating an empirical constitutive model for the material stress response. Numerical simulations of bubble dynamics with different constitutive models and material parameters are used to identify the best match to the experimental data. However, these model-driven approaches fail when the assumed constitutive models are not appropriate, e.g., the material exhibits unmodeled behavior such as damage or fracture. To address these limitations, we present a data-driven identification approach by optimizing the distance between material and mechanical spaces without prescribing a constitutive model. The material space is composed of experimental data and the mechanical by the equations of motion for the bubble oscillations. Computing the material stress contribution directly from the LIC bubble dynamics enables constitutive-model-free inference of the material stress response and provides insight into potential high-rate processes, such as damage, in hydrogels. We show that this framework recovers a data-driven stress-strain-strain–rate relationship and performance comparable to model-driven approaches. We will also present a strategy for model discovery at the meeting. [1] J. B. Estrada, C. Barajas, D. L. Henann, E. Johnsen, and C. Franck, High strain-rate soft material characterization via inertial cavitation, Journal of the Mechanics and Physics of Solids, 112:291–317, 2018.