Metasurface-programmable radio environments are considered a key ingredient of next-generation wireless networks. Yet, identifying a metasurface configuration that yields a desired wireless functionality in an unknown complex environment was so far only achieved with closed-loop iterative feedback schemes. Here, we introduce open-loop wave control in metasurface-programmable complex media by estimating the parameters of a compact physics-based forward model. Our experiments demonstrate orders-of-magnitude advantages over deep-learning-based digital-twin benchmarks in terms of accuracy, compactness and required calibration examples. Strikingly, our parameter estimation also works without phase information and without providing measurements for all considered scattering coefficients. These unique generalization capabilities of our pure-physics model unlock unforeseen and previously inaccessible frugal wave control protocols that significantly alleviate the measurement complexity. For instance, we achieve coherent wave control (focusing or perfect absorption) and phase-shift-keying backscatter communications in metasurface-programmable complex media with intensity-only measurements. Our approach is also directly relevant to dynamic metasurface antennas, microwave-based signal processors and emerging in situ reconfigurable nanophotonic, optical and room-acoustical systems.