This article presents an experimental realization of open-loop wave control in metasurface-programmable complex media using a compact physics-based forward model. The study demonstrates significant advantages over deep-learning-based digital twin benchmarks in terms of accuracy, compactness, and calibration examples. The model enables frugal wave control protocols, including coherent wave control and phase-shift-keying backscatter communications, using intensity-only measurements. The physical model's unique generalization capabilities allow it to estimate parameters without phase information or full scattering coefficient measurements, unlocking previously inaccessible wave control methods. The model is validated in a metasurface-programmable chaotic cavity, achieving accurate end-to-end channel estimation even under rich scattering conditions. The physical model outperforms linear and deep-learning models in accuracy and parameter efficiency, and enables the retrieval of phase information from intensity-only data. The model's ability to predict scattering coefficients without calibration data for all coefficients is also demonstrated. The study highlights the potential of physics-based models for end-to-end channel estimation in metasurface-programmable complex media, offering significant improvements over existing methods. The results show that physics-based models can achieve high accuracy with fewer parameters and enable novel wave control protocols, such as coherent perfect absorption, in metasurface-programmable complex media. The study also demonstrates the model's ability to predict scattering coefficients not included in the calibration data, and its effectiveness in phaseless calibration scenarios. The physical model's ability to predict scattering coefficients without phase information or full scattering coefficient measurements is a key contribution of this work. The study provides a framework for open-loop wave control in metasurface-programmable complex media, with potential applications in smart radio environments, reconfigurable holographic antennas, and other emerging systems. The results demonstrate the effectiveness of physics-based models in enabling frugal wave control in complex media, with significant implications for future wireless communication and signal processing technologies.This article presents an experimental realization of open-loop wave control in metasurface-programmable complex media using a compact physics-based forward model. The study demonstrates significant advantages over deep-learning-based digital twin benchmarks in terms of accuracy, compactness, and calibration examples. The model enables frugal wave control protocols, including coherent wave control and phase-shift-keying backscatter communications, using intensity-only measurements. The physical model's unique generalization capabilities allow it to estimate parameters without phase information or full scattering coefficient measurements, unlocking previously inaccessible wave control methods. The model is validated in a metasurface-programmable chaotic cavity, achieving accurate end-to-end channel estimation even under rich scattering conditions. The physical model outperforms linear and deep-learning models in accuracy and parameter efficiency, and enables the retrieval of phase information from intensity-only data. The model's ability to predict scattering coefficients without calibration data for all coefficients is also demonstrated. The study highlights the potential of physics-based models for end-to-end channel estimation in metasurface-programmable complex media, offering significant improvements over existing methods. The results show that physics-based models can achieve high accuracy with fewer parameters and enable novel wave control protocols, such as coherent perfect absorption, in metasurface-programmable complex media. The study also demonstrates the model's ability to predict scattering coefficients not included in the calibration data, and its effectiveness in phaseless calibration scenarios. The physical model's ability to predict scattering coefficients without phase information or full scattering coefficient measurements is a key contribution of this work. The study provides a framework for open-loop wave control in metasurface-programmable complex media, with potential applications in smart radio environments, reconfigurable holographic antennas, and other emerging systems. The results demonstrate the effectiveness of physics-based models in enabling frugal wave control in complex media, with significant implications for future wireless communication and signal processing technologies.