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Acoustic holograms offer precise three-dimensional control of sound fields with immense potential for non-invasive therapies and contactless manipulation. However, conventional phase-only design methods suffer from a fundamental performance gap between theoretical predictions and physical implementation, especially for creating multi-functional devices. These approaches design idealized phase maps while neglecting complex wave physics within hologram structures and distorting effects of heterogeneous biological tissues. Here, we introduce the End-to-End Heterogeneous Physics-Constrained (E2E-HPC) framework, a deep learning paradigm that resolves this gap by directly designing the physical hologram structure. Our framework is guided by integrated, differentiable models that account for both the hologram’s intricate internal acoustics and wave propagation through complex media like the skull. This heterogeneous physics-constrained approach eliminates the performance limitations of conventional methods, improving the resulting acoustic pattern's fidelity by over 6 dB in Peak Signal-to-Noise Ratio (PSNR) and recovering ~16% of the correlation fidelity lost in physical implementation. Beyond single-target design, we demonstrate the framework's extensibility for multi-functional controlsby creating a single hologram capable of both simultaneous, high-fidelity focusing on multiple axial planes and dynamic pattern switching by modulating the input frequency. As a proof-of-concept for therapeutic applications, we showcase real-time, frequency-specific switching of thermal patterns. These results establish a robust platform for designing physically realizable, multi-functional acoustic holograms for challenging biomedical applications.