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Multi-physics simulations play a crucial role in understanding complex systems. However, their computational demands are often prohibitive due to high dimensionality and complex interactions, such that actual calculations often rely on approximations. To address this, we introduce a data-driven approach to approximate interactions among degrees of freedom of no direct interest and thus significantly reduce computational costs. Focusing on a semiconductor laser as a case study, we demonstrate the superiority of this method over traditional analytical approximations in both accuracy and efficiency. Our approach streamlines simulations, offering promise for complex multi-physics systems, especially for scenarios requiring a large number of individual simulations.