The design of adaptive architected materials for extreme environments requires a precise understanding of energy dissipation at the micro-scale. In such systems, gaseous constituents operate in non-equilibrium regimes where constituent-specific temperatures diverge and a phenomenon known as temperature overshoot could occur. While macroscopic multi-temperature (MT) models provide a robust theoretical framework, their integration into real-time design optimization for 3D metamaterials is often hindered by the computational cost and numerical stiffness of the governing hyperbolic-parabolic systems. This study investigates the potential of scientific machine learning as a surrogate modeling paradigm to accelerate the design of gas-filled architected materials. We evaluate a comparative framework utilizing both Gaussian Process Regression (GPR) and Physics-Informed Neural Networks (PINNs). While GPR provides a high-fidelity statistical baseline for interpolating microscopic parameters, the PINN architecture is evaluated for its ability to regularize the solution by embedding field balance laws directly into the loss function. The investigation focuses on identifying the limits of convergence and the sensitivity of the loss landscape under high-gradient shock conditions. Preliminary results quantify how uncertainties in constituent properties propagate to macroscopic shock thickness and energy dissipation. We provide a critical assessment of the trade-offs between the statistical reliability of data-driven surrogates and the physical rigor of physics-informed constraints. This work bridges theoretical thermodynamics and practical materials design, establishing a roadmap for developing intelligent fluidic systems where the gas phase is a programmable component for shock mitigation.