SCALE: Simulation-Calibrated Amortized Learning for Energy Materials (A hybrid architecture connecting deterministic modeling, real-world data, and transformer-scale inference for accelerated energy-materials discovery)

SCALE (Simulation‑Calibrated Amortized Learning for Energy Materials) is a physics‑grounded learning architecture that fuses deterministic scientific operators, experimental calibration, and transformer‑scale inference to accelerate the discovery of energy materials. It converts expensive mechanistic computations and measured data into reusable models for rapid screening, ranking, inverse design, and active learning. In a case study on solid‑state metal‑hydride hydrogen‑storage, SCALE calibrated a phase‑equilibrium capacity operator against 381 experimental anchors, generated 5,000 teacher labels, and used a 2.90‑million‑parameter edge‑biased graph transformer to achieve high surrogate fidelity (MAE 0.0582 wt% H₂, RMSE 0.0833 wt% H₂, R² 0.9927, Pearson r 0.9963) while reducing per‑candidate screening cost by 10⁷–10⁸ times.

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