Accurate crystal structure prediction (CSP) requires accounting for finite-temperature and nuclear quantum effects, yet first-principles evaluation of the free energy surface (FES) remains prohibitive for high-throughput searches. We observe that the self-consistent harmonic approximation (SCHA) FES, as a function of nuclear centroid positions, shares the same mathematical structure as a potential-energy surface and can therefore be directly learned by a deep neural network potential. The resulting deep free energy (DF) model, constructed via a two-level concurrent-learning workflow, evaluates free energies, forces, and stresses in a single forward pass. Applied to the La-Sc-H system at 200 GPa and 300 K, DF-based CSP reproduces the stability of the experimentally observed ${\mathrm{LaH}}_{10}$ and ${\mathrm{LaSc}}_2{\mathrm{H}}_{24}$, and identifies $P4/mmm$ ${\mathrm{LaScH}}_8$ as thermodynamically stable on the free energy convex hull, a stability absent on the classical potential-energy surface. Benchmarked on the ${\mathrm{LaH}}_{10}$ system, the DF model achieves a $1.72\times {10}^6$-fold cost reduction relative to DFT-level SSCHA. The DF framework provides a scalable route for incorporating finite-temperature and nuclear quantum effects into high-throughput crystal structure prediction.

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• High-pressure studies
• Interatomic & molecular potentials
• Potential energy surfaces
• Crystal structures
• Hydrides
• Deep learning
• Density functional calculations