Several long-debated dynamical and elastic unusual properties of $\delta$-Pu are captured within a unified theoretical framework. This outcome is achieved owing to machine learning accelerated ab initio simulations enabling a fine description of strong electronic correlations and explicit temperature effects. First, the experimental negative thermal expansion and equilibrium volume of pure $\delta$-Pu are correctly depicted. Second, the extreme softening of the phonon spectrum, related to huge anharmonic effects, is demonstrated to be responsible for the anomalous decrease of the bulk modulus with temperature, as measured experimentally. Lastly, our model successfully reproduces experimental elastic properties of alloyed $\delta$-Pu between $T=100$ and $800\mathrm{K}$.

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• Anharmonic lattice dynamics
• Elasticity
• First-principles calculations
• Phonons
• Crystal structures
• Ab initio molecular dynamics
• Machine learning