Bulk elastic properties of minerals occurring in Earth's lower mantle are conventionally determined by measuring their unit-cell volumes at high pressures and fitting the data to a pre-defined equation of state. However, this approach is problematic in the case of ferropericlase, the second most abundant mineral in the lower mantle. Under the influence of pressure, iron atoms in ferropericlase undergo a spin crossover from high-spin to low-spin state, leading to a gradual volume reduction and softening of the bulk modulus. Using equations of state to describe the anomalous elastic behaviour of ferropericlase across the spin crossover introduces inherent biases through the choice of functional and use of priors. Instead, limitations in the availability of experimental data can be addressed by using machine learning techniques to directly infer physical properties of ferropericlase from experimental pressure-volume (P-V) data and estimate uncertainties.

We present recently published results on the relationship between pressure, iron content (X) and elastic properties of ferropericlase. New data from continuous compression experiments in diamond anvil cells is combined with X-ray diffraction data from literature on (Mg1-x,Fex)O with x = 0.05 to 0.60. Mixture Density Networks are then trained on the compiled data set to infer P-V-X relationships. We use the probability density functions for volume predicted by the networks to assess uncertainties in the P-V curve of ferropericlase resulting from measurement uncertainties, data gaps and the use of a variety of experimental designs and pressure scales. We also derive the bulk modulus from the derivative of the predicted P-V curve, allowing us to constrain the effect of iron content on the spin crossover-induced bulk modulus softening. Our findings have important implications for the interpretation of seismic observations of the lower mantle, particularly in iron-enriched regions near the core-mantle boundary, and help quantifying the uncertainty of such interpretations.