Understanding the thermal properties of disordered systems is of fundamental importance for condensed matter physics - and it is of great relevance for practical applications as well. The manufacturing of window glass, the performance degradation of fiber-optics and the scalability of next-generation phase- change memories all depend on the thermal properties of amorphous solids. While macroscopic properties such as the thermal conductivity are usually well-characterised experimentally, their microscopic origin is often largely unknown. This is because the thermal properties of amorphous solids are determined by their vibrational (and possibly electronic) properties, which in turn depend upon the atomic-level structure. Hence there is a pressing need for atomistic simulations, which can in principle unravel the connection between microscopic structure and functional properties such as thermal conductivity. However, the large (long) length (time) scales involved are usually well beyond the reach of ab initio calculations. On the other hand, many interesting amorphous materials are characterised by a very complex structure. This often prevents the construction of classical interatomic potentials which would enable simulations on much larger (longer) length (time) scales – if compared to those achievable by first-principles simulations. One way to get past this deadlock is to harness machine-learning (ML) algorithms to build interatomic potentials: these can be nearly as computationally efficient as classical force fields for molecular dynamics simulations while retaining much of the accuracy of first-principles calculations. Here, we discuss the contribution of these ML-based potentials to our understanding of the thermal properties of amorphous solids. We focus on neural-network potentials (NNPs) and Gaussian approximation potentials (GAPs), two of the most widespread theoretical frameworks available to date. We review the work that has been devoted to investigate, via NNPs, the thermal properties of phase-change materials, a class of systems widely used in the context of non-volatile memories. In addition, we present recent results on the vibrational properties of amorphous carbon, studied via GAPs. In light of these results, we argue that ML-based potentials are among the best options available to further our understanding of the vibrational and thermal properties of complex amorphous solids
