Data-driven approaches match or outperform humans at a number of tasks, including pattern recognition in images and text or planning and strategy in rule-based games. The application of machine learning techniques is also promising for accelerating materials design. However, experimental data for training is typically scarce and sparse. The interplay between physics-based simulations and data-driven models is particularly advantageous. It allows relying on transferable laws rather than only fitting data in a black box fashion. Meanwhile, learning from data
provides a unique opportunity to parameterize and augment physics-based models, or completely replace them.

Models can be built that map the structure and composition of materials to their properties. With such models, it is
then possible to rapidly screen libraries of candidate materials for a desired application before going to the lab. Generative models go one step further and allow tackling the inverse problem: given the desired property, automatically suggesting a new optimal material that achieves it.

How to represent matter so that it can be read into or written by a computer program is key for these coupled tasks of property prediction and materials optimization. Strategies are needed to represent materials in a machine-readable way that is data-efficient, expressive, respectful of physical invariants and, ideally, invertible.

Here, we will discuss our current efforts in building bottom-up atom-level representations for materials design. These include variational autoencoders for dimensionality reduction and inverse design in molecules and polymers,
representation and unsupervised learning for graphs and sequences in crystals and polymers, generative models to
accelerate Monte Carlo simulations of alloy phase diagrams or end-to-end differentiable simulations.