Better-conditioned Inverse Problems in Computational Materials Science

Inverse problems are a general class of problems that involve calibrating the parameters of a model using measurements of its outputs, typically from real-world experiments.

Many such problems occur across computational science, e.g. in the calibration of constitutive parameters such as elastic moduli on the basis of simulations.

This PhD project will tackle inverse problems in compuational materials science the framework of Machine Learning Interatomic Potentials (MLIPs). Inverse problems are often mathematically ill-posed, meaning there is no single, stable, well-defined solution.

This issue may be resolved numerically either using classical optimisation approaches which select a single solution (that may be an artefact of the choice of optimizer) or using tools from computational statistics and machine learning such as Bayesian inference which mitigate the ill-conditioning of the problem by incorporating prior information.