PhD Studentship: Better-conditioned Inverse Problems in Computational Materials Science

Supervisors:

Prof. James Kermode (Engineering) and Dr. Thomas Hudson (Maths) 

Summary:  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 (and other examples below) on the basis of computational simulations. However, these 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 statistics and machine learning such as Bayesian inference which mitigate the ill-conditioning of the problem by incorporating prior information. 

Many machine-learning models for interatomic interactions have been proposed recently: together, these allow flexible descriptions of atomic environments [1]. This flexibility comes with the challenge of needing to choose parameters for these models that accurately describe complex material processes and produce predictions which agree with experimental observations. A promising route to tackling inverse problems efficiently is through end-to-end differentiable simulations (e.g. jax-md, Molly.jl), where the final output quantity of interest can be differentiated with respect to the model parameters. This enables rapid optimisation of and sampling over model parameters to match available reference data.

In this PhD project you will build on the atomic cluster expansion (ACE) approach (e.g. using the ACEpotentials.jl or MACE codes) to tackle inverse problems. This approach is attractive for inverse problems as it provides a complete basis set for atomic environments; incorporation of this basis in linear models gives rise to analytically tractable uncertainty estimates on output quantities of interest. 

As a first goal, linear ACE models will be trained to predict simple material properties such as elastic constants, with the goal of producing improved priors that restrict models to realistic ranges of the target property. The initial focus will be on single-component materials where there is no internal relaxation, later moving to multi-component materials and impurities. The project will be extended to more complex quantities of interest.

About the CDT:

HetSys is an EPSRC-supported Centre for Doctoral Training. It recruits enthusiastic students from across physical sciences, mathematics and engineering who enjoy using their mathematical skills and thinking flexibly to solve complex problems. By developing these skills HetSys trains people to challenge current state-of-the-art in computational modelling of heterogeneous, ‘real world’ systems across a range of research themes such as nanoscale devices, new catalysts, superalloys, smart fluids, space plasmas etc. They have recently been awarded £11m to train PhD cohorts in computation modelling.

HetSys is built around a closely knit, highly collaborative team of academics from five science departments at Warwick with a strong track record in leading large projects. With its project partners HetSys develops talented PhD students to push boundaries in this exciting field. The students have the potential to inspire new ideas, approaches and innovation and become future leaders in developing new technologies. HetSys builds on Warwick's cross-departmental scientific computing research community and the Warwick Centre for Predictive Modelling.

https://warwick.ac.uk/fac/sci/hetsys/themes/projectopportunities/

Previous applicants need not apply.

For more funding details visit: https://warwick.ac.uk/fac/sci/hetsys/apply/funding/

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