Preconditioners for Large-Scale Atomistic Simulations

Atomistic simulations are an indispensible tool of modern materials science, solid state physics and chemistry, as they allow scientists to study individual atoms and molecules in a way that is impossible in laboratory experiments. Understanding atomistic processes opens up avenues for the manipulation of matter at the atomic scale in order to achieve superior material properties (e.g., electrical, chemical, mechanical, etc.) for applications in science, engineering, and technology. This proposal focuses on the development of efficient and robust numerical algorithms for large-scale atomistic simulations.

The main bottleneck in current state of the art algorithms are preconditioners. In the context of this research preconditioners can be understood as operators transforming the space of atomistic configurations in order to give it "better" properties that enable the formulation of more efficient and more reliable computational algorithms. The state of the art molecular modelling software uses general purpose preconditioners that are not specifically targeted at large-scale atomistic systems, and are not particularly effective.

We propose to combine the wide-ranging complementary expertise of the PIs in molecular modelling, numerical optimisation, analysis and numerics of differential equations, and multiscale modelling, to construct novel preconditioners targeted specifically for interatomic potentials used in materials science applications that will achieve significant improvements in efficiency and reliability of state of the art methods.

Similar challenges arise also in phase space sampling techniques such as Markov Chain Monte Carlo methods, Hybrid Monte Carlo methods, or in transition state search. We will modify existing algorithms to take advantage of the hessian information provided by the preconditioners we will develop.

The new algorithms we will develop will enable scientists to study more complex systems and obtain more reliable results from simulations. The applications of the project are primarily in academic and industrial materials science. Our ambitious aim is to apply the new algorithms to the study of nano-particles consisting of hundreds of atoms.

Immediate Beneficiaries

The project proposes substantial improvements to the efficiency and reliability of numerical algorithms for atomistic modelling of materials. The immediate beneficiaries of this work are researchers working in both the methodology and applications of computational molecular modelling. Methodology research will benefit from the new concepts we propose, in particular the targeted development of preconditioners based on analytic insight into the structure of the molecular models, and the methods we will develop for a rigorous analysis of our algorithms. Researchers applying computational molecular modelling techniques for the study of large molecular systems will directly benefit from substantial improvements in performance and reliability of the new algorithms over the current state of the art, which will allow them to study larger and more complex systems.

Broader Impact

The broader impact of the research arises from its applications in academic and industrial materials science and biochemistry research. The new algorithms we will develop will enable scientists to study larger system sizes and obtain more reliable results from simulations. Materials science progress that will be achieved through improved simulation tools leads, for example, to improved manufacturing processes, and the development of new materials with superior properties (e.g., strength, weight, or even entirely new and unexpected properties). For example, such improvements in engineering materials and manufacturing processes have the potential to significantly reduce energy consumption. One of the the most important applications of computational biochemistry is computer-aided drug design, which involves the design of molecules that can interact in specific ways with proteins and other types of macro-molecules and makes heavy use of similar molecular modelling software as computational materials science.