Preconditioners for Large-Scale Atomistic Simulations

原子模拟是现代材料科学、固态物理和化学不可或缺的工具，因为它们允许科学家以实验室实验中不可能的方式研究单个原子和分子。了解原子过程开辟了在原子尺度上操纵物质以实现优异材料性能(例如，电、化学、机械等)的途径。在科学、工程和技术方面的应用。该方案致力于为大规模原子模拟开发高效和健壮的数值算法。目前算法的主要瓶颈是预条件子。在这项研究的背景下，预条件子可以被理解为变换原子构型空间的算子，以便赋予它更好的属性，从而能够形成更有效和更可靠的计算算法。最先进的分子建模软件使用的通用预处理器不是专门针对大规模原子系统的，也不是特别有效。我们建议结合PI在分子建模、数值优化、微分方程的分析和数值以及多尺度建模方面的广泛互补专业知识，构建专门针对材料科学应用中的原子间势的新型预处理器，这将显著提高最先进方法的效率和可靠性。类似的挑战也出现在相空间采样技术中，如马尔科夫链蒙特卡罗方法、混合蒙特卡罗方法或过渡态搜索。我们将修改现有的算法，以利用我们将开发的预条件函数提供的赫辛信息。我们将开发的新算法将使科学家能够研究更复杂的系统，并从模拟中获得更可靠的结果。该项目的应用主要是在学术和工业材料科学方面。我们雄心勃勃的目标是将新算法应用于由数百个原子组成的纳米粒子的研究。

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.