Theory and Application of Coarse Graining

计算机模拟是一个基本的工具，用于推进知识和理解几乎每一个领域的科学努力，从描述酶催化或生物学复杂脂质膜的行为，到天体物理学中行星和星系的运动。然而，一些过程，如剪切流下聚合物构型的变化或材料的结构破坏，跨越足够大的长度和时间尺度，用最先进的计算机进行完全原子模拟是无法实现的。粗粒化（CG）是一种处理这类系统的技术，它在保留正确的动力学和统计特性的同时减少了有效自由度。我的长期目标是：i)在空间和时间上增加几个数量级的系统，可以用模拟方法处理，ii)使模拟足够精确，以完全取代实验。这些目标可以通过推进CG方法的理论和应用以及构建真正的多体势来实现。该提案获得了3名博士生、1名PDF和几名本科生的资助，其短期目标主要集中在以下三个主题：CG溶剂模型考虑一个CG方案，该方案将溶剂分子分组成立方体，类似于连续介质力学中使用的流体元素。这些物体比分子更粗，但比连续体更细，可以以物理正确的方式跨越这两个极限。它们可用于取代原子模拟中的溶剂分子，从而导致显著的加速，或与流体动力学模拟配对，以产生自一致的多尺度模拟方法。描述复杂的材料（如嵌入在聚合物基质中的纳米颗粒）或复杂的流体流动（如通过碳纳米管过滤器的流动）需要多尺度方法。本提案寻求建立一个物理正确的CG溶剂。我的团队开发的CG理论允许将CG“粒子”与原子粒子结合起来的混合模拟方法的正确表述。这是扩展模拟时间和长度尺度的关键，允许用原子分辨率处理系统的某些部分，并使用CG描述不太重要的部分。本提案将发展这样的混合方法与完整的动力学，包括耗散和波动的影响。真正的多体势模拟一个系统在广泛的物理条件下的能力需要精确的势，原则上是多体势。实际上，今天所有的模拟都使用有效的二体势，因此局限于它们被参数化的相空间区域。该建议寻求使用机器学习来帮助建立多体势的高阶项模型，从原子系统开始，最终取代对实验的需求。

Computer simulation is a foundational tool used to advance knowledge and understanding in virtually every field of scientific endeavour, from describing enzyme catalysis or the behaviour of complex lipid membranes in biology, to the motion of planets and galaxies in astrophysics. However some processes, such as changes in polymer configurations under sheared flows or the structural failure of materials, span sufficiently large length and time scales to be inaccessible with fully atomistic simulation using state-of-the-art computers. Coarse graining (CG) is a technique for treating such systems that reduces the effective number of degrees of freedom while retaining the correct dynamical and statistical properties. My long-term goals are: i) to increase by several orders of magnitude in space and time the systems that can be treated with simulation methodologies, and ii) to make simulation accurate enough to completely replace experiment.  These goals can be reached by advancing the theory and application of CG methods and by constructing true, many-body potentials. With funding for 3 PhD students, 1 PDF, and several undergraduate students, this proposal has short-term goals focused on the following three themes: CG Solvent Models Consider a CG scheme that groups solvent molecules into cubes resembling the fluid elements used in continuum mechanics. These objects are coarser than molecular but finer than continuum and can bridge these two limits in a physically correct manner. They can be used to replace solvent molecules in atomistic simulations, leading to significant speedup, or be paired with a hydrodynamic simulation to produce a self-consistent multiscale simulation methodology. A multiscale methodology is required for describing complex materials (like nanoparticles embedded in polymer matrices) or complex fluid flows (like flows through carbon nanotube filters).  This proposal seeks to build a physically correct CG solvent. Combining Atomistic and CG Simulations The CG theory developed in my group allows for the correct formulation of hybrid simulation methods incorporating CG "particles" with atomistic ones. This is the key to expanding the time and length scales of simulations by allowing some parts of the system to be treated with atomic resolution, and less important parts with a CG description.  This proposal will develop such hybrid methods with the complete dynamics, including the effects of dissipation and fluctuations. True Many-Body Potentials The ability to simulate a system over a wide range of physical conditions requires the exact potential, which in principle is many-body.  Virtually all simulations today use effective two-body potentials and are thus limited to the regions of phase space in which they are parameterized.  This proposals seeks to use machine learning to help build models of higher-order terms in many-body potentials, starting with atomistic systems, to ultimately replace the need for experiment.