Theory and Application of Coarse Graining

计算机模拟是一种基础工具，用于增进几乎所有科学领域的知识和理解，从描述生物中的酶催化或复杂类脂膜的行为，到天体物理学中的行星和星系的运动。然而，一些过程，如剪切流动下聚合物构型的变化或材料的结构失效，跨越了足够长的长度和时间尺度，无法使用最先进的计算机进行完全原子模拟。粗粒化(CG)是一种处理这类系统的技术，它减少了有效自由度数，同时保持了正确的动力学和统计特性。我的长期目标是：i)将可以用模拟方法处理的系统在空间和时间上增加几个数量级；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通过构建真正的多体势能来实现。通过资助3名博士生、1名PDF和几名本科生，这项提案的短期目标集中在以下三个主题上：CG溶剂模型考虑一种CG方案，该方案将溶剂分子分组为立方体，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，但比连续介质更细，可以以物理上正确的方式弥合这两个极限。它们可以用来取代原子模拟中的溶剂分子，导致显著的加速，或者与流体动力学模拟相结合，产生自洽的多尺度模拟方法。描述复杂材料(如嵌入在聚合物基质中的纳米颗粒)或复杂流体流动(如通过碳纳米管过滤器的流动)需要多尺度方法学。该建议旨在构建物理上正确的CG溶剂。结合原子学和CG模拟，在我的团队中开发的CG理论允许正确地制定混合模拟方法，将CG“粒子”与原子论粒子结合在一起。这是扩展模拟时间和长度尺度的关键，允许用原子分辨率来处理系统的某些部分，而用CG描述来处理不太重要的部分。这项建议将开发这种具有完整动力学的混合方法，包括耗散和涨落的影响。真正的多体势能在广泛的物理条件下模拟系统的能力需要精确的势能，原则上是多体势能。现在几乎所有的模拟都使用有效的二体势能，因此局限于它们被参数化的相空间区域。这项建议寻求使用机器学习来帮助建立多体势能中高阶项的模型，从原子系统开始，最终取代实验的需要。

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.