Theory and Application of Coarse Graining

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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.