Constrained Minimization for Interactive Modeling Using Parallel and Vector Supercomputers

本文研究了求解满足一组非线性等式约束的非线性能量函数的局部最小值的并行算法。约束最小化器是系统中的瓶颈，该系统允许用户交互地移动蛋白质模型中的原子，同时系统自动最小化蛋白质能量并保持表示刚性键长的约束。本研究探讨了拉格朗日乘子方法，该方法可以使用并行处理找到局部约束最小值。要研究的具体实现包括使用共享内存的多指令多数据（MIMD）计算机（特别是Cray Y-MPI）和具有超立方体内存连接的MIMD计算机（iPSC/860）。研究比较了不同MIMD计算机在约束最小化算法中不同步骤的性能。使用比较结果，目标是通过在不同的超级计算机上同时运行步骤，将总求解时间减少两个数量级。该研究还考察了在不破坏交互性能的情况下计算远距离静电相互作用的方法。一种方法包括为一个处理器上的每个原子计算邻居列表，而其他处理器使用前一次迭代中的列表评估静电相互作用。理解成千上万的非键相互作用的影响是相当困难的。该研究还讨论了确定要显示哪些交互以及如何显示交互的可视化方法。可视化避免了屏幕的杂乱，同时显示了相互作用的原子，相互作用的强度和类型（吸引或排斥），以及理想的分离。这种可视化的目标是帮助用户紧密地包装内部侧链。

This research examines parallel algorithms for finding a local minimum of a nonlinear energy function that satisfies a set of nonlinear equality constraints. A constrained minimizer is the bottleneck in a system that lets a user interactively move atoms in a protein model while the system automatically minimizes protein energy and maintains constraints denoting rigid bond lengths. This research examines Lagrange multiplier methods that can find a local constrained minimum using parallel processing. Particular implementations to study include multiple-instruction, multiple-data (MIMD) computers that use shared memory (in particular, a Cray Y-MPI) and MIMD computers with hypercube memory connections (iPSC/860). The research compares the performance of different MIMD computers on different steps in the constrained minimization algorithm. Using the comparison results, the goal will be to reduce the total solution-time two orders-of magnitude by concurrently running steps on separate supercomputers. The research also examines methods that compute long-distance electrostatic interactions without destroying interactive performance. One method includes computing a neighbor list for each atom on one processor while the other processors evaluate electrostatic interactions using the list from previous iteration. Understanding effects from thousands of non-bonded interactions is quite difficult. The research also addresses visualization methods for determining which interaction to display and how to display them. The visualization avoids cluttering the screen while indicating the interacting atoms, strength and type (attraction or repulsion) of interaction, and ideal separation. A goal with this visualization is to help a user tightly pack interior sidechains.