MDC: A High-Performance Problem-Solving Environment for Optimization and Control of Chemical and Biological Processes

本研究的主要目标是开发高性能的问题解决环境（PSE），用于化学和生物过程的优化和控制，最初的重点是生物工程应用。这些过程的优化和控制需要在二维或三维空间中重复求解时变偏方程（PDEs）。这一问题的要求必须通过交互的方式来解决，只有大规模并行计算机才能满足这一要求。目前还不存在这样一个全面而强大的PSE，它的发展对计算和计算机科学提出了重大挑战。最初的应用是设计和优化一个小直径的生物人工动脉。在美国，每年进行的血管置换手术超过60万例，其中许多涉及合成聚合物替代品，以替代由于缺乏生物相容性而失败的小直径血管，这对于生物人工动脉来说不是问题。基于连续力学理论的PDE模型描述了组织中细胞、纤维和应力的分布，将用于模拟生物人工动脉的进化压实。生物人工动脉的最终性能的优化是寻求的，特别是承受脉动动脉压力的能力。具有类似数学结构的PDE系统通常作为需要控制和优化的化学过程的模型出现。该项目包括与几个工业和政府实验室的科学家和工程师合作，并提供加工应用。为了优化或控制由偏微分方程描述的过程，采用多采样方法将原始时间区间划分为子区间。采用并行自适应有限元方法对各子区间上的偏微分方程进行空间离散，得到一个大的代数方程组。然后使用大规模非线性规划技术，根据状态和控制变量以及连续性约束（等式和不等式）对参数或控制变量进行优化。成功开发这样的PSE需要在pde、DAEs、大规模优化、并行计算、计算环境以及化学和生物过程的自适应方法方面具有丰富的知识和研究经验。研究团队成员涵盖了广泛的专业知识，并且彼此之间有成功的合作记录。

The primary goal of this research is the development of high-performance problem solving environment (PSE) for the optimization and control of chemical and biological processes, with initial emphasis on bioengineering applications. The optimization and control of such processes requires the repetitive solution of time-dependent partial equations (PDEs) in two or three spatial dimensions. The requirements of this problem, which must be solved interactively, can only be met by the use of massively parallel computers. Such a comprehensive and powerful PSE does not currently exist, and its development presents significant computational and computer science challenges. The initial application is the design and optimization of a small diameter bioartificial artery. Over 600,000 surgical procedures for blood vessel replacement are conducted in the U.S. annually, many involving synthetic polymer substitutes for small diameter blood vessels that fail due to lack of biocompatability, which is not an issue for bioartificial arteries. A PDE model based on continuum mechanical theory that describes the distribution of cells, fibers, and stresses in a tissue will be used to simulate the evolving compaction of a bioartificial artery. Optimization of the ultimate properties of the bioartificial artery is sought, in particular the ability to withstand pulsatile arterial pressure. PDE systems of a similar mathematical structure commonly arise as models for chemical processes with a need for their control and optimization. The project includes collaboration with and input from scientists and engineers at several industrial and government laboratories with applications in processing. To optimize or control a process described by PDEs, the original time interval is divided into subintervals in a multiple- shooting type approach. The PDEs on each subinterval are discretized in space via parallel adaptive finite el ement methods to give a large system of algebraic equations (DAEs). Parameters or control variables are then optimized, subject to state and control variable and continuity constraints (equality and inequality) using large-scale nonlinear programming techniques. Extensive knowledge and research experience in adaptive methods for PDEs, DAEs, large-scale optimization, parallel computing, computing environments, and chemical and biological processes, are required to successfully develop such a PSE. The reaerch team members cover this broad range of expertise, and have a successful record of collaboration with each other.