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

这项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。这类过程的优化和控制需要在两个或三个空间维度上重复求解依赖时间的偏方程。这个问题的要求必须交互地解决，只有使用大规模并行计算机才能满足。如此全面和强大的PSE目前还不存在，它的发展给计算和计算机科学带来了巨大的挑战。最初的应用是设计和优化一种小直径的生物人工动脉。美国每年进行60多万例血管置换手术，其中许多涉及合成聚合物替代品，用于替代因缺乏生物相容性而失败的小直径血管，这对生物人工动脉来说不是问题。基于连续介质力学理论的PDE模型描述了组织中细胞、纤维和应力的分布，将被用来模拟生物人工动脉的演变紧实化。寻求生物人工动脉的最终特性的最优化，特别是承受动脉搏动性压力的能力。具有类似数学结构的PDE系统通常作为化学过程的模型而出现，需要对其进行控制和优化。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投入，这些实验室在加工方面有应用。为了优化或控制由PDES描述的过程，原始时间间隔在多个拍摄类型的方法中被划分为子间隔。通过并行自适应有限元方法对每个子区间上的偏微分方程组进行空间离散，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，在状态和控制变量以及连续性约束(相等和不等)的约束下，对参数或控制变量进行优化。要成功开发这样的PSE，需要在PDE、DAE、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拥有丰富的知识和研究经验。REAERCH团队成员涵盖了广泛的专业知识，并拥有相互合作的成功记录。

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.