"SciNapse: A Problem Solving Environment" Stanly Steinberg University of New Mexico Department of Mathematics and Statistics Albuquerque, NM, 97110 USA E-mail:stanly@math.unm.edu I am interested in developing general methods for solving modeling problems of the type that appear in engineering and science. The current methods of solving such problems range from simple analytic and numerical models to numerical codes that consume a major portion of the computing cycles on the largest computers. A most important characteristic of such problems is that their effective solution requires a wide range of analytic and numerical techniques, so wide that an individual cannot be an expert in all the required areas. I am interested in how well and how much of such expertise can be "effectively" captured in a problem solving environment. The problem solving environment must be capable of using a computer algebra system to do analytic calculations and of using high-speed large-scale floating-point computation. In addition, the problem solving environment needs a user interface that allows an easy description of the problem and a comprehensible presentation of any results, either analytic or numeric. Knowledge engineering techniques are used to capture the known solution technology. I will describe the SciNapse system which is an example of such a problem solving environment on which I have worked for over three years. Recently, a product, SciFinance, which is based on SciNapse and is used to model financial derivative, has been marketed by SciComp, Inc. In my opinion, within a few years, most users will interact with computers using problem solving environments, which should strongly impact how scientific computing will be taught at universities. Engineers and Scientists should find SciNapse interesting because this system gives a glimpse of what the future will probably look like, while mathematicians should find SciNapse interesting because problem solving environments will become repositories for large volumes of mathematical knowledge, including theoretical results, and their construction will employ a large number of mathematicians. SciNapse SciNapse is a problem solving environment for numerically solving partial differential equations. The main interface to the system is the ``problem specification language.'' This language allows an initial-boundary value problem for a system of partial differential equations to be specified in terms of invariant differential operators or in a particular coordinate system. The region in which the differential equations hold is specified in terms of a union of rectangles in some coordinate system. This allows rather general regions appropriate for discretization using grids with the same structure as rectangular grids. The methods for discretizing the differential equations and the boundary conditions can be specified by giving keywords for common methods or by giving detailed mathematical replacement rules, or some combination of both. In the case of finite-difference discretizations, simple ways exist for specifying grid staggering and the placement of the boundaries in the staggered grid. The SciNapse system includes a template language for specifying algorithms. One typical use for templates is to specify the over-all time evolution in terms of a general method for taking individual time steps. Then the particular method for taking a time step can be chosen from a library of templates, e.g. Runge-Kutta-Fehlberg or Dormand-Prince integrators, or a new template may be written. If the method is implicit, then a solver may also be chosen from a library of solvers, e.g. preconditioned conjugate gradient or quasi-minimal residual, or a new solver template can be written. SciNapse has heuristics for choosing solvers, and many other features of the solution algorithm. The SciNapse system is implemented in Mathematica and the templates are executable Mathematica code, so they can easily be tested for correctness in Mathematica. SciNapse is a knowledge-based program synthesis system implemented with objects, transformation rules, and a reasoning system. A great deal of knowledge engineering has gone into providing the system with extensive information about how to solve initial boundary value problems in an intelligent manner. The system starts with an abstract notion of what is needed to write a program recorded in its objects and starts filling in the details based on rules associated with the objects. Information may be given to SciNapse in files written by the user, from a simple terminal interface, or in a graphical user interface. When SciNapse realizes that it doesn't have a piece of information that it needs to specify a problem, it will ask the user for that information, typically by giving a menu of alternatives. Users can have the system use its own knowledge whenever possible or can request that they be asked to confirm system choices. If some information has already been given to SciNapse, then the reasoning system uses this to eliminate alternatives. Using constraints (hard and fast rules about legal options and combinations), heuristic rules of thumb for making decisions, and defaults, SciNapse can take much of the burden of writing a program off the user. Collaborators: R.L. Akers, E. Kant, C. Randall, R.L. Young, Stanly Steinberg, Professor of Mathematics Department of Mathematics and Statistics University of New Mexico Albuquerque NM 87131-1141 USA stanly@math.unm.edu http://math.unm.edu/~stanly/ Phone: 505-277-5323, FAX 505-277-5505 Office: Humanities 436 Consultant SciComp Inc. 5806 Mesa Drive, Suite 250 Austin, TX 78731 phone: 512-451-1050 fax: 512-451-1622 stanly@scicomp.com http://www.scicomp.com/