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Collaborative Environments for Scientific Computing 11th ICMCM & SC ‘97 Collaborative Environments for Scientific Computing: The Task of Algorithm/Software Selection N. Ramakrishnan, A. Joshi, E.N. Houstis and J.R. Rice Department of Computer Sciences Purdue University, IN 47907 Department of Computer Sciences, Purdue University

Collaborative Environments for Scientific Computing 11th ICMCM & SC ‘97 Outline o PSEs for Scientific Computing o Advisory Systems in Scientific Computing o The PYTHIA Project o Networked Scientific Computing o Case Studies / Experimental Results o Conclusion Department of Computer Sciences, Purdue University

Collaborative Environments for Scientific Computing 11th ICMCM & SC ‘97 Problem Solving Environments (PSEs) o What are PSEs? “A PSE is a computer system that provides all the computational facilities necessary to solve a target class of problems.” o Features o Advanced Solution Methods o Automatic/SemiAutomatic Selection of Solution Methods o Ways to easily include new techniques o Other Features o Check formulation, select, assess correctness o Manage overall computational process o PSEs = User Interface + Libraries + Knowledge Bases + Integration o Example PSEs o MATLAB - Linear Algebra o Mathematica - Symbolic & Numeric Computation o ELLPACK, //ELLPACK, PDELab - PDE Problems o NetSolve - Optimization Department of Computer Sciences, Purdue University

Collaborative Environments for Scientific Computing 11th ICMCM & SC ‘97 Advisory Systems in Scientific Computing o Necessary to supplement PSEs o Similar in idea to recommender systems o Automatic Algorithm Selection Systems o Motivations o Multiple Solution Approaches o Resource Limitations o Complex factors influencing applicability of algorithms o Computation Steering o Accept problem definition, performance criteria o Suggest software components and hardware resources o Example o “Use the 5-point star algorithm with a 200x200 grid.“ o “Implement the algorithm on an nCUBE/2 with 16 processors.” Department of Computer Sciences, Purdue University

Collaborative Environments for Scientific Computing 11th ICMCM & SC ‘97 The PYTHIA Project o Automatic Algorithm Selection for o 2-D Linear, Elliptic PDEs o Numerical Quadrature o Uses o Databases of previously solved problems along with performance information for various methods on them Problem features for classifying problems o (Optimization) Group collections of problems with o “similar” features into problem classes Mechanisms for comparing features to find “similar” o problems and problem classes o Three Key Components PEM (Performance Evaluation Module) o AFD (Automatic Feature Determination) o KE (Knowledge Engine) o Department of Computer Sciences, Purdue University

Collaborative Environments for Scientific Computing 11th ICMCM & SC ‘97 Case Study 1: Numerical Quadrature y o Uses y = f(x) 124 routines o 286 test problems o o Select a method to evaluate an integral with a constraint a b x on relative accuracy so that the number of function evaluations is minimized o Performance Evaluation Run routines on applicable integrands and code results o as nfe predicates Software “Exits” o occurrence of roundoff error o difficulties in integrand behavior o divergent (or slowly) convergent integrals o limiting number of cycles o Department of Computer Sciences, Purdue University

Collaborative Environments for Scientific Computing 11th ICMCM & SC ‘97 Case Study 1: Numerical Quadrature (Contd.) o AFD Module o Determines o whether integrand can be expressed as w(x)f(x) o the location of singularities of f o if there are singularities of f’ o locations of discontinuities o range of integration o behavior of non-specific type o features of data points (on a grid) o User Input o Results o Best Algorithm Selection - 89% o Second Best Selection - 5% o ‘Reasonable’ Selection - 3% o ‘Hopeless’ Cases (!) - 3% Department of Computer Sciences, Purdue University

Collaborative Environments for Scientific Computing 11th ICMCM & SC ‘97 Case Study 1: Numerical Quadrature (Contd.) o Rules uncovered method (Problem, qags) :- accuracy(Problem, Acc), image(Problem, type6), sing(Problem), endptsing(Problem), noderivsing(Problem), range(Problem, finite). o Success mainly due to the methodology of data collection o Uncovered broad heuristics o similar to decision-tree models and lookup tables o confirmed to popular opinion o Examples Adaptive algos. use lesser nfes than non-adaptive ones o (for high accuracy results) Adaptive algos. take longer to meet low-accuracy constraints o Department of Computer Sciences, Purdue University

Collaborative Environments for Scientific Computing 11th ICMCM & SC ‘97 Case Study 2: PDEs PDE Problem Features: operator, domain, boundary User’s performance objectives: conditions, I/O functions Error: less than 0.02% Memory Usage: less than 5 MB Execution Time: at most 10 minutes Service Charge: less than $10 Classification Module Inference PYTHIA’s Engine KB PYTHIA’s recommendation: Use 5-point star with a 200 x 200 grid on an nCube/2 using 16 processors. Department of Computer Sciences, Purdue University

Collaborative Environments for Scientific Computing 11th ICMCM & SC ‘97 Networked Scientific Computing o A ‘Net-centric’ Scenario for Scientific Computing o Distributed Software + Information Resources o Need to be identified and ‘linked’ together o View of software changes from a product to a service o Improvements in QoS o Enabled by o HPCC technologies o Complexity of Application Software o Multi-disciplinary nature of large scale application research o Necessity to combine NC based supercomputer resources o Network Computational Servers o provide on-line access to PSEs o Need for Agent Based Environments Department of Computer Sciences, Purdue University

Collaborative Environments for Scientific Computing 11th ICMCM & SC ‘97 Example Systems o Provide access to software libraries & documents o Netlib (UTK, ORNL, AT&T) o Enable PSEs to be accessed over the Web o Web //ELLPACK, Net //ELLPACK (Purdue) o NetSolve (UTK) o Index software modules acc. to functionality o GAMS (NIST) o Provide access to performance data, evaluation etc. o NEOS (ANL) o The Matrix Market (NIST) o Interface to HPCC repositories o NHSE (CRPC) Department of Computer Sciences, Purdue University

Collaborative Environments for Scientific Computing 11th ICMCM & SC ‘97 Collaborative Scenario for Algorithm Selection o Assume o Multiple PYTHIA ‘servers’ each with specialized KB o Need o to model collaborative scenario and environments o to dynamically accommodate servers o to determine ‘most reasonable’ PYTHIA o to learn mappings from problems to PYTHIA servers o to handle (dis)appearance of servers with time o to provide ‘learning’ and ‘stable’ modes of operation o efficient mechanisms to switch between these modes Department of Computer Sciences, Purdue University

Collaborative Environments for Scientific Computing 11th ICMCM & SC ‘97 PYTHIA Agents User Interface, Query Mechanism o ‘Memory of Agents’ o Two modes of operation Local Data, Remote Agent Info. o Learning Mode (LM) o Stable Mode (SM) Content: PYTHIA-TALK o “Cache Invalidation” Strategies o Time Based Communication: KQML, TCP/IP o Reactive o Time based Reactive o Proactive o Learning facilitated by notion of reasonableness Department of Computer Sciences, Purdue University

Collaborative Environments for Scientific Computing 11th ICMCM & SC ‘97 PYTHIA Agents (Contd.) - Mechanisms for Collaboration o An Acceptance System for Agents o Based on Epistemic Utility Theory o Quantitative Measure of Reasonableness based on Levi’s theory of knowledge o uses truth + utility o r(q) = p(q)U t (q) + p(not(q))U f (q) o o p(q) determined by PYTHIA o U t (q) = -U f (q) = f(N e ) where N e = number of exemplars f: squashing function o o A two-phase technique an unsupervised technique to generate exemplars o a supervised method to learn mappings from problems to agents o Department of Computer Sciences, Purdue University

Collaborative Environments for Scientific Computing 11th ICMCM & SC ‘97 Overall Strategy o Establish PYTHIA servers with specialized KBs o Delegate a central PYTHIA agent o For each PDE problem o Query each agent o Determine most reasonable agent o Form one exemplar from this data (& learn) o Use the mapping so learnt o to determine agents for new problems o When does mapping become invalid? o when abilities of agents change (Dynamic Scenario) Department of Computer Sciences, Purdue University

Collaborative Environments for Scientific Computing 11th ICMCM & SC ‘97 Experimental Results (Static Case) o Classes defined based on solution properties Solution-Singular (6), Solution-Analytic (35), Solution-Oscillatory (34), o Solution-Boundary-Layer (32), Boundary-Conditions-Mixed (74) These classes are not mutually exclusive!! o o Multiple Agent Scenarios 6,5,4 and 3 agents o o 167 PDE problems 111 problems - Larger Training Set o 56 problems - Smaller Training Set o o Comparison with other learning mechanisms Department of Computer Sciences, Purdue University