Intelligence in scientific computing
Communications of the ACM
The structure-mapping engine: algorithm and examples
Artificial Intelligence
Compositional modeling: finding the right model for the job
Artificial Intelligence - Special issue: Qualitative reasoning about physical systems II
Artificial Intelligence - Special issue: Qualitative reasoning about physical systems II
Towards the effective parallel computation of matrix pseudospectra
ICS '01 Proceedings of the 15th international conference on Supercomputing
Influence-based model decomposition for reasoning about spatially distributed physical systems
Artificial Intelligence
STA: Spatio-Temporal Aggregation with Applications to Analysis of Diffusion-Reaction Phenomena
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Spatial aggregation: theory and applications
Journal of Artificial Intelligence Research
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Spatial aggregation: language and applications
AAAI'96 Proceedings of the thirteenth national conference on Artificial intelligence - Volume 1
Automated mathematical modeling from experimental data: anapplication to material science
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
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Qualitative assessment of scientific computations is an emerging application area that applies a data-driven approach to characterize, at a high level, phenomena including conditioning of matrices, sensitivity to various types of error propagation, and algorithmic convergence behavior. This paper develops a spatial aggregation approach that formalizes such analysis in terms of model selection utilizing spatial structures extracted from matrix perturbation datasets. We focus in particular on the characterization of matrix eigenstructure, both analyzing sensitivity of computations with spectral portraits and determining eigenvalue multiplicity with Jordan portraits. Our approach employs spatial reasoning to overcome noise and sparsity by detecting mutually reinforcing interpretations, and to guide subsequent data sampling. It enables quantitative evaluation of properties of a scientific computation in terms of confidence in a model, explainable in terms of the sampled data and domain knowledge about the underlying mathematical structure. Not only is our methodology more rigorous than the common approach of visual inspection, but it also is often substantially more efficient, due to well-defined stopping criteria. Results show that the mechanism efficiently samples perturbation space and successfully uncovers high level properties of matrices.