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Mathematical models are used extensively in studies of cardiac electrophysiology and arrhythmia mechanisms. Models can generate novel predictions, suggest experiments, and provide a quantitative understanding of underlying mechanisms. Limitations of present modeling approaches, however, include non-uniqueness of both parameters and the models themselves, and difficulties in accounting for experimental variability. We describe new approaches that can begin to address these limitations, and show how these can provide novel insight into mathematical models of cardiac myocytes.