Topological techniques for characterization of patterns in differential equations
Complex data can be challenging to untangle. Recent advances in computing capabilities has allowed for practical application of tools from algebraic topology, which have proven to be useful for qualitative and quantitative analysis of complex data. The primary tool in computational topology is persistent homology. It provides a valuable lens through which to study and characterize complex data arising as orbits of dynamical systems and solutions of PDEs. In some cases, this includes leveraging tools from machine learning to classify data based on topological characteristics. We see a unique ...
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