Daniel A. Messenger, April Tran, Vanja Dukic, David M. Bortz
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The weak form is a ubiquitous, well-studied, and widely-utilized mathematical
tool in modern computational and applied mathematics. In this work we provide a
survey of both the history and recent developments for several fields in which
the weak form can play a critical role. In particular, we highlight several
recent advances in weak form versions of equation learning, parameter
estimation, and coarse graining, which offer surprising noise robustness,
accuracy, and computational efficiency. We note that this manuscript is a companion piece to our October 2024 SIAM
News article of the same name. Here we provide more detailed explanations of
mathematical developments as well as a more complete list of references.
Lastly, we note that the software with which to reproduce the results in this
manuscript is also available on our group's GitHub website
https://github.com/MathBioCU .
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