This work addresses two central challenges in data-driven discovery of governing equations: high signal noise, and assessment of a discovery method given non-unique solutions. First, the toolkit offers several independently deployable modules that mitigate high noise, especially in the context of a sparse solution assumption (e.g, SINDy). It thus offers solutions to the widespread and difficult problem of noisy data. Second, the toolkit has modules that leverage linear dependence of functionals’ time-series to enable principled transformations of a discovered solution to other equivalent solutions. This allows more accurate assessment of a discovery method’s effectiveness, by showing whether an apparently incorrect discovered solution is in fact close to the ``true” solution. It also generates a range of possible equivalent solutions, giving domain experts broader insight into possible sets of governing equations beyond a single discovered solution.

The paper can be found online at toolkitForHighNoise.

A local copy is here.