Model Discovery for PDEs

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COURSE WEBPAGE: Inferring Structure of Complex Systems

This lecture discusses how to discovery dynamical models from time series measurements of spatio-temporal (partial differential equations -- PDEs) dynamical systems. The algorithmic procedure formulates the problem in terms of Ax=b where sparsity is promoted in the solution. The method is demonstrated on Burgers equation.
  1. Nathan Kutz
  2. Nathan Kutz
  3. Kutz
  4. model discovery
  5. sparse regression
  6. SINDy
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Комментарии
Автор

Thank you for this lecture. How would you deal with (unknown but smooth) spatial inhomogeneities? Can those be found through optimization or? I have some real world data suffers from this.

NeuralEnginr
Автор

The way the reshaping been done, it seems the columns are stacked spatially and not temporally, i.e vector looks like this [all temporal solutions at x1; all temporal solutions at x2; temporal solutions at xm] instead of [all spatial solutions at t2; all spatial solutions at t3; all spatial solutions at tn-1]. Anyone can please clarify what difference will the two different type of reshaping make and which one is followed in lecture? from the code, it looks the first type but the way professor explains; it seems like second type.

VIVEKPANDEYIITB