Towards stable real-world equation discovery with assessing
  differentiating quality influence
Mikhail Masliaev Ilya Markov Alexander Hvatov
This paper explores the critical role of differentiation approaches for
data-driven differential equation discovery. Accurate derivatives of the input
data are essential for reliable algorithmic operation, particularly in
real-world scenarios where measurement quality is inevitably compromised. We
propose alternatives to the commonly used finite differences-based method,
notorious for its instability in the presence of noise, which can exacerbate
random errors in the data. Our analysis covers four distinct methods:
Savitzky-Golay filtering, spectral differentiation, smoothing based on
artificial neural networks, and the regularization of derivative variation. We
evaluate these methods in terms of applicability to problems, similar to the
real ones, and their ability to ensure the convergence of equation discovery
algorithms, providing valuable insights for robust modeling of real-world
processes.