Science Advances

Supplementary Materials

This PDF file includes:

  • Introduction
  • PDE-FIND
  • Examples
  • Limitations
  • fig. S1. Steps in the PDE functional identification of nonlinear dynamics (PDEFIND)
    algorithm, applied to infer the Navier-Stokes equations from data.
  • fig. S2. The numerical solution to the KdV equation plotted in space-time.
  • fig. S3. The numerical solution to the Burgers’ equation plotted in space-time.
  • fig. S4. The magnitude of the numerical solution to the Schrödinger’s equation
    plotted in space-time.
  • fig. S5. The magnitude of the numerical solution to the nonlinear Schrödinger’s
    equation plotted in space-time.
  • fig. S6. The numerical solution to the Kuramoto-Sivashinsky equation plotted in
    space-time.
  • fig. S7. The numerical solution to the reaction-diffusion equation plotted in spacetime.
  • fig. S8. A single snapshot of the vorticity field is illustrated for the fluid flow past
    a cylinder.
  • fig. S9. A single stochastic realization of Brownian motion.
  • fig. S10. Five empirical distributions, illustrating the statistical spread of a
    particle’s expected location over time, are presented.
  • fig. S11. Five empirical distributions, illustrating the statistical spread of a
    particle’s expected location over time, are presented.
  • fig. S12. The numerical solution to the misidentified Kuramoto-Sivashinsky
    equation.
  • fig. S13. The numerical solution to the misidentified nonlinear Schrödinger
    equation.
  • fig. S14. Results of PDE-FIND applied to Burgers’ equation for varying levels of
    noise.
  • table S1. Summary of regression results for a wide range of canonical models of
    mathematical physics.
  • table S2. Summary of PDE-FIND for identifying the KdV equation.
  • table S3. Summary of PDE-FIND for identifying Burgers’ equation.
  • table S4. Summary of PDE-FIND for identifying the Schrödinger equation.
  • table S5. Summary of PDE-FIND for identifying the nonlinear Schrödinger
    equation.
  • table S6. Summary of PDE-FIND for identifying the Kuramoto-Sivashinsky
    equation.
  • table S7. Summary of PDE-FIND for identifying reaction-diffusion equation.
  • table S8. Summary of PDE-FIND for identifying the Navier-Stokes equation.
  • table S9. Accuracy of PDE-FIND on Burgers’ equation with various grid sizes.
  • References (23–50)

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