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Data-driven Evolution Equation Reconstruction for Parameter-Dependent Nonlinear Dynamical Systems.

David W Sroczynski1, Or Yair2, Ronen Talmon2

  • 1Department of Chemical and Biological Engineering, Princeton University, Princeton, NJ 08540.

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|April 30, 2019
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Summary
This summary is machine-generated.

This study presents a data-driven method to predict chemical reaction dynamics without prior physical knowledge. It constructs system realizations from observational data, enabling predictions even for complex, unexplained variables.

Keywords:
diffusion mapskineticsmachine learningmodel developmentreaction mechanisms

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Area of Science:

  • Chemical reaction dynamics
  • Data-driven modeling
  • Systems theory

Background:

  • Traditional chemical reaction studies often rely on predefined mechanistic equations.
  • Obtaining closed-form equations can be challenging when the underlying physical mechanism is unknown.
  • Experimental data, however, can offer insights even without complete physical interpretation.

Purpose of the Study:

  • To develop a data-driven approach for constructing system realizations from observational data.
  • To enable prediction of chemical reaction dynamics without requiring prior physical or chemical knowledge.
  • To build intrinsic 'information geometries' from observed data for robust system representation.

Main Methods:

  • Utilized data-driven methods to analyze experimental observations of chemical reaction dynamics.
  • Constructed minimal and robust realizations of the system directly from the data.
  • Derived evolution equations for a data-driven realization of the original system.

Main Results:

  • Successfully generated predictive evolution equations from observational data.
  • Demonstrated the approach on systems including the cusp singularity and nonisothermal CSTR.
  • Showed predictive capability even when observable quantities lacked simple physical explanations.

Conclusions:

  • Data-driven approaches can circumvent the need for complete physical understanding in modeling chemical dynamics.
  • This method allows for prediction by interrogating agnostically organized observation databases.
  • The approach shows promise for analyzing complex systems where mechanistic insights are limited.