LAPSE:2021.0802
Postprint
LAPSE:2021.0802
A 2-stage Approach to Parameter Estimation of Differential Equations using Neural ODEs
William Bradley, Fani Boukouvala
November 7, 2021
Modeling physio-chemical relationships using dynamic data is a common task in fields throughout science and engineering. A common step in developing generalizable, mechanistic models is to fit unmeasured parameters to measured data. However, fitting differential equation-based models can be computation intensive and uncertain due to the presence of nonlinearity, noise, and sparsity in the data, which in turn causes convergence to local minima and divergence issues. This work proposes a merger of Machine Learning (ML) and mechanistic approaches by employing ML models as a means to fit nonlinear mechanistic ODEs. Using a two-stage indirect approach, Neural ODEs are used to estimate state derivatives, which are then used to estimate the parameters of a more interpretable mechanistic ODE model. In addition to its computational efficiency, the proposed method demonstrates the ability of Neural ODEs to better estimate derivative information than interpolating methods based on algebraic data-driven models. Most notably, the proposed method is shown to yield accurate predictions even when little information is known about the parameters of the ODE equations. The proposed parameter estimation approach is believed to be most advantageous when the ODE to be fit is strongly nonlinear with respect its unknown parameters.
Keywords
Neural ODEs, Neural-Networks, Nonlinear programming, parameter estimation
Suggested Citation
Bradley W, Boukouvala F. A 2-stage Approach to Parameter Estimation of Differential Equations using Neural ODEs. (2021). LAPSE:2021.0802
Author Affiliations
Bradley W:
Boukouvala F: Georgia Institute of Technology
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Journal Name
Industrial and Engineering Chemistry Research, Accepted for publication
Year
2021
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Nov 7, 2021
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fani.boukouvala