2025-07-24 –, Main Room 3
Parameter estimation for ODEs is a fundamental problem in modeling and dynamics. The algebraic approach in Bassik et al. does not suffer from difficulties inherent in nonlinear optimization (the need for good initial guess, getting stuck in local minima, etc), but degrades severely in the presence of measurement noise. We combined the algebraic approach with Gaussian Process Regression to increase robustness to noise. In this talk, we will demo a Julia implementation of this new algorithm.
A typical approach to estimating parameters from experiments uses nonlinear optimization to search for parameters which minimize error against observed data. This inherits various difficulties from nonlinear optimization: the need for good initial guesses, getting stuck in local minima, and only finding a single solution.
An algorithm in Bassik et al. [1] reduces the task of parameter estimation to solving an algebraic system by using baryrational interpolation to estimate derivatives. This method shows excellent performance on noise-free or synthetic data, but due to the reliance on interpolation degrades severely with even minimal measurement noise.
To overcome this limitation, we replaced the baryrational interpolation with Gaussian Process Regression (GPR) and automatically learn the noise hyperparameter from the data. Tentative benchmarks show that this simple replacement significantly improves robustness to measurement noise in observed data.
We have implemented new algorithms in Julia package ParameterEstimation.jl. We are currently developing a set of examples and benchmarks to demonstrate its applicability to realistic data with noise.
During the presentation, we will demonstrate the use of the new algorithm using a simple example. If time permits, we plan to include a short demo to demonstrate the new capabilities of the packages.
Parameter estimation is an important step of model design, so we expect that the talk would be of interest to practitioners in modeling and control.
The github pages of the relevant packages:
https://github.com/iliailmer/ParameterEstimation.jl
https://github.com/orebas/ODEParameterEstimation (testing version)
This work is a joint result by Oren Bassik, Alexander Demin, and Alexey Ovchinnikov.
[1] Ovchinnikov A., Bassik O., Berman Y., Go S., Hong H., Ilmer I., Rackauckas C., Soto P., and Yap C. (2023). Robust Parameter Estimation for Rational Ordinary Differential Equations, preprint is available at https://arxiv.org/abs/2303.02159.
