Diffusion Tempering Improves Parameter Estimation with Probabilistic Integrators for Ordinary Differential Equations
This work addresses the problem of local minima and sensitivity in parameter estimation for ODEs in scientific modeling, offering an incremental improvement for researchers in computational science and systems biology.
The authors tackled the challenge of parameter estimation in ordinary differential equations (ODEs) by proposing diffusion tempering, a regularization technique for probabilistic numerical methods, which improved convergence in gradient-based optimization and reliably estimated parameters for a Hodgkin-Huxley model with a practically relevant number of parameters.
Ordinary differential equations (ODEs) are widely used to describe dynamical systems in science, but identifying parameters that explain experimental measurements is challenging. In particular, although ODEs are differentiable and would allow for gradient-based parameter optimization, the nonlinear dynamics of ODEs often lead to many local minima and extreme sensitivity to initial conditions. We therefore propose diffusion tempering, a novel regularization technique for probabilistic numerical methods which improves convergence of gradient-based parameter optimization in ODEs. By iteratively reducing a noise parameter of the probabilistic integrator, the proposed method converges more reliably to the true parameters. We demonstrate that our method is effective for dynamical systems of different complexity and show that it obtains reliable parameter estimates for a Hodgkin-Huxley model with a practically relevant number of parameters.