Diffusion Tempering Improves Parameter Estimation with Probabilistic Integrators for Ordinary Differential Equations

arXiv:2402.12231v1 Announce Type: new
Abstract: 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 …

abstract arxiv cs.lg differentiable differential diffusion dynamics experimental gradient optimization ordinary parameters science systems type