Regression with Differential equations (ODEs / PDEs)


in the field of mathematical modelling of biological or physical processes, most of them cannot be described by simple (linear or nonlinear) relationships between predictor X and outcome Y, but only implicitly via differential equations, such as Ordinary differential equations (ODEs) or Partial differential equations (PDEs). Prominent examples for ODEs are predator-prey interactions, a typical example for a PDE is the diffusion equation.

However, I found only very few information regarding using ODEs or PDEs in regression. Is there a certain technical term for that, or is this field not very well developed? Are there corresponding packages available in R?