# Differential Algebra for Model Comparison

arXiv: https://arxiv.org/abs/1603.09730 · HTML: https://mlsanity.com/paper/1603.09730/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Mar 2016.

## Built on by (most cited first, 2 of 2)

- [Gaussian Process Priors for Systems of Linear Partial Differential Equations with Constant Coefficients](https://mlsanity.com/paper/2212.14319/) (2022)
- [Gaussian Process Priors for Boundary Value Problems of Linear Partial Differential Equations](https://mlsanity.com/paper/2411.16663/) (2024)

## Abstract (arXiv)

We present a method for rejecting competing models from noisy time-course data that does not rely on parameter inference. First we characterize ordinary differential equation models in only measurable variables using differential algebra elimination. Next we extract additional information from the given data using Gaussian Process Regression (GPR) and then transform the differential invariants. We develop a test using linear algebra and statistics to reject transformed models with the given data in a parameter-free manner. This algorithm exploits the information about transients that is encoded in the model's structure. We demonstrate the power of this approach by discriminating between different models from mathematical biology.