# ODIN: ODE-Informed Regression for Parameter and State Inference in Time-Continuous Dynamical Systems

## TL;DR

This paper introduces ODIN, a Gaussian process-based method for efficient parameter and state inference in time-continuous dynamical systems, excelling in data-scarce scenarios and aiding model selection.

## Contribution

It presents a novel ODE-informed regression approach that improves accuracy and efficiency over existing methods for parameter inference in dynamical systems.

## Key findings

- Outperforms state-of-the-art in accuracy
- Reduces computational cost
- Shows promise in model selection

## Abstract

Parameter inference in ordinary differential equations is an important problem in many applied sciences and in engineering, especially in a data-scarce setting. In this work, we introduce a novel generative modeling approach based on constrained Gaussian processes and leverage it to build a computationally and data efficient algorithm for state and parameter inference. In an extensive set of experiments, our approach outperforms the current state of the art for parameter inference both in terms of accuracy and computational cost. It also shows promising results for the much more challenging problem of model selection.