# Parameter and Uncertainty Estimation for Dynamical Systems Using Surrogate Stochastic Processes

arXiv: https://arxiv.org/abs/1802.00852 · HTML: https://mlsanity.com/paper/1802.00852/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Feb 2018.

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

- [Estimating the Distribution of Parameters in Differential Equations with Repeated Cross-Sectional Data](https://mlsanity.com/paper/2404.14873/) (2024)
- [Learning stochasticity: a nonparametric framework for intrinsic noise estimation](https://mlsanity.com/paper/2511.13701/) (2025)

## Abstract (arXiv)

Inference on unknown quantities in dynamical systems via observational data is essential for providing meaningful insight, furnishing accurate predictions, enabling robust control, and establishing appropriate designs for future experiments. Merging mathematical theory with empirical measurements in a statistically coherent way is critical and challenges abound, e.g.,: ill-posedness of the parameter estimation problem, proper regularization and incorporation of prior knowledge, and computational limitations on full uncertainty qualification. To address these issues, we propose a new method for learning parameterized dynamical systems from data. In many ways, our proposal turns the canonical framework on its head. We first fit a surrogate stochastic process to observational data, enforcing prior knowledge (e.g., smoothness), and coping with challenging data features like heteroskedasticity, heavy tails and censoring. Then, samples of the stochastic process are used as "surrogate data" and point estimates are computed via ordinary point estimation methods in a modular fashion. An attractive feature of this approach is that it is fully Bayesian and simultaneously parallelizable. We demonstrate the advantages of our new approach on a predator prey simulation study and on a real world application involving within-host influenza virus infection data paired with a viral kinetic model.