# A Bayesian Approach for Spatio-Temporal Data-Driven Dynamic Equation Discovery

arXiv: https://arxiv.org/abs/2209.02750 · HTML: https://mlsanity.com/paper/2209.02750/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Sep 2022.

## Built on by (most cited first, 3 of 3)

- [Data-Efficient Kernel Methods for Learning Differential Equations and Their Solution Operators: Algorithms and Error Analysis](https://mlsanity.com/paper/2503.01036/) (2025)
- [MDBench: Benchmarking Data-Driven Methods for Model Discovery](https://mlsanity.com/paper/2509.20529/) (2025)
- [A joint optimization approach to identifying sparse dynamics using least squares kernel collocation](https://mlsanity.com/paper/2511.18555/) (2025)

## Abstract (arXiv)

Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent real-world dynamics well. Since the true dynamics of these complex systems are generally unknown, learning the governing equations can improve our understanding of the mechanisms driving the systems. Here, we develop a Bayesian approach to data-driven discovery of non-linear spatio-temporal dynamic equations. Our approach can accommodate measurement noise and missing data, both of which are common in real-world data, and accounts for parameter uncertainty. The proposed framework is illustrated using three simulated systems with varying amounts of observational uncertainty and missing data and applied to a real-world system to infer the temporal evolution of the vorticity of the streamfunction.