# Safe Active Learning for Gaussian Differential Equations

arXiv: https://arxiv.org/abs/2412.09053 · HTML: https://mlsanity.com/paper/2412.09053/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 47 references that are in the map.
- First posted on arXiv 12 Dec 2024.

## Builds on (most cited first, 5 of 5)

- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Bayesian Neural Ordinary Differential Equations](https://mlsanity.com/paper/2012.07244/) (2020)
- [Active Learning of Linear Embeddings for Gaussian Processes](https://mlsanity.com/paper/1310.6740/) (2013)
- [Uncertainty and Structure in Neural Ordinary Differential Equations](https://mlsanity.com/paper/2305.13290/) (2023)
- [Optimal Experimental Design for Universal Differential Equations](https://mlsanity.com/paper/2408.07143/) (2024)

## Built on by (most cited first, 1 of 1)

- [Causal Structure Learning for Dynamical Systems with Theoretical Score Analysis](https://mlsanity.com/paper/2512.14361/) (2025)

## Abstract (arXiv)

Gaussian Process differential equations (GPODE) have recently gained momentum due to their ability to capture dynamics behavior of systems and also represent uncertainty in predictions. Prior work has described the process of training the hyperparameters and, thereby, calibrating GPODE to data. How to design efficient algorithms to collect data for training GPODE models is still an open field of research. Nevertheless high-quality training data is key for model performance. Furthermore, data collection leads to time-cost and financial-cost and might in some areas even be safety critical to the system under test. Therefore, algorithms for safe and efficient data collection are central for building high quality GPODE models. Our novel Safe Active Learning (SAL) for GPODE algorithm addresses this challenge by suggesting a mechanism to propose efficient and non-safety-critical data to collect. SAL GPODE does so by sequentially suggesting new data, measuring it and updating the GPODE model with the new data. In this way, subsequent data points are iteratively suggested. The core of our SAL GPODE algorithm is a constrained optimization problem maximizing information of new data for GPODE model training constrained by the safety of the underlying system. We demonstrate our novel SAL GPODE's superiority compared to a standard, non-active way of measuring new data on two relevant examples.