# Scalable Variational Inference for Dynamical Systems

arXiv: https://arxiv.org/abs/1705.07079 · HTML: https://mlsanity.com/paper/1705.07079/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 May 2017.

## Built on by (most cited first, 12 of 12)

- [Reconstructing Nonlinear Dynamical Systems from Multi-Modal Time Series](https://mlsanity.com/paper/2111.02922/) (2021)
- [Fenrir: Physics-Enhanced Regression for Initial Value Problems](https://mlsanity.com/paper/2202.01287/) (2022)
- [A Deterministic Sampling Method via Maximum Mean Discrepancy Flow with Adaptive Kernel](https://mlsanity.com/paper/2111.10722/) (2021)
- [Learning to Suggest Breaks: Sustainable Optimization of Long-Term User Engagement](https://mlsanity.com/paper/2211.13585/) (2022)
- [Data-Adaptive Probabilistic Likelihood Approximation for Ordinary Differential Equations](https://mlsanity.com/paper/2306.05566/) (2023)
- [Variational Mixtures of ODEs for Inferring Cellular Gene Expression Dynamics](https://mlsanity.com/paper/2207.04166/) (2022)
- [Probabilistic Constrained Reinforcement Learning with Formal Interpretability](https://mlsanity.com/paper/2307.07084/) (2023)
- [Distributional Gradient Matching for Learning Uncertain Neural Dynamics Models](https://mlsanity.com/paper/2106.11609/) (2021)
- [An information field theory approach to Bayesian state and parameter estimation in dynamical systems](https://mlsanity.com/paper/2306.02150/) (2023)
- [Using Intermediate Forward Iterates for Intermediate Generator Optimization](https://mlsanity.com/paper/2302.02336/) (2023)
- [Uncertainty Informed Optimal Resource Allocation with Gaussian Process based Bayesian Inference](https://mlsanity.com/paper/2307.00032/) (2023)
- [Modeling Dynamic Mixtures of Time-Delay Systems from Streaming Time Series](https://mlsanity.com/paper/2605.26191/) (2026)

## Abstract (arXiv)

Gradient matching is a promising tool for learning parameters and state dynamics of ordinary differential equations. It is a grid free inference approach, which, for fully observable systems is at times competitive with numerical integration. However, for many real-world applications, only sparse observations are available or even unobserved variables are included in the model description. In these cases most gradient matching methods are difficult to apply or simply do not provide satisfactory results. That is why, despite the high computational cost, numerical integration is still the gold standard in many applications. Using an existing gradient matching approach, we propose a scalable variational inference framework which can infer states and parameters simultaneously, offers computational speedups, improved accuracy and works well even under model misspecifications in a partially observable system.