# Geometric path augmentation for inference of sparsely observed stochastic nonlinear systems

arXiv: https://arxiv.org/abs/2301.08102 · HTML: https://mlsanity.com/paper/2301.08102/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 109 references that are in the map.
- First posted on arXiv 19 Jan 2023.

## Builds on (most cited first, 16 of 16)

- [Latent Space Oddity: on the Curvature of Deep Generative Models](https://mlsanity.com/paper/1710.11379/) (2017)
- [TrajectoryNet: A Dynamic Optimal Transport Network for Modeling Cellular Dynamics](https://mlsanity.com/paper/2002.04461/) (2020)
- [GPflow: A Gaussian process library using TensorFlow](https://mlsanity.com/paper/1610.08733/) (2016)
- [Interacting particle solutions of Fokker-Planck equations through gradient-log-density estimation](https://mlsanity.com/paper/2006.00702/) (2020)
- [Sparse learning of stochastic dynamic equations](https://mlsanity.com/paper/1712.02432/) (2017)
- [geomstats: a Python Package for Riemannian Geometry in Machine Learning](https://mlsanity.com/paper/1805.08308/) (2018)
- [Simulating Diffusion Bridges with Score Matching](https://mlsanity.com/paper/2111.07243/) (2021)
- [Fast and Robust Shortest Paths on Manifolds Learned from Data](https://mlsanity.com/paper/1901.07229/) (2019)
- [Learning Stochastic Differential Equations With Gaussian Processes Without Gradient Matching](https://mlsanity.com/paper/1807.05748/) (2018)
- [Approximate Bayes learning of stochastic differential equations](https://mlsanity.com/paper/1702.05390/) (2017)
- [Deterministic particle flows for constraining stochastic nonlinear systems](https://mlsanity.com/paper/2112.05735/) (2021)
- [Bayesian Quadrature on Riemannian Data Manifolds](https://mlsanity.com/paper/2102.06645/) (2021)
- [Manifold Learning with Contracting Observers for Data-driven Time-series Analysis](https://mlsanity.com/paper/1604.04492/) (2016)
- [Deterministic particle flows for constraining SDEs](https://mlsanity.com/paper/2110.13020/) (2021)
- [Inferring network connectivity from event timing patterns](https://mlsanity.com/paper/1803.09974/) (2018)
- [Convergence of the Expectation-Maximization Algorithm Through Discrete-Time Lyapunov Stability Theory](https://mlsanity.com/paper/1810.02022/) (2018)

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

- [Geometric constraints improve inference of sparsely observed stochastic dynamics](https://mlsanity.com/paper/2304.00423/) (2023)

## Abstract (arXiv)

Stochastic evolution equations describing the dynamics of systems under the influence of both deterministic and stochastic forces are prevalent in all fields of science. Yet, identifying these systems from sparse-in-time observations remains still a challenging endeavour. Existing approaches focus either on the temporal structure of the observations by relying on conditional expectations, discarding thereby information ingrained in the geometry of the system's invariant density; or employ geometric approximations of the invariant density, which are nevertheless restricted to systems with conservative forces. Here we propose a method that reconciles these two paradigms. We introduce a new data-driven path augmentation scheme that takes the local observation geometry into account. By employing non-parametric inference on the augmented paths, we can efficiently identify the deterministic driving forces of the underlying system for systems observed at low sampling rates.