Closing the Approximation Gap in Simulation-free Latent SDEs
stat.ML, cs.LG
Submitted: 2026-06-15
Updated: 2026-09-30
Code: https://github.com/coursekevin/arlatentsde
License: http://creativecommons.org/licenses/by/4.0/
The gist: Recovering dynamical systems from noisy observations is a recurring challenge across scientific domains, including neuroscience and physics.
Terminology
Abstract
Recovering dynamical systems from noisy observations is a recurring challenge across scientific domains, including neuroscience and physics. Latent stochastic differential equations (SDEs) address this by modeling the system as an unobserved state that evolves according to a learnable SDE and generates the observations. Variational inference (VI) provides a tractable objective for fitting latent SDEs. Traditional VI algorithms evaluate this objective by numerical simulation over a time discretization, trading fidelity for computational cost. A recent class of algorithms, simulation-free VI, sidesteps this tradeoff by parameterizing the posterior through its instantaneous marginals rather than its drift. In this work, we show that the efficiency of existing simulation-free VI algorithms comes at a price: their parameterizations restrict the approximate posterior to a subset of the SDEs available to simulation-based methods, degrading posterior inference and parameter learning. We propose Helmholtz-SDE, a simulation-free VI algorithm that closes this gap by optimizing over path laws compatible with a prescribed collection of marginals. Helmholtz-SDE recovers dynamics more faithfully than prior simulation-free methods, with the largest gains under high posterior uncertainty. It further matches the performance of simulation-based VI at a fraction of the runtime.
Sources
- Universal Differential Equations as a Common Modeling Language for Neuroscience
- Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit
- Project and Generate: Divergence-Free Neural Operators for Incompressible Flows
- HDNet: Physics-Inspired Neural Network for Flow Estimation based on Helmholtz Decomposition
- Probabilistic Inference and Learning with Stein's Method
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