Closing the Approximation Gap in Simulation-free Latent SDEs
2026-06-15 • Machine Learning
Machine Learning
AI summaryⓘ
The authors address the problem of learning hidden dynamic systems from noisy data using mathematical models called stochastic differential equations (SDEs). They explain that current methods either use computationally expensive simulations or faster approaches that simplify the problem but lose accuracy. Their new method, Helmholtz-SDE, improves on the faster simulation-free techniques by allowing a richer set of possible solutions, leading to better recovery of the system's behavior. This method performs similarly to simulation-based methods but runs much faster, especially when the data is uncertain.
stochastic differential equationslatent variable modelsvariational inferencesimulation-free algorithmsposterior distributionpath lawsdynamical systemsparameter learningneuroscience modelingnumerical simulation
Authors
Henry D. Smith, Brian L. Trippe, Scott W. Linderman
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.