
Probabilistic Solutions To Ordinary Differential Equations As NonLinear Bayesian Filtering: A New Perspective
We formulate probabilistic numerical approximations to solutions of ordi...
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Convergence Rates of Gaussian ODE Filters
A recentlyintroduced class of probabilistic (uncertaintyaware) solvers...
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Probabilistic simulation of partial differential equations
Computer simulations of differential equations require a time discretiza...
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Bayesian Filtering for ODEs with Bounded Derivatives
Recently there has been increasing interest in probabilistic solvers for...
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Approximate Numerical Integration of the Chemical Master Equation for Stochastic Reaction Networks
Numerical solution of the chemical master equation for stochastic reacti...
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Velocity variations at Columbia Glacier captured by particle filtering of oblique timelapse images
We develop a probabilistic method for tracking glacier surface motion ba...
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A MultiScan Labeled Random Finite Set Model for Multiobject State Estimation
State space models in which the system state is a finite setcalled the...
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A Fourier State Space Model for Bayesian ODE Filters
Gaussian ODE filtering is a probabilistic numerical method to solve ordinary differential equations (ODEs). It computes a Bayesian posterior over the solution from evaluations of the vector field defining the ODE. Its most popular version, which employs an integrated Brownian motion prior, uses Taylor expansions of the mean to extrapolate forward and has the same convergence rates as classical numerical methods. As the solution of many important ODEs are periodic functions (oscillators), we raise the question whether Fourier expansions can also be brought to bear within the framework of Gaussian ODE filtering. To this end, we construct a Fourier state space model for ODEs and a `hybrid' model that combines a Taylor (Brownian motion) and Fourier state space model. We show by experiments how the hybrid model might become useful in cheaply predicting until the end of the time domain.
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