Everything about ODE filter
Probabilistic numerical ODE solver
ODE filters are a class of probabilistic numerical methods for solving ordinary differential equations (ODEs) that frame the problem of finding a solution to an initial value problem as a Bayesian inference task. Solutions are modeled as probability distributions that also account for the discretization error introduced through the numerical approximation. This probabilistic treatment provides an computation-aware alternative to classical numerical ODE-solvers, which typically only provide point-wise error bounds. It further enables sampling of joint trajectories from the posterior, as well as quantifying uncertainty about the underlying ODE itself. ODE filters offer a flexible framework for incorporating additional information, such as measurements or conservation laws. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: ODE filterA 5-minute orientation
- Skim a recent paper: A Review on Kalman Filter ModelsInfluential work since 2022
- Pick up a classic book: The UNIX operating systemThe most-reprinted book on the subject
- Read the landmark paper: Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space ModelsCited 2,373 times
- Go sideways: Markov kernelA closely related topic
- Go sideways: Radon transformA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
Monte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models
Empirical Mode Decomposition as a Filter Bank
An evaluation of the two-dimensional Gabor filter model of simple receptive fields in cat striate cortex
An ODE-Based Trust Region Filter Algorithm for Unconstrained Optimization
MIXED ODE-MC MODEL FOR SOOT CAKE FORMATION IN A SQUARE CHANNEL WALL-FLOW FILTER
AN IMPROVED ODE-TYPE FILTER METHOD FOR NONLINEAR COMPLEMENTARITY PROBLEM
🆕 Influential since 2022
A Review on Kalman Filter Models
Secure Filter Design of Fuzzy Switched CPSs With Mismatched Modes and Application: A Multidomain Event-Triggered Strategy
A hybrid deep learning model based on parallel architecture TCN-LSTM with Savitzky-Golay filter for wind power prediction
Novel Neural Network Fractional-Order Sliding-Mode Control With Application to Active Power Filter
Real-Time Nonlinear Model Predictive Control of Active Power Filter Using Self-Feedback Recurrent Fuzzy Neural Network Estimator
📚 Books worth reading
The UNIX operating systemChristian, Kaare, Kaare Christian · 1983
The Neurophysiological Bases of Auditory PerceptionEnrique A. Lopez-Poveda, Alan R. Palmer · 2010
All wound upStephanie Pearl-McPhee · 2011
Practical Parameter Estimation for Engineers & ScientistsPhil B Brubaker · 2013
Social networking and the webMarvin V. Zelkowitz · 2009
Stochastic approximation and its applicationsHanfu Chen · 2002
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
- Markov kernel In probability theory, a Markov kernel (also known as a stochastic kernel or probability kernel) is a map that in the general theory of Markov processes…
- Radon transform In mathematics, the Radon transform is the integral transform which takes a function f defined on the plane to a function Rf defined on the (two-dimensional)…
- Momentum map In mathematics, specifically in symplectic geometry, the momentum map (or, by false etymology, moment map) is a tool associated with a Hamiltonian action…
- Hamiltonian vector field In mathematics and physics, a Hamiltonian vector field on a symplectic manifold is a vector field defined for any energy function or Hamiltonian. Named…
- Shilov boundary In functional analysis, the Shilov boundary is the smallest closed subset of the structure space of a commutative Banach algebra where an analog of the…
- Kähler manifold In mathematics and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a…
- Kernel embedding of distributions In machine learning, the kernel embedding of distributions (also called the kernel mean or mean map) comprises a class of nonparametric methods in which…
- Kosmann lift In differential geometry, the Kosmann lift, named after Yvette Kosmann-Schwarzbach, of a vector field X {\displaystyle X\,} on a Riemannian manifold (…