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Found 9 papers, 4 papers with code
Approximate Bayesian Neural Operators: Uncertainty Quantification for Parametric PDEs
Neural operators are a type of deep architecture that learns to solve (i. e. learns the nonlinear solution operator of) partial differential equations (PDEs).
ProbNum: Probabilistic Numerics in Python
Probabilistic numerical methods (PNMs) solve numerical problems via probabilistic inference.
Linear-Time Probabilistic Solution of Boundary Value Problems
We propose a fast algorithm for the probabilistic solution of boundary value problems (BVPs), which are ordinary differential equations subject to boundary conditions.
Probabilistic Numerical Method of Lines for Time-Dependent Partial Differential Equations
Thereby, we extend the toolbox of probabilistic programs for differential equation simulation to PDEs.
Probabilistic ODE Solutions in Millions of Dimensions
Probabilistic solvers for ordinary differential equations (ODEs) have emerged as an efficient framework for uncertainty quantification and inference on dynamical systems.
Linear-Time Probabilistic Solutions of Boundary Value Problems
We propose a fast algorithm for the probabilistic solution of boundary value problems (BVPs), which are ordinary differential equations subject to boundary conditions.
A Probabilistic State Space Model for Joint Inference from Differential Equations and Data
Mechanistic models with differential equations are a key component of scientific applications of machine learning.
Stable Implementation of Probabilistic ODE Solvers
Probabilistic solvers for ordinary differential equations (ODEs) provide efficient quantification of numerical uncertainty associated with simulation of dynamical systems.
Differentiable Likelihoods for Fast Inversion of 'Likelihood-Free' Dynamical Systems
To address this shortcoming, we employ Gaussian ODE filtering (a probabilistic numerical method for ODEs) to construct a local Gaussian approximation to the likelihood.
