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Bayesian Numerical Integration with Neural Networks
Bayesian probabilistic numerical methods for numerical integration offer significant advantages over their non-Bayesian counterparts: they can encode prior information about the integrand, and can quantify uncertainty over estimates of an integral.
Uncertainty and Structure in Neural Ordinary Differential Equations
As a first contribution, we show that basic and lightweight Bayesian deep learning techniques like the Laplace approximation can be applied to neural ODEs to yield structured and meaningful uncertainty quantification.
Combining Slow and Fast: Complementary Filtering for Dynamics Learning
This filtering technique combines two signals by applying a high-pass filter to one signal, and low-pass filtering the other.
Structure-preserving Gaussian Process Dynamics
On the other hand, classical numerical integrators are specifically designed to preserve these crucial properties through time.
ResNet After All: Neural ODEs and Their Numerical Solution
If the trained model is supposed to be a flow generated from an ODE, it should be possible to choose another numerical solver with equal or smaller numerical error without loss of performance.
When are Neural ODE Solutions Proper ODEs?
If the trained model is supposed to be a flow generated from an ODE, it should be possible to choose another numerical solver with equal or smaller numerical error without loss of performance.
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.
