16 papers with code • 0 benchmarks • 0 datasets
Numerical integration is the task to calculate the numerical value of a definite integral or the numerical solution of differential equations.
To this end, adaptive schemes have been developed that rely on error estimators based on Taylor series expansions.
For training, we instantiate the computational graph corresponding to the derivative of the network.
Gulisashvili et al. [Quant.
Our multiscale hierarchical time-stepping scheme provides important advantages over current time-stepping algorithms, including (i) circumventing numerical stiffness due to disparate time-scales, (ii) improved accuracy in comparison with leading neural-network architectures, (iii) efficiency in long-time simulation/forecasting due to explicit training of slow time-scale dynamics, and (iv) a flexible framework that is parallelizable and may be integrated with standard numerical time-stepping algorithms.
The advantages and disadvantages of this new methodology are highlighted on a set of benchmark tests including the Genz functions, and on a Bayesian survey design problem.
We introduce the code i-flow, a python package that performs high-dimensional numerical integration utilizing normalizing flows.
In the absence of DPP machinery to derive an efficient sampler and analyze their estimator, the idea of Monte Carlo integration with DPPs was stored in the cellar of numerical integration.
We propose a scalable framework for inference in an inhomogeneous Poisson process modeled by a continuous sigmoidal Cox process that assumes the corresponding intensity function is given by a Gaussian process (GP) prior transformed with a scaled logistic sigmoid function.
Stochastic differential equations are an important modeling class in many disciplines.