Numerical Integration
53 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.
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Latest papers
Combining Normalizing Flows and Quasi-Monte Carlo
charlyandral/qmc_norm_flows
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Recent advances in machine learning have led to the development of new methods for enhancing Monte Carlo methods such as Markov chain Monte Carlo (MCMC) and importance sampling (IS).
Stability-Informed Initialization of Neural Ordinary Differential Equations
This paper addresses the training of Neural Ordinary Differential Equations (neural ODEs), and in particular explores the interplay between numerical integration techniques, stability regions, step size, and initialization techniques.
Efficient Numerical Integration in Reproducing Kernel Hilbert Spaces via Leverage Scores Sampling
In this work we consider the problem of numerical integration, i. e., approximating integrals with respect to a target probability measure using only pointwise evaluations of the integrand.
A hybrid approach for solving the gravitational N-body problem with Artificial Neural Networks
veronicasaz/planetarysystem_hnn
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To increase the robustness of a method that uses neural networks, we propose a hybrid integrator that evaluates the prediction of the network and replaces it with the numerical solution if considered inaccurate.
Stochastic Latent Transformer: Efficient Modelling of Stochastically Forced Zonal Jets
ira-shokar/stochastic_latent_transformer
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We present a novel probabilistic deep learning approach, the 'Stochastic Latent Transformer' (SLT), designed for the efficient reduced-order modelling of stochastic partial differential equations.
A stochastic optimization approach to train non-linear neural networks with a higher-order variation regularization
While the $(k, q)$-VR terms applied to general parametric models are computationally intractable due to the integration, this study provides a stochastic optimization algorithm, that can efficiently train general models with the $(k, q)$-VR without conducting explicit numerical integration.
Minimizing robust density power-based divergences for general parametric density models
Density power divergence (DPD) is designed to robustly estimate the underlying distribution of observations, in the presence of outliers.
Designing Stable Neural Networks using Convex Analysis and ODEs
fsherry/non-expansive-odes
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Motivated by classical work on the numerical integration of ordinary differential equations we present a ResNet-styled neural network architecture that encodes non-expansive (1-Lipschitz) operators, as long as the spectral norms of the weights are appropriately constrained.
Learning Survival Distribution with Implicit Survival Function
bcai0797/isf
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Survival analysis aims at modeling the relationship between covariates and event occurrence with some untracked (censored) samples.
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.
