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.
When the input function to the operator is unobserved and has a GP prior, the NVKM constitutes a powerful method for both single and multiple output regression, and can be viewed as a nonlinear and nonparametric latent force model.
Transient stability analysis (TSA) plays an important role in power system analysis to investigate the stability of power system.
Ordinary differential equations (ODEs), commonly used to characterize the dynamic systems, are difficult to propose in closed-form for many complicated scientific applications, even with the help of domain expert.
We introduced the least-squares ReLU neural network (LSNN) method for solving the linear advection-reaction problem with discontinuous solution and showed that the method outperforms mesh-based numerical methods in terms of the number of degrees of freedom.
Discovering dynamical models to describe underlying dynamical behavior is essential to draw decisive conclusions and engineering studies, e. g., optimizing a process.
In this study we consider the pricing of energy derivatives when the evolution of spot prices is modeled with a normal tempered stable driven Ornstein-Uhlenbeck process.
However both DEM and classical PINN formulations struggle to resolve fine features of the stress and displacement fields, for example concentration features in solid mechanics applications.
We use this to develop BoXHED 2. 0, a quantum leap over the tree-boosted hazard package BoXHED 1. 0.
For this special case, both generic approaches based on learning the vector field of the latent ODE and specialized approaches based on learning the Hamiltonian that generates the vector field exist.
Viewing optimization methods as numerical integrators for ordinary differential equations (ODEs) provides a thought-provoking modern framework for studying accelerated first-order optimizers.