Monte Carlo and quasi-Monte Carlo methods

By Russel E. Caflisch. 1998

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Citations in the corpus

Measuring Sample Quality with Stein's Method (2015, background): “Unif(0, 1) sample, a deterministic Sobol sequence [26], and a deterministic kernel herding sequence [27] defined by the norm khkH = R”
Maximum Efficiency Beam Synthesis of Radiating Planar Arrays for Wireless Power Transmission (2013, methodology): “, based on Monte-Carlo techniques [25]) can be used to speed-up the process.”
Learning variable impedance control (2011, methodology): “The important conclusion is that it is possible to evaluate Equation (11) using Monte Carlo sampling (Caflisch 1998) of the control system, i.e. our optimal control problem can be solved as an estimation problem.”
Deep Autoencoder based Energy Method for the Bending, Vibration, and Buckling Analysis of Kirchhoff Plates (2020, methodology): “This issue can be avoided by random sampling and therefore, the Monte Carlo integration method [49] is employed in DAEM for the integral calculation.”
Deep Parametric Continuous Convolutional Neural Networks (2018, methodology): “Motivated by monte-carlo integration [5] we derive our continuous convolution operator.”
Numerical Methods and Smolyak Quadrature for Nonlinear Stochastic Partial Differential Equations (2003, unknown): “( 1) yields the stochastic PDE −∇· (κ(x,u,ω)∇u(x,ω)) = f (x,ω), x∈ R, (5) ∂ ∂n (κ(x,u,ω))∇u(x,ω) = fN(x,ω), x∈ ΓN, ΓN ∪ ΓD = ∂R (6) u(x,ω) = fD(x,ω), x∈ ΓD, (7) for Γ-almost allω ∈Ω.”
Reduced basis methods for partial differential equations with stochastic influences (2013, methodology): “, using the quasi–Monte Carlo method, the random selection of the samples is replaced by a deterministic sequence of properly chosen points, so-called quasi-random or low-discrepancy sequences [15].”
An extended stochastic finite element method for solving stochastic partial differential equations on random domains (2008, methodology): “A natural way to solve a stochastic problem defined on a random domain consists in using a classical stochastic finite element method with remeshings, such as Monte-Carlo simulations [9,10], response surface method, projection [11] or regression [12] methods.”