Accurate Simulation Algorithms Research Articles

Functional central limit theorems for rough volatility

AbstractThe non-Markovian nature of rough volatility makes Monte Carlo methods challenging, and it is in fact a major challenge to develop fast and accurate simulation algorithms. We provide an efficient one for stochastic Volterra processes, based on an extension of Donsker’s approximation of Brownian motion to the fractional Brownian case with arbitrary Hurst exponent $H \in (0,1)$ H ∈ ( 0 , 1 ) . Some of the most relevant consequences of this ‘rough Donsker (rDonsker) theorem’ are functional weak convergence results in Skorokhod space for discrete approximations of a large class of rough stochastic volatility models. This justifies the validity of simple and easy-to-implement Monte Carlo methods, for which we provide detailed numerical recipes. We test these against the current benchmark hybrid scheme and find remarkable agreement (for a large range of values of $H$ H ). Our rDonsker theorem further provides a weak convergence proof for the hybrid scheme itself and allows constructing binomial trees for rough volatility models, the first available scheme (in the rough volatility context) for early exercise options such as American or Bermudan options.

Cytomulate: accurate and efficient simulation of CyTOF data

Recently, many analysis tools have been devised to offer insights into data generated via cytometry by time-of-flight (CyTOF). However, objective evaluations of these methods remain absent as most evaluations are conducted against real data where the ground truth is generally unknown. In this paper, we develop Cytomulate, a reproducible and accurate simulation algorithm of CyTOF data, which could serve as a foundation for future method development and evaluation. We demonstrate that Cytomulate can capture various characteristics of CyTOF data and is superior in learning overall data distributions than single-cell RNA-seq-oriented methods such as scDesign2, Splatter, and generative models like LAMBDA.

Moth-Flame Algorithm for Accurate Simulation of a Non-Uniform Electric Field in the Presence of Dielectric Barrier

In this paper, a proposed moth-flame optimization (MFO) technique has been investigated for obtaining an accurate simulation of the non-uniform electric field represented by a needle-to-plane gap configuration. The needle electrode is connected to the high-voltage (HV) terminal, while the earthed terminal is connected to the plane electrode. In addition to the non-uniformity of the field, a transverse dielectric barrier has been presented and investigated along the gap with a different thickness and location. The MFO works to optimize the error given by a numerical equation published before for calculating this field problem in the presence of a transverse barrier. This numerical equation was based on a correction coefficient called <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\left ({\beta }\right)$ </tex-math></inline-formula> , which is dependant on three values, relative permittivity, barrier location, and barrier thickness. The MFO is working to minimize the error given by <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula> using two new optimization factors in the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\beta $ </tex-math></inline-formula> equation. To ensure the accurate validation of MFO with a minimum error for field problem simulation, various artificial intelligence (AI) optimization techniques have been compared with the MFO obtained results. The comparative study shows that MFO is more effective, especially at 30% of the gap length from the HV electrode which represents the region of highly non-uniform field along the gap configuration. The numerical results of the field simulation that are held by different types of AI techniques are compared with those obtained from the accurate simulation results using the finite-element method. The value of the error between the numerical and simulation results shows that MFO is the most effective optimization techniques that can be used in the numerical equation to obtain the best value of the correction factor. With MFO, good agreement has been reached between the proposed numerical equation and the accurate simulation values of the electric field problem.

Fast simulation of multivariate nonstationary process and its application to extreme winds

Simulation of the devastating excitations such as the ground motion and transient extreme winds is an important task in the structural response analysis when it comes to the nonlinearity, system stochasticity, parametric excitations and so on. Although the classic spectral representation method (SRM) is widely used in the nonstationary process simulation, it suffers from lower efficiency due to the unavailability of use of fast Fourier transform (FFT). In this study, the classic SRM is extended to the nonstationary process with the time-varying coherence. Then, the FFT-aided and almost accurate simulation algorithm for the nonstationary process with the time-varying coherence is developed with the help of the proper orthogonal decomposition (POD) which is used to factorize the decomposed evolutionary spectra. Especially, the more efficient simulation for the nonstationary process with time-invariant coherence is also proposed, where the spectral matrix decomposition, use of POD and execution of FFT can be reduced significantly. Two examples including downburst and typhoon winds are employed to evaluate the accuracy and efficiency of the proposed method. Results show that the method has the good performance in terms of the efficiency and accuracy.

Whitecapping

The work we describe addresses the process of whitecapping. We first argue that, when the winds are strong enough, the ocean surface must develop an alternative means to dissipate energy when its flux from large to small scales becomes too large. We then show that the resulting Phillips' spectrum, which holds at small or meter length scales, is dominated by sharp crested waves. We next idealize such a sea locally by a family of close to maximum amplitude Stokes waves and show, using highly accurate simulation algorithms based on a conformal map representation, that perturbed Stokes waves develop the universal feature of an overturning plunging jet. We analyze both the cases when surface tension is absent and present. In the latter case, we show the plunging jet is regularized by capillary waves that rapidly become nonlinear Crapper waves in whose trough pockets whitecaps may be spawned. We are careful not to claim this as the definitive mechanism for whitecaps because three‐dimensional effects, although qualitatively discussed, are not included in the analysis.

Fully vectorial laser resonator modeling of continuous-wave solid-state lasers including rate equations, thermal lensing and stress-induced birefringence.

The computer-aided design of high quality mono-mode, continuous-wave solid-state lasers requires fast, flexible and accurate simulation algorithms. Therefore in this work a model for the calculation of the transversal dominant mode structure is introduced. It is based on the generalization of the scalar Fox and Li algorithm to a fully-vectorial light representation. To provide a flexible modeling concept of different resonator geometries containing various optical elements, rigorous and approximative solutions of Maxwell's equations are combined in different subdomains of the resonator. This approach allows the simulation of plenty of different passive intracavity components as well as active media. For the numerically efficient simulation of nonlinear gain, thermal lensing and stress-induced birefringence effects in solid-state active crystals a semi-analytical vectorial beam propagation method is discussed in detail. As a numerical example the beam quality and output power of a flash-lamp-pumped Nd:YAG laser are improved. To that end we compensate the influence of stress-induced birefringence and thermal lensing by an aspherical mirror and a 90° quartz polarization rotator.

On the Simulation of Nonlinear Bidimensional Spiking Neuron Models

Bidimensional spiking models are garnering a lot of attention for their simplicity and their ability to reproduce various spiking patterns of cortical neurons and are used particularly for large network simulations. These models describe the dynamics of the membrane potential by a nonlinear differential equation that blows up in finite time, coupled to a second equation for adaptation. Spikes are emitted when the membrane potential blows up or reaches a cutoff θ. The precise simulation of the spike times and of the adaptation variable is critical, for it governs the spike pattern produced and is hard to compute accurately because of the exploding nature of the system at the spike times. We thoroughly study the precision of fixed time-step integration schemes for this type of model and demonstrate that these methods produce systematic errors that are unbounded, as the cutoff value is increased, in the evaluation of the two crucial quantities: the spike time and the value of the adaptation variable at this time. Precise evaluation of these quantities therefore involves very small time steps and long simulation times. In order to achieve a fixed absolute precision in a reasonable computational time, we propose here a new algorithm to simulate these systems based on a variable integration step method that either integrates the original ordinary differential equation or the equation of the orbits in the phase plane, and compare this algorithm with fixed time-step Euler scheme and other more accurate simulation algorithms.

Stochastic modeling of polarized light scattering using a Monte Carlo based stencil method

This paper deals with an efficient and accurate simulation algorithm to solve the vector Boltzmann equation for polarized light transport in scattering media. The approach is based on a stencil method, which was previously developed for unpolarized light scattering and proved to be much more efficient (speedup factors of up to 10 were reported) than the classical Monte Carlo while being equally accurate. To validate what we believe to be the new stencil method, a substrate composed of spherical non-absorbing particles embedded in a non-absorbing medium was considered. The corresponding single scattering Mueller matrix, which is required to model scattering of polarized light, was determined based on the Lorenz-Mie theory. From simulations of a reflected polarized laser beam, the Mueller matrix of the substrate was computed and compared with an established reference. The agreement is excellent, and it could be demonstrated that a significant speedup of the simulations is achieved due to the stencil approach compared with the classical Monte Carlo.

Lagrangian dynamics of flexible manipulators using angular velocities instead of transformation matrices

An approach that uses angular velocities and 3×3 rotation matrices to represent the link kinematics of flexible manipulators efficiently is presented. A truncated method expansion is used to model link deflection. A recursive computational procedure is presented that is similar to the Newton-Euler dynamics formulation for rigid manipulators. The full nonlinear inverse dynamic equations are calculated in recursive form for manipulators with an arbitrary number of flexible links. Kinematics are computed recursively from the base to the tip, and torques are computed on the return recursion. On the basis of this formulation, a fast and accurate simulation algorithm is presented. It is shown that this method offers significant improvement in computational speed without degrading numerical accuracy. The modeling accuracy of the method and some practical implementational problems are discussed.

Simulation of neutron transport in a low-capture medium by the Monte Carlo method

This article shows that the results of one-velocity transport in an infinate homogeneous medium can be simply and accurately simulated, and that for low-capture exterior media sufficiently accurate simulation algorithms based on diffusion macrosteps are possible not only over tangent spheres but also over tangent half-spaces. A diagram shows the exterior and interior media, position of the original and image source relative to the tangent plane of the interior media. It was shown that there is an optimal distance to the interior below which half-space macrosteps are effective, and above which spherical macrosteps are. The authors note that circular cylinder distance to the tangent plane is always equal to the radius of the tangent sphere.