相关论文: Reducing Noise for PIC Simulations Using Kernel De…

Kernel Density Estimation (KDE) is a cornerstone of nonparametric statistics, yet it remains sensitive to bandwidth choice, boundary bias, and computational inefficiency. This study revisits KDE through a principled convolutional framework,…

Smoothing short-wavelength charge density variations can stabilize explicit electrostatic particle-in-cell (PIC) plasma simulations against grid heating and cold beam instabilities, which cause unphysical heating when the Debye length is…

We analyze the noise in macro-particle methods used in plasma physics and fluid dynamics, leading to approaches for minimizing the total error, focusing on electrostatic models in one dimension. We describe kernel density estimation for…

We propose a sparse grids based adaptive noise reduction strategy for electrostatic particle-in-cell (PIC) simulations. Our approach is based on the key idea of relying on sparse grids instead of a regular grid in order to increase the…

Variational quantum circuits (VQCs) solving partial differential equations (PDEs) on near-term quantum hardware face a critical challenge: hardware noise degrades solution fidelity and disrupts convergence. We present a systematic study of…

Particle-in-cell (PIC) is the most used algorithm to perform self-consistent tracking of intense charged particle beams. It is based on depositing macro-particles on a grid, and subsequently solving on it the Poisson equation. It is well…

The particle-in-cell (PIC) method has been widely used for plasma simulation, because of its noise-reduction capability and moderate computational cost. The immersed finite element (IFE) method is efficient for solving interface problems on…

Data-driven discovery of PDEs has made tremendous progress recently, and many canonical PDEs have been discovered successfully for proof-of-concept. However, determining the most proper PDE without prior references remains challenging in…

Near-term quantum computers have been built as intermediate-scale quantum devices and are fragile against quantum noise effects, namely, NISQ devices. Traditional quantum-error-correcting codes are not implemented on such devices and to…

We propose a general framework for quantum error mitigation that combines and generalizes two techniques: probabilistic error cancellation (PEC) and zero-noise extrapolation (ZNE). Similarly to PEC, the proposed method represents ideal…

Particle-in-cell (PIC) simulations are essential for studying kinetic plasma processes, but they often suffer from statistical noise, especially in plasmas with fast flows. We have also found that the typical central difference scheme used…

In density estimation, the mean integrated squared error (MISE) is commonly used as a measure of performance. In that setting, the cross-validation criterion provides an unbiased estimator of the MISE minus the integral of the squared…

Current quantum computers suffer from a level of noise that prohibits extracting useful results directly from longer computations. The figure of merit in many near-term quantum algorithms is an expectation value measured at the end of the…

We propose a novel method for density estimation that leverages an estimated score function to debias kernel density estimation (SD-KDE). In our approach, each data point is adjusted by taking a single step along the score function with a…

Although recent advances in simulating open quantum systems have lead to significant progress, the applicability of numerically exact methods is still restricted to rather small systems. Hence, more approximate methods remain relevant due…

Efficient simulation of stochastic partial differential equations (SPDE) on general domains requires noise discretization. This paper employs piecewise linear interpolation of noise in a fully discrete finite element approximation of a…

We address the problem of signal denoising via transform-domain shrinkage based on a novel $\textit{risk}$ criterion called the minimum probability of error (MPE), which measures the probability that the estimated parameter lies outside an…

First-principles particle-in-cell (PIC) simulation is a powerful tool for understanding plasma behavior, but this power often comes at great computational expense. Artificially reducing the ion/electron mass ratio is a time-honored practice…

Minimizing the Mean Squared Error (MSE) is a key objective in machine learning and is commonly used for imputing missing values. While this approach provides accurate point estimates, it introduces systematic biases in downstream analyses.…

In this work, we derive particle schemes, based on micro-macro decomposition, for linear kinetic equations in the diffusion limit. Due to the particle approximation of the micro part, a splitting between the transport and the collision part…