Stochastic variational principles for the collisional Vlasov–Maxwell and Vlasov–Poisson equations

In this work, we recast the collisional Vlasov–Maxwell and Vlasov–Poisson equations as systems of coupled stochastic and partial differential equations, and we derive stochastic variational principles which underlie such reformulations. We also propose a stochastic particle method for the collisional Vlasov–Maxwell equations and provide a variational characterization of it, which can be used as a basis for a further development of stochastic structure-preserving particle-in-cell integrators.

SHPOS: A Theoretical Guaranteed Accelerated Particle Optimization Sampling Method

Recently, the Stochastic Particle Optimization Sampling (SPOS) method is proposed to solve the particle-collapsing pitfall of deterministic Particle Variational Inference methods by ultilizing the stochastic Overdamped Langevin dynamics to enhance exploration. In this paper, we propose an accelerated particle optimization sampling method called Stochastic Hamiltonian Particle Optimization Sampling (SHPOS). Compared to the first-order dynamics used in SPOS, SHPOS adopts an augmented second-order dynamics, which involves an extra momentum term to achieve acceleration. We establish a non-asymptotic convergence analysis for SHPOS, and show that it enjoys a faster convergence rate than SPOS. Besides, we also propose a variance-reduced stochastic gradient variant of SHPOS for tasks with large-scale datasets and complex models. Experiments on both synthetic and real data validate our theory and demonstrate the superiority of SHPOS over the state-of-the-art.

Implementation of a Lagrangian Stochastic Particle Trajectory Model (LaStTraM) to Simulate Concentration and Flux Footprints Using the Microclimate Model ENVI-Met

The number of studies evaluating flux or concentration footprints has grown considerably in recent years. These footprints are vital to understand surface–atmosphere flux measurements, for example by eddy covariance. The newly developed backwards trajectory model LaStTraM (Lagrangian Stochastic Trajectory Model) is a post-processing tool, which uses simulation results of the holistic 3D microclimate model ENVI-met as input. The probability distribution of the particles is calculated using the Lagrangian Stochastic method. Combining LaStTraM with ENVI-met should allow us to simulate flux and concentration footprints in complex urban environments. Applications and evaluations were conducted through a comparison with the commonly used 2D models Kormann Meixner and Flux Footprint Predictions in two different meteorological cases (stable, unstable) and in three different detector heights. LaStTraM is capable of reproducing the results of the commonly used 2D models with high accuracy. In addition to the comparison with common footprint models, studies with a simple heterogeneous and a realistic, more complex model domain are presented. All examples show plausible results, thus demonstrating LaStTraM’s potential for the reliable calculation of footprints in homogeneous and heterogenous areas.

An efficient algorithm of the unified stochastic particle Bhatnagar-Gross-Krook method for the simulation of multi-scale gas flows

The unified stochastic particle method based on the Bhatnagar-Gross-Krook model (USP-BGK) has been proposed recently to overcome the low accuracy and efficiency of the traditional stochastic particle methods, such as the direct simulation Monte Carlo (DSMC) method, for the simulation of multi-scale gas flows. However, running with extra virtual particles and space interpolation, the previous USP-BGK method cannot be directly transplanted into the existing DSMC codes. In this work, the implementation of USP-BGK is simplified using new temporal evolution and spatial reconstruction schemes. As a result, the present algorithm of the USP-BGK method is similar to the DSMC method and can be implemented efficiently based on any existing DSMC codes just by modifying the collision module.

Development of a Backward–Forward Stochastic Particle Tracking Model for Identification of Probable Sedimentation Sources in Open Channel Flow

As reservoirs subject to sedimentation, the dam gradually loses its ability to store water. The identification of the sources of deposited sediments is an effective and efficient means of tackling sedimentation problems. A state-of-the-art Lagrangian stochastic particle tracking model with backward–forward tracking methods is applied to identify the probable source regions of deposited sediments. An influence function is introduced into the models to represent the influence of a particular upstream area on the sediment deposition area. One can then verify if a specific area might be a probable source by cross-checking the values of influence functions calculated backward and forward, respectively. In these models, the probable sources of the deposited sediments are considered to be in a grid instead of at a point for derivation of the values of influence functions. The sediment concentrations in upstream regions must be known a priori to determine the influence functions. In addition, the accuracy of the different types of diffusivity at the water surface is discussed in the study. According to the results of the case study of source identification, the regions with higher sediment concentrations computed by only backward simulations do not necessarily imply a higher likelihood of sources. It is also shown that from the ensemble results when the ensemble mean of the concentration is higher, the ensemble standard deviation of the concentration is also increased.

An Efficient Algorithm of the Unified Stochastic Particle Bhatnagar-Gross-Krook Method for the Simulation of Multi-Scale Gas Flows

The unified stochastic particle method based on the Bhatnagar-Gross-Krook model (USP-BGK) has been proposed recently to overcome the low accuracy and efficiency of the traditional stochastic particle methods, such as the direct simulation Monte Carlo (DSMC) method, for the simulation of multi-scale gas flows. However, running with extra virtual particles and space interpolation, the previous USP-BGK method cannot be directly transplanted into the existing DSMC codes. In this work, the implementation of USP-BGK is simplified using new temporal evolution and spatial reconstruction schemes. As a result, the present algorithm of the USP-BGK method is similar to the DSMC method and can be implemented efficiently based on any existing DSMC codes just by modifying the collision module.