Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “PARTICLE TRAJECTORY”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 235 records · Page 13
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Summertime Carbonaceous Aerosol in Interior Versus Coastal Northern Alaska

Abstract Rapid warming is likely increasing primary production and wildfire occurrence in the Arctic. Projected changes in carbonaceous aerosols during the summer will impact atmospheric chemistry and climate, but our understanding of these processes is limited by sparse observations. Here, we characterize carbonaceous aerosol in Alaska, USA: Toolik Field Station in the Interior and the Atmospheric Radiation Measurement facility at Utqiaġvik on the Arctic coast, during the summers of 2022 and 2023. We estimated PM 2.5 and PM 10 concentrations using laser light scattering (PurpleAir sensors) and examined total carbon (TC) and its organic carbon (OC) and elemental carbon (EC) fractions in total suspended particles (TSP). We investigated the dominant sources of carbonaceous aerosol using air mass backward‐trajectories from the NOAA HYSPLIT model and radiocarbon source apportionment of TC. TC concentrations were about twice as high in the Interior compared to the coast, with contemporary sources dominating at both Toolik (95%–99%) and Utqiaġvik (86%–89%) over minor contributions from fossil sources. Elevated PM, TC, OC, and EC concentrations coincided with major boreal forest fire activity in North America that brought smoke to the region. The radiocarbon signature of EC measured at Toolik during these wildfire events indicated that over 90% of the EC came from contemporary sources. Our measurements demonstrate the potential for Arctic aerosol concentrations to respond significantly to climate warming‐induced changes to the landscape and emphasize the need for continuous atmospheric monitoring to advance our understanding of this rapidly changing environment.

Welch, Allison M. [Department of Earth System Scie↗
DOE OSTI2025

Investigation of post-breakup Coulomb acceleration using a trajectory model

Intermediate mass fragments ejected during the deexcitation of excited projectilelike fragments may promptly decay following ejection; the daughter particles that are subsequently produced are subject to interactions with the residual nucleus that affect final-state observables, a process herein referred to as post-breakup Coulomb acceleration. A simple classical Coulomb interaction model was used to study modification of 8 Be (2 + ), 5 Li (3/2 – ), 7 Li (7/2 – ), 7 Be (7/2 – ), and states in 12 B emitted following heavy-ion collisions of 28 Si + 12 C at 35 MeV/nucleon. Here, in contrast to previous work studying 8 Be (2 + ), excellent agreement between simulation and experiment was obtained using only Coulomb forces when either a Lorentzian or R-matrix line shape was used to describe the initial relative energy rather than a Gaussian. In consideration of the obtained results, improvements to the model and evaluation of experimental data are discussed as future directions, but it was concluded that the effects observed in the present data can be accurately described using only elements of classical mechanics and that the process is largely understood for a wide range of state lifetimes and mass and charge (a)symmetries.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Dynamics of Plasma Blobs in Curved Magnetic Geometries [Poster]

Plasma blobs are structures within a bulk plasma which are characterized by an increased density relative to the bulk, and movement as coherent objects across magnetic field lines. In general, ions and electrons will follow helical trajectories through a magnetic field, with direction of gyration dependent on sign of the particle’s charge, and helix gyroradius proportional to particle speed, and inversely proportional to magnetic field strength.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Plasma electron hole kinematics. Hole tracking Particle-In-Cell simulation

The kinematics of a 1-D electron hole is studied using a novel Particle-In-Cell simulation code. A hole tracking technique enables us to follow the trajectory of a fast-moving solitary hole and study quantitatively hole acceleration and coupling to ions. We observe a transient at the initial stage of hole formation when the hole accelerates to several times the cold-ion sound speed. Artificially imposing slow ion speed changes on a fully formed hole causes its velocity to change even when the ion stream speed in the hole frame greatly exceeds the ion thermal speed, so there are no reflected ions. The behavior that we observe in numerical simulations agrees very well with our analytic theory of hole momentum conservation and the effects of “jetting.”

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Langevin Dynamics modeling of gas-phase ion-ion recombination (Final Technical Report)

A self-consistent trajectory simulation approach to model MN reactions (Fig. 1) which incorporates the probability of electron transfer as a Monte Carlo operator (Fig. 2) was developed and published as Liu et al. J. Chem. Phys. 159, 114111 (2023). The electron transfer probability p ET estimated using the two-state Landau-Zener (LZ) theory was incorporated into classical trajectory simulations to elicit predictions of MN reaction cross-section σ (vacuum) or rate constant β (finite pressure). Electronic structure calculations with multireference configuration interaction (MRCI) and large correlation consistent basis sets were used to derive inputs to the LZ theory. The key advance of our trajectory simulation approach is the incorporation of electron transfer probability and the inclusion of the effect of ion-neutral interactions on MN using a Langevin representation of the effect of neutral gas on ions. For H + – H - and Li + – H(D) - pairs, our approach quantitatively agrees with measured speed-dependent cross-sections for up to ~10 5 m/s. For the ion pair Ne + – Cl - , our predictions of the MN rate constant at ~1 torr are a factor of ~2 – 3 higher than the experimentally measured value. Similarly, for Xe + – F - in the pressure range of ~20000 – 80000 Pa, our predictions of the MN rate constant are ~20% lower but are in excellent qualitative agreement with experimental data. The paradigm of using trajectory simulations to self-consistently model MN reactions is the basis for inclusion of additional non-classical, and static magnetic and electric field effects. Subsequent work, published as Roy et al. focused on modeling recombination rate constant for three ion pairs (rare gas Ar + cation and halide anions): Ar + – Cl - , Ar + – Br - , Ar + – I - , 2) considering spin-orbit couplings in the electronic structure calculations to obtain high-fidelity estimates of the electron transfer probability and incorporated within the classical trajectory simulations to elicit predictions. In addition to calculations of ion-ion recombination rate constants, a classical trajectory simulation technique (published as Roy et al. J. Chem. Phys. 162(9), 094104 (2023)) that uses quaternions to represent orientation of non-spherical particles (ions or aerosol particles) was developed to simulate the recombination of diatomic or more generally, polyatomic molecules. Finally, several other ion pairs such as Ne + – Cl - , Kr + – Cl - , were explored using the developed semi-classical trajectory simulations to understand various challenges in tackling electronic structure calculations. Using empirical approaches to parameterize the electron transfer radius, trajectory simulations were also used to probe the effect of ion number density on MN rate constant.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Reconstruction of effective potential from statistical analysis of dynamic trajectories

The broad incorporation of microscopic methods is yielding a wealth of information on the atomic and mesoscale dynamics of individual atoms, molecules, and particles on surfaces and in open volumes. Analysis of such data necessitates statistical frameworks to convert observed dynamic behaviors to effective properties of materials. Here, we develop a method for the stochastic reconstruction of effective local potentials solely from observed structural data collected from molecular dynamics simulations (i.e., data analogous to those obtained via atomically resolved microscopies). Using the silicon vacancy defect in graphene as a model, we apply the statistical framework presented herein to reconstruct the free energy landscape from the calculated atomic displacements. Evidence of consistency between the reconstructed local potential and the trajectory data from which it was produced is presented, along with a quantitative assessment of the uncertainty in the inferred parameters.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Scaling of silicon nanoparticle growth in low temperature flowing plasmas

Low temperature plasmas are an emerging method to synthesize high quality nanoparticles (NPs). An established and successful technique to produce NPs is using a capacitively coupled plasma (CCP) in cylindrical geometry. Although a robust synthesis technique, optimizing or specifying NP properties using CCPs, is challenging. In this paper, results from a computational investigation for the growth of silicon NPs in flowing inductively coupled plasmas (ICPs) using Ar/SiH 4 gas mixtures of up to a few Torr are discussed. ICPs produce more locally constrained and quiescent plasma potentials. These positive plasma potentials produce an electrostatic trap for negatively charged NPs, which can significantly extend the residence time of NPs in the plasma, which in turn provides a controllable period for particle growth. The computational platforms used in this study consist of a two-dimensional plasma hydrodynamics model, a three-dimensional nanoparticle growth and trajectory tracking model, and a molecular dynamics simulation for deriving reactive sticking coefficients of silane radicals on Si NPs. Trends for the nanoparticle growth as a function of SiH 4 inlet fraction, gas residence time, energy deposition per particle, pressure, and reactor diameter are discussed. The general path for particle synthesis is the trapping of small NPs in the positive electrostatic potential, followed by entrainment in the gas flow upon reaching a critical particle size. Optimizing or controlling NP synthesis then depends on the spatial distribution of plasma potential, the density of growth species, and the relative time that particles spend in the electrostatic trap and flowing through higher densities of growth species upon leaving the trap.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Modelling dust transport in DIII-D with DTOKS-Upgrade

Comprehensive upgrades to the dust transport code Dust in TOKamaks (DTOKS) that extend the plasma-dust interaction model are presented and compared with recent measurements of dust transport in DIII-D. Simulations incorporating variation in physical properties of graphite dust with temperature and size in a stationary plasma background suggest a substantial decrease in lifetimes due principally to thermal expansion. The trajectories of 53 dust grains identified from analysis of visible camera data taken across two similar shots were used to measure the dust particle velocity distributions. Dust tracks terminated mostly at the outer divertor strike point having a mean observation time of 2.1 ± 0.4 ms. Stochastic modelling of 200 graphite dust particles in the DIII-D tokamak performed with DTOKS-U using plasma simulations generated by OEDGE found similar behaviour, with particles ablating rapidly after acquiring a positive charge in the region close to the outer strike point, creating an acute source of neutral carbon atoms. The simulated mean lifetime, 11 ± 2 ms, showed approximate agreement with experimental observation when corrected by accounting for dust visibility and ignoring the longest trajectories 1.5 ± 0.2 ms. Synthetic diagnostic data generated from coupling the results of DTOKS-U with the visualisation software Calcam offers a powerful new tool for validation of simulations and predictive calculations of dust dynamics.

Physics↗
DOE OSTI2026

Data-driven Mori–Zwanzig modeling of Lagrangian particle dynamics in turbulent flows

The dynamics of Lagrangian particles in turbulence play a crucial role in mixing, transport, and dispersion in complex flows. Their trajectories exhibit highly nontrivial statistical behavior, motivating the development of surrogate models that can reproduce these trajectories without incurring the high computational cost of direct numerical simulations of the full Eulerian field. This task is particularly challenging because reduced-order models typically lack access to the full set of interactions with the underlying turbulent field. Novel data-driven machine learning techniques can be powerful in capturing and reproducing complex statistics of the reduced-order/surrogate dynamics. In this work, we show how one can learn a surrogate dynamical system that is able to evolve a turbulent Lagrangian trajectory in a way that is point-wise accurate for short-time predictions (with respect to Kolmogorov time) and stable and statistically accurate at long times. This approach is based on the Mori–Zwanzig formalism, which prescribes a mathematical decomposition of the full dynamical system into resolved dynamics that depend on the current state and the past history of a reduced set of observables, and the unresolved orthogonal dynamics due to unresolved degrees of freedom of the initial state. We show how by training this reduced order model on a point-wise error metric on short time-prediction, we are able to correctly learn the dynamics of Lagrangian turbulence, such that also the long-time statistical behavior is stably recovered at test time. This opens up a range of applications, for example, for the control of active Lagrangian agents in turbulence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Statistical Learning for Nonlinear Model Reduction from Local Simulations of Stochastic and Particle- and Agent-Based Systems

Stochastic physical systems across the sciences that have very high-dimensional state spaces, with a large number of fast degrees of freedom that force direct simulators to proceed by integration steps that are orders of magnitude smaller than events of interests (e.g., particle collisions). Examples range from molecular motion to dynamics of large populations of cells. A grand challenge in the simulation and understanding of such systems is the systematic construction of accurate, interpretable, reduced models, enabling faster simulations, revealing fundamental properties of the dynamics, and predicting phenomena of interest that the original simulator could not reached with sufficient accuracy or within a given computational budget. In this projected we developed novel statistical estimation/machine learning techniques for analyzing and building empirical reduced models for important families of high-dimensional stochastic systems, in particular: - we developed techniques for estimating interaction kernels in interacting particle- and agent-based systems, which are ubiquitous in Physics, Biology and many other sciences, given observed trajectories of the system; - we developed techniques for nonlinear model reduction for high-dimensional stochastic systems that have a small number of unknown, nonlinear slow variables, and a large number of fast modes, that are possibly of large magnitude, given observed short trajectories of the system in the form of bursts of trajectories from different initial conditions; - we developed novel techniques for estimating linear dynamical systems on graphs when both the dynamics and the underlying graph are unknown, and we have a sparse set of space-time observations; - we considered the problem of estimating an unknown nonlinear observation function of a standard process (e.g. Brownian motion), so that we can recognized if an observed dynamics is "just" a nonlinear version of a known dynamics; we also developed benchmarks for learning algorithms aimed at learning and classifying diffusion processes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

The impact of cold electrons and cold ions in magnetospheric physics

A review of the impact of the cold-ion and cold-electron populations in the Earth’s magnetosphere is presented in this paper. The cold populations are defined by total energy less than approximately 100 eV, i.e. in the energy range which is strongly affected by spacecraft charging and that often dominates the total plasma density. We also include the warm plasma cloak in the review, since it overlaps partially with the cold energy range and is a population that is still not well understood. The known impacts of cold ions and cold electrons that are discussed are: the source of magnetospheric plasma, solar-wind/magnetosphere coupling, magnetotail reconnection and substorms, Kelvin-Helmholtz instabilities at the magnetopause, chorus, hiss, electromagnetic-ion-cyclotron and ultra-low-frequency wave-particle interactions, aurora structuring and spacecraft charging. Other possible impacts are associated with refilling on open-drift trajectories, the remnant layer and plasmapause disruption. A discussion of the difficulty of cold-plasma measurements and the need for new measurement techniques that measure the full cold-ion and cold-electron distribution functions is also presented. There remain a lot of unknowns about the cold-ion and cold-electron populations, associated with their origin, properties, drivers and impacts. These populations will need to be fully understood before the magnetosphere-ionosphere system can be fully understood.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Measurement report: A comparison of ground-level ice-nucleating-particle abundance and aerosol properties during autumn at contrasting marine and terrestrial locations

Abstract. Ice-nucleating particles (INPs) are an essential class of aerosols found worldwide that have far-reaching but poorly quantified climate feedback mechanisms through interaction with clouds and impacts on precipitation. These particles can have highly variable physicochemical properties in the atmosphere, and it is crucial to continuously monitor their long-term concentration relative to total ambient aerosol populations at a wide variety of sites to comprehensively understand aerosol–cloud interactions in the atmosphere. Hence, our study applied an in situ forced expansion cooling device to measure ambient INP concentrations and test its automated continuous measurements at atmospheric observatories, where complementary aerosol instruments are heavily equipped. Using collocated aerosol size, number, and composition measurements from these sites, we analyzed the correlation between sources and abundance of INPs in different environments. Toward this aim, we have measured ground-level INP concentrations at two contrasting sites, one in the Southern Great Plains (SGP) region of the United States with a substantial terrestrially influenced aerosol population and one in the Eastern North Atlantic Ocean (ENA) region with a primarily marine-influenced aerosol population. These measurements examined INPs mainly formed through immersion freezing and were performed at a ≤ 12 min resolution and with a wide range of heterogeneous freezing temperatures (Ts above −31 °C) for at least 45 d at each site. The associated INP data analysis was conducted in a consistent manner. We also explored the additional offline characterization of ambient aerosol particle samples from both locations in comparison to in situ data. From our ENA data, on average, INP abundance ranges from ≈ 1 to ≈ 20 L−1 (−30 °C ≤ T ≤ −20 °C) during October–November 2020. Backward air mass trajectories reveal a strong marine influence at ENA with 75.7 % of air masses originating over the Atlantic Ocean and 96.6 % of air masses traveling over open water, but analysis of particle chemistry suggests an additional INP source besides maritime aerosols (e.g., sea spray aerosols) at ENA. In contrast, 90.8 % of air masses at the SGP location originated from the North American continent, and 96.1 % of the time, these air masses traveled over land. As a result, organic-rich SGP aerosols from terrestrial sources exhibited notably high INP abundance from ≈ 1 to ≈ 100 L−1 (−30 °C ≤ T ≤ −15 °C) during October–November 2019. The probability density function of aerosol surface area-scaled immersion freezing efficiency (ice nucleation active surface site density; ns) was assessed for selected freezing temperatures. While the INP concentrations measured at SGP are higher than those of ENA, the ns(T) values of SGP (≈ 105 to ≈ 107 m−2 for −30 °C ≤ T ≤ −15 °C) are reciprocally lower than ENA for approximately 2 orders of magnitude (≈ 107 to ≈ 109 m−2 for −30 °C ≤ T ≤ −15 °C). The observed difference in ns(T) mainly stems from varied available aerosol surface areas, Saer, from two sites (Saer,SGP > Saer,ENA). INP parameterizations were developed as a function of examined freezing temperatures from SGP and ENA for our study periods.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Particle production by a relativistic semitransparent mirror in (1+3)D Minkowski spacetime

Production of massless, scalar particles by a relativistic, semitransparent, plane mirror in (1+3)D Minkowski spacetime based on the Barton-Calogeracos (BC) action is investigated. The corresponding Bogoliubov coefficients are derived for a mirror with arbitrary, relativistic trajectories. We apply our derived formula to two specific trajectories. One is commonly used in the (1+1)D literature to mimic gravitational collapse theoretically, and the other is proposed to be realizable experimentally. In addition, we identify the relation between the particle spectrum and the particle production probability, and we demonstrate the equivalence between our approach and the existing approach in the literature, which is restricted to (1+1)D. In short, our treatment extends the study to (1+3)D spacetime for a relativistic, plane mirror. Finally, we offer a third approach for finding the particle spectrum using the S-matrix formalism.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Chaotic and integrable magnetic fields in one-dimensional hybrid Vlasov–Maxwell equilibria

The construction of kinetic equilibrium states is important for studying stability and wave propagation in collisionless plasmas. Thus, many studies over the past decades have been focused on calculating Vlasov–Maxwell equilibria using analytical and numerical methods. However, the problem of kinetic equilibrium of hybrid models is less studied, and self-consistent treatments often adopt restrictive assumptions ruling out cases with irregular and chaotic behaviour, although such behaviour is observed in spacecraft observations of space plasmas. In this paper, we develop a one-dimensional (1-D), quasineutral, hybrid Vlasov–Maxwell equilibrium model with kinetic ions and massless fluid electrons and derive associated solutions. The model allows for an electrostatic potential that is expressed in terms of the vector potential components through the quasineutrality condition. The equilibrium states are calculated upon solving an inhomogeneous Beltrami equation that determines the magnetic field, where the inhomogeneous term is the current density of the kinetic ions and the homogeneous term represents the electron current density. We show that the corresponding 1-D system is Hamiltonian, with position playing the role of time, and its trajectories have a regular, periodic behaviour for ion distribution functions that are symmetric in the two conserved particle canonical momenta. For asymmetric distribution functions, the system is nonintegrable, resulting in irregular and chaotic behaviour of the fields. The electron current density can modify the magnetic field phase space structure, inducing orbit trapping and the organization of orbits into large islands of stability. Thus, the electron contribution can be responsible for the emergence of localized electric field structures that induce ion trapping. We also provide a paradigm for the analytical construction of hybrid equilibria using a rotating two-dimensional harmonic oscillator Hamiltonian, enabling the calculation of analytic magnetic fields and the construction of the corresponding distribution functions in terms of Hermite polynomials.

Kaltsas, Dimitrios A. (ORCID:0000000300769015)↗
DOE OSTI2025

Real-time tracking and analysis of gas bubble dynamics in laser powder bed fusion using in-situ X-ray characterization and machine learning

Porosity defects remain a significant challenge in the laser powder bed fusion (LPBF) process, adversely affecting the mechanical properties and reliability of additively manufactured components. Here, this study investigates the real-time formation and trajectory of gas bubbles during LPBF of Al6061 alloy using advanced in-situ X-ray characterization and machine learning. The unsupervised Gaussian mixture model and particle tracking algorithm developed are able to precisely track and quantify the properties of gas bubbles and keyhole pores. Our analysis identified five distinct types of gas bubble formation and movement patterns, emphasizing the diverse origins and behaviors of these defects. It enables precise quantification of trajectories, velocities, and morphological changes of gas bubbles, offering a granular view of the subsurface dynamics within the melt pool. Additionally, we explored keyhole-induced pore dynamics, revealing the critical role of keyhole oscillation and collapse for the formation of both large and small gas pores. It defines four different regions of gas bubble movement within the melt pool, providing a clearer understanding of how local fluid dynamics affect pore behavior. The results underscore the importance of integrating in-situ experimental observation and automated machine learning to develop a more robust predictive model for defect formation in LPBF.

In-situ X-ray imaging↗
DOE OSTI2024

Hopping and crawling DNA-coated colloids

Understanding the motion of particles with multivalent ligand-receptors is important for biomedical applications and material design. Yet, even among a single design, the prototypical DNA-coated colloids, seemingly similar micrometric particles hop or roll, depending on the study. We shed light on this problem by observing DNA-coated colloids diffusing near surfaces coated with complementary strands for a wide array of coating designs. We find colloids rapidly switch between 2 modes: They hop—with long and fast steps—and crawl—with short and slow steps. Both modes occur at all temperatures around the melting point and over various designs. The particles become increasingly subdiffusive as temperature decreases, in line with subsequent velocity steps becoming increasingly anticorrelated, corresponding to switchbacks in the trajectories. Overall, crawling (or hopping) phases are more predominant at low (or high) temperatures; crawling is also more efficient at low temperatures than hopping to cover large distances. We rationalize this behavior within a simple model: At lower temperatures, the number of bound strands increases, and detachment of all bonds is unlikely, hence, hopping is prevented and crawling favored. We thus reveal the mechanism behind a common design rule relying on increased strand density for long-range self-assembly: Dense strands on surfaces are required to enable crawling, possibly facilitating particle rearrangements.

Science & Technology - Other Topics↗
DOE OSTI2022

Pulsed power to control growth of silicon nanoparticles in low temperature flowing plasmas

Low-temperature plasmas have seen increasing use for synthesizing high-quality, mono-disperse nanoparticles (NPs). Recent work has highlighted that an important process in NP growth in plasmas is particle trapping—small, negatively charged nanoparticles become trapped by the positive electrostatic potential in the plasma, even if only momentarily charged. In this article, results are discussed from a computational investigation into how pulsing the power applied to an inductively coupled plasma (ICP) reactor may be used for controlling the size of NPs synthesized in the plasma. The model system is an ICP at 1 Torr to grow silicon NPs from an Ar/SiH 4 gas mixture. This system was simulated using a two-dimensional plasma hydrodynamics model coupled to a three-dimensional kinetic NP growth and trajectory tracking model. The effects of pulse frequency and pulse duty cycle are discussed. We identified separate regimes of pulsing where particles become trapped for one pulsed cycle, a few cycles, and many cycles—each having noticeable effects on particle size distributions. For the same average power, pulsing can produce a stronger trapping potential for particles when compared to continuous wave power, potentially increasing particle mono-dispersity. Pulsing may also offer a larger degree of control over particle size for the same average power. Experimental confirmation of predicted trends is discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

A Pseudoreversible Normalizing Flow for Stochastic Dynamical Systems with Various Initial Distributions

Here, we present a pseudoreversible normalizing flow method for efficiently generating samples of the state of a stochastic differential equation (SDE) with various initial distributions. The primary objective is to construct an accurate and efficient sampler that can be used as a surrogate model for computationally expensive numerical integration of SDEs, such as those employed in particle simulation. After training, the normalizing flow model can directly generate samples of the SDE’s final state without simulating trajectories. The existing normalizing flow model for SDEs depends on the initial distribution, meaning the model needs to be retrained when the initial distribution changes. The main novelty of our normalizing flow model is that it can learn the conditional distribution of the state, i.e., the distribution of the final state conditional on any initial state, such that the model only needs to be trained once and the trained model can be used to handle various initial distributions. This feature can provide a significant computational saving in studies of how the final state varies with the initial distribution. Additionally, we propose to use a pseudoreversible network architecture to define the normalizing flow model, which has sufficient expressive power and training efficiency for a variety of SDEs in science and engineering, e.g., in particle physics. We provide a rigorous convergence analysis of the pseudoreversible normalizing flow model to the target probability density function in the Kullback–Leibler divergence metric. Numerical experiments are provided to demonstrate the effectiveness of the proposed normalizing flow model.

97 MATHEMATICS AND COMPUTING↗