SEARCH · Engineering Papers

Results for “advection”

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.

SourceResearch connectionFrom yearThrough year

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

At least 649 records · Page 36

All sources NASA NTRS DOE OSTI

DOE OSTI2021

Effect of CO 2 -brine-rock reactions on pore architecture and permeability in dolostone: Implications for CO 2 storage and EOR

Geologic carbon sequestration (GCS) is considered a feasible technology for storing substantive volumes of greenhouse gases in subsurface geological formations. In the reservoir, far from carbon dioxide (CO 2 ) injection wells or in post-injection scenarios, diffusion dominates over advection. This condition conjoins with spatially distributed geochemical reactions to induce heterogeneous changes in pore architecture, i.e. pore body and throat sizes or surface roughness. These changes can affect CO 2 transport properties and storage capacity. In this work, we investigated mineral dissolution and precipitation in dolomite samples saturated with a CO 2 -saturated brine at 93 °C and 34.5 MPa, aged without flow. Two rock types samples, i.e. intergranular- and vuggy-dominant, were selected to investigate changes in pore size, porosity and permeability under reactive conditions. Mineral dissolution and precipitation were characterized using scanning electron microscopy. Changes in pore size were quantified via time-domain nuclear magnetic resonance (TD-NMR) transverse relaxation time (T 2 ) and diffusion coefficient (D) distributions. We show that mineral dissolution likely occurs in highly permeable pathways. These observations are confirmed through analysis of (T 2 ) and diffusion coefficient (D) distributions. In contrast to results during CO 2 -enriched brine continuous injection, mineral precipitation was observed in micropores. The leftward shift of the T 2 peaks, corresponding to micropores, also evidenced mineral precipitation in lowpermeability zones. However, microscale alterations resulted only in a subtle increase in porosity and permeability. Results in this study shed light on effects of geochemical reactions on alteration of rock properties in diffusion-dominated regions during CO 2 storage.

58 GEOSCIENCES↗

DOE OSTI2022

Flow structures of the cross-flow over a five-layer helically coiled steam generator geometry

The helically-coiled heat exchanger (HCSG) offers advantages over straight tubes such as compactness in geometry, increased heat transfer coefficients, and capability to absorb thermal expansion. In this study, the time-resolved velocity field data of shell-side crossflow over a five-layer helically coiled steam generator geometry was obtained using Particle Image Velocimetry (PIV) between adjacent rods in four regions with up to 5000 frames per second (5 kHz) at approximately Re u = 3600. The slant rod bundle created different flow patterns in different regions. Proper Orthogonal Decomposition (POD) revealed high-energy-mode flow structures. Due to the confined flow channel geometry, the large flow structures were not advected resulting in no strong POD mode paring. Continuous Wavelet Transform (CWT) visualized the characteristics of flow fluctuation in time and frequency domain simultaneously, which ranged in Strouhal number, S u , between 0.03 and 1.17. In the wake regions of the rods, flows changed in both pattern and magnitude over time. Once a pattern formed, it continued for relatively shorter than straight tube arrays, before changing the pattern again. The histograms of the POD time coefficients presented this multimodal flow characteristics. The current study focuses more on whole flow field analyses in the selected regions rather than local point-wise analyses. Finally, this study revealed that various Strouhal numbers can exist in the helically coiled heat exchanger geometry, which was not observed in straight tube arrays. In particular, Strouhal numbers smaller than 0.1 do not seem to be caused by vortex shedding but seem to be the result of the combination of complex geometry and possible multimodal trends. Based on the current observation, further works would involve intensive instantaneous point-wise analyses on the interactions between important locations such as separation points, stagnation points, shear layers, etc.

42 ENGINEERING↗

DOE OSTI2020

Some observations concerning "laminarization" in heated vertical tubes

For low "turbulent" Reynolds numbers in strongly-heated vertical gas flow, fundamental results of existing direct numerical simulation (DNS) databases have been examined to deduce differences between cases which "revert" to turbulent and those that yield integral parameters which correspond to laminar flow (henceforth laminarizing or laminarized). The objectives of this paper are (1) to examine the streamwise evolution of near-wall flow structures and (2) to determine which, if any, proposed laminarization parameters could be used to discriminate between turbulent and laminarizing flows resulting. Views of streamlines in r-θ cross sections showed evidence of a ring of irregular-shaped streamwise vortices near the wall at all locations. The transverse advection of these vortices is hypothesized to provide a path of least resistance to the transport of streamwise momentum in the wall-normal direction. It is demonstrated that a steady streamwise laminar vortex can provide apparent turbulent momentum transport (as a consequence of the Reynolds decomposition) such that a reasonable mean velocity profile is predicted near the wall. For the present cases, the values of the non-dimensional radius (y c,w + = Re τ,w ) and of the modified wall Reynolds number did discriminate whether turbulent or laminarizing flow resulted.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2023

Analytical solution and parameter estimation for heat of wetting and vapor adsorption during spontaneous imbibition in tuff

An analytical expression is derived for the thermal response observed during spontaneous imbibition of water into a dry core of zeolitic tuff. Sample tortuosity, thermal conductivity, and thermal source strength are estimated from fitting an analytical solution to temperature observations during a single laboratory test. Here, the closed-form analytical solution is derived using Green's functions for heat conduction in the limit of “slow” water movement; that is, when advection of thermal energy with the wetting front is negligible. The solution has four free fitting parameters and is efficient for parameter estimation. Laboratory imbibition data used to constrain the model include a time series of the mass of water imbibed, visual location of the wetting front through time, and temperature time series at six locations. The thermal front reached the end of the core hours before the visible wetting front. Thus, the predominant form of heating during imbibition in this zeolitic tuff is due to vapor adsorption in dry zeolitic rock ahead of the wetting front. The separation of the wetting front and thermal front in this zeolitic tuff is significant, compared to wetting front behavior of most materials reported in the literature. This work is the first interpretation of a thermal imbibition response to estimate transport (tortuosity) and thermal properties (including thermal conductivity) from a single laboratory test.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Modelling and analysis of salt-convection effect on oxide reduction process for uranium oxides using smoothed particle hydrodynamics

Oxygen ion transport via molten salt continuum is a key kinetic feature of electrochemical reduction process for uranium oxides in molten salt. During the electrolysis, the evolution of oxygen ion concentration field in molten salt continuum appears from porous metallic layer to open bulk salt. Despite the important role affecting process throughput, its effect coupled with controlled salt movement was not adequately investigated. To capture the reactive oxygen ion transport phenomena, a multidimensional reduction model based on smoothed particle hydrodynamics (SPH) was combined with the advection-diffusion model. A pelletized oxide fuel bed capturing interconnected salt continuum is considered as a reactant material geometry, which allows forced convective delivery of molten salt through the reactant materials with a relatively low pressure head. Here, in this study, reduction time of a pelletized-fuel bed was quantified with respect to key design parameters of the reactant material configuration. The simulation results demonstrated the advantage of salt convection which effectively removes oxygen ion products from the reactant materials and consequently accelerates the reduction process. Moreover, the reduction-time correlation of a single pelletized fuel was developed as a function of relevant dimensionless parameters and was extended to the application for a pelletized-fuel bed. Finally, several insights and implications in the use of a pelletized oxide fuel were presented. The developed SPH-based framework enabled multi-physics analysis of governing dynamics in appreciating and screening candidate reactant material configurations in a cost-effective manner.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2026

Reservoir-scale model of geologic hydrogen production from serpentinization: Cyclic injection in a dual-permeability fracture-matrix system

Geologic hydrogen (GeoH 2 ) from serpentinization is a promising low-carbon resource, but its reservoir-scale behavior remains poorly understood. We develop a dual-permeability reactive transport model for an injector–producer well pair in ultramafic rock that couples multiphase flow, heat transfer, geochemistry, and porosity–permeability evolution. Here, the model is calibrated to olivine flow-through experiments and upscaled to two-year long simulations with continuous injection and cyclic injection with shut-in-to-injection ratios (SIR = 1, 0.5, 0.1). Olivine reacts along high-flux pathways to form lizardite and magnetite, increasing pH; H 2 (aq) and H 2 (g) peak early and then decline as exsolution and advective export outpace local generation. Continuous injection yields the highest cumulative H 2 but the lowest water-use efficiency (1.138 x 10 –6 mol/kgw). Cyclic injection increases this ratio to 1.35 x 10 –6 , 1.377 x 10 –6 , and 1.182 x 10 –6 mol/kgw for SIR = 1, 0.5, and 0.1, respectively; SIR = 0.5 provides a ~20% improvement over continuous injection and the best compromise for pilot design.

08 HYDROGEN↗

DOE OSTI2021

The simulation of 3D hypervelocity spallation using a hydrocode PAGOSA with FLIP+MPM

n this work, a hydrocode PAGOSA with FLIP+MPM is presented and exercised to investigate the fracture in ductile material. The merit of PAGOSA with FLIP+MPM to solve the advection problem is first illustrated by a solid piston periodically moving in a sealed tube with air. Furthermore, the ability of PAGOSA with FLIP+MPM to capture the fracture in material is shown by a simple stretching fracture in ductile material. In both of two benchmark problems, the PAGOSA results and analytical solutions are also presented for comparison. Then PAGOSA with FLIP+MPM is used to model complex spall in ductile material, which is a challenging problem in engineering applications. The convergences of PAGOSA with FLIP+MPM—based on both the mesh size and the marker density—are investigated by monitoring free surface velocity. To further show the ability of PAGOSA with FLIP+MPM to predict fracture in ductile material, the numerical results are compared with the experimental results and other published numerical results. Moreover, the effect of the spall parameter in PAGOSA with FLIP+MPM on the numerical simulation is also analyzed by investigating the free surface velocity. Finally, the effects of the peak compressive stress, the tensile strain rate, and the loading rate on the spallation are further investigated. The numerical results show that PAGOSA with FLIP+MPM can improve PAGOSA's performance when applied to predicting fracture in ductile materials, and is robust enough to accurately predict spall fracture in ductile materials.

42 ENGINEERING↗

DOE OSTI2020

Temporal flow variations interact with spatial physical heterogeneity to impact solute transport in managed river corridors

The interactions between surface water and groundwater in river corridors lead to temporal fluctuations in subsurface water fluxes which have a critical role on solute transport dynamics. Here, we develop a framework to analyze the relative impacts of different temporal frequencies of the flow field in a spatially heterogeneous aquifer on solute transport. Our analysis indicates that the advection-dispersion equation behaves as a low-pass filter by wiping out the effect of high-frequency velocity fluctuations on the first two spatial moments of the solute plume, namely its center of mass and spreading. The concepts discussed in the theoretical analysis are then applied to understand solute transport dynamics at the 300 Area of the Hanford site (USA) adjacent to the Columbia River. We examine the temporal behavior of the solute plume's spatial moments for different temporal frequencies utilizing geostatistical parameters estimated in the 300 Area. Due to the proximity to the Columbia river, groundwater fluxes at the Hanford site are highly dynamic resulting in a large range of characteristic temporal frequencies. Nonetheless, similar to the theoretical analysis, our results show that the effect of high-frequency fluctuations is filtered, with most of the solute transport dynamics being controlled by fluctuations characterized by a large characteristic period.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

High-order partitioned spectral deferred correction solvers for multiphysics problems

We present an arbitrarily high-order, conditionally stable, partitioned spectral deferred correction (SDC) method for solving multiphysics problems using a sequence of pre-existing single-physics solvers. This method extends the work in [1], [2], which used implicit-explicit Runge-Kutta methods (IMEX) to build high-order, partitioned multiphysics solvers. We consider a generic multiphysics problem modeled as a system of coupled ordinary differential equations (ODEs), coupled through coupling terms that can depend on the state of each subsystem; therefore the method applies to both a semi-discretized system of partial differential equations (PDEs) or problems naturally modeled as coupled systems of ODEs. The sufficient conditions to build arbitrarily high-order partitioned SDC schemes are derived. Based on these conditions, various of partitioned SDC schemes are designed. The stability of the first-order partitioned SDC scheme is analyzed in detail on a coupled, linear model problem. We show that the scheme is conditionally stable, and under conditions on the coupling strength, the scheme can be unconditionally stable. We demonstrate the performance of the proposed partitioned solvers on several classes of multiphysics problems with moderate coupling strength. They include a stiff linear system of ODEs, advection-diffusion-reaction systems, and fluid-structure interaction problems with both incompressible and compressible flows, where we verify the design order of the SDC schemes and study various stability properties. We also directly compare the accuracy, stability, and cost of the proposed partitioned SDC solver with the partitioned IMEX method in [1], [2] on this suite of test problems. The results suggest that the high-order partitioned SDC solvers are more robust than the partitioned IMEX solvers for the numerical examples considered in this work, while the IMEX methods require fewer implicit solves.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Multi-stage preconditioners for thermal–compositional–reactive flow in porous media

We present a family of multi-stage preconditioners for coupled thermal-compositional-reactive reservoir simulation problems. The most common preconditioner used in industrial practice, the Constrained Pressure Residual (CPR) method, was designed for isothermal models and does not offer a specific strategy for the energy equation. For thermal simulations, inadequate treatment of the temperature unknown can cause severe conver-gence degradation. When strong thermal diffusion is present, the energy equation exhibits significant elliptic behavior that cannot be accurately corrected by CPR's second stage. In this work, we use Schur-complement decompositions to extract a temperature subsystem and apply an Algebraic MultiGrid (AMG) approximation as an additional preconditioning stage to improve the treatment of the energy equation. We present results for several two-dimensional hot air injection problems using an extra heavy oil, including challenging reactive In-Situ Combustion (ISC) cases. We show improved performance and robustness across different thermal regimes, from advection dominated (high Péclet number) to diffusion dominated (low Péclet number). The number of linear iterations is reduced by 40–85% compared to standard CPR for both homogeneous and heterogeneous media, and the new methods exhibit almost no sensitivity to the thermal regime.

42 ENGINEERING↗

DOE OSTI2022

An optimization method for chaotic turbulent flow

Evidence indicates that quantities-of-interest in some turbulent flows can be controlled despite the overall chaotic dynamics. It is typically thought that this is via relatively deterministic, larger-scale components of the turbulence. However, finding such controls, if they exist, is challenging because chaos causes sensitivity gradients to explode and the search space to become intractably non-convex. This challenge is analyzed, and a penalty method is introduced to cope with it. In the new approach, the time domain is broken into segments approximately matching the chaos time scales, so that the solution within each segment is both physical and relatively deterministic. The initial condition of each segment is included in an adjoint-based gradient optimization, which temporarily introduces artificial Δq discontinuities in the overall solution. The optimization then proceeds in stages with increasing penalization of Δq. The method is developed and illustrated for a logistic map, the Lorenz Equation, and an advection augmented Kuramoto–Sivashinsky Equation. These examples show how the Δq temporarily increases the search scale prior to the strong Δq → 0 penalization that recovers a physical solution. It is then applied to turbulent Kolmogorov flow, for which it also far outperforms a standard adjoint-based gradient search. Finally, the utility of such an optimized chaotic solution is discussed.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Conservative DG method for the micro-macro decomposition of the Vlasov–Poisson–Lenard–Bernstein model

The micro-macro (mM) decomposition approach is considered for the numerical solution of the Vlasov– Poisson–Lenard–Bernstein (VPLB) system, which is relevant for plasma physics applications. In the mM approach, the kinetic distribution function is decomposed as $f$ = $\mathscr{E}$[$ρ_f$] + g , where $\mathscr{E}$ is a local equilibrium distribution, depending on the macroscopic moments $ρ_f$ = $∫_{\mathbb{R}}$ $efdv$ = $\langle$$ef$$\rangle$$_{\mathbb{R}}$, where e = (1, $v$, $\frac{1}{2}$ $v^2$) T , and $g$, the microscopic distribution, is defined such that $\langle$$eg$$\rangle$$_{\mathbb{R}}$ = 0. We aim to design numerical methods for the mM decomposition of the VPLB system, which consists of coupled equations for $ρ_f$ and $g$. To this end, we use the discontinuous Galerkin (DG) method for phase-space discretization, and implicit-explicit (IMEX) time integration, where the phase-space advection terms are integrated explicitly and the collision operator is integrated implicitly. We give special consideration to ensure that the resulting mM method maintains the $\langle$$eg$$\rangle$$_{\mathbb{R}}$ = 0 constraint, which may be necessary for obtaining (i) satisfactory results in the collision dominated regime with coarse velocity resolution, and (ii) unambiguous conservation properties. The constraint-preserving property is achieved through a consistent discretization of the equations governing the micro and macro components. Here, we present numerical results that demonstrate the performance of the mM method. The mM method is also compared against a corresponding DG-IMEX method solving directly for $f$.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

A gradient-based deep neural network model for simulating multiphase flow in porous media

We report simulation of multiphase flow in porous media is crucial for the effective management of subsurface energy and environment-related activities. The numerical simulators used for modeling such processes rely on spatial and temporal discretization of the governing mass and energy balance partial-differential equations (PDEs) into algebraic systems via finite-difference/volume/element methods. These simulators usually require dedicated software development and maintenance, and suffer low efficiency from a runtime and memory standpoint for problems with multi-scale heterogeneity, coupled-physics processes or fluids with complex phase behavior. Therefore, developing cost-effective, data-driven models can become a practical choice, and in this work, we choose deep learning approaches as they can handle high dimensional data and accurately predict state variables with strong nonlinearity. In this paper, we describe a gradient-based deep neural network (GDNN) constrained by the physics related to multiphase flow in porous media. We tackle the nonlinearity of flow in porous media induced by rock heterogeneity, fluid properties, and fluid-rock interactions by decomposing the nonlinear PDEs into a dictionary of elementary differential operators. We use a combination of operators to handle rock spatial heterogeneity and fluid flow by advection. Since the augmented differential operators are inherently related to the physics of fluid flow, we treat them as first principles prior knowledge to regularize the GDNN training. We use the example of pressure management at geologic CO 2 storage sites, where CO 2 is injected in saline aquifers and brine is produced, and apply GDNN to construct a predictive model that is trained with physics-based simulation data and emulates the physics process. We demonstrate that GDNN can effectively predict the nonlinear patterns of subsurface responses, including the temporal and spatial evolution of the pressure and saturation plumes. We also successfully extend the GDNN to convolutional neural network (CNN), namely gradient-based CNN (GCNN), and validate its capability to improve the prediction accuracy. GDNN has great potential to tackle challenging problems that are governed by highly nonlinear physics and enable the development of data-driven models with higher fidelity.

42 ENGINEERING↗

DOE OSTI2022

Assessment of diffuse-interface methods for compressible multiphase fluid flows and elastic-plastic deformation in solids

This work describes three diffuse-interface methods for the simulation of immiscible, compressible multiphase fluid flows and elastic-plastic deformation in solids. The first method is the localized-artificial-diffusivity approach of Cook, Subramaniam et al., and Adler and Lele, in which artificial diffusion terms are added to the individual phase mass fraction transport equations and are coupled with the other conservation equations. The second method is the gradient-form approach that is based on the quasi-conservative method of Shukla et al., in which the diffusion and sharpening terms (together called regularization terms) are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations. The third approach is the divergence-form approach that is based on the fully conservative method of Jain et al., in which the regularization terms are added to the individual phase volume fraction transport equations and are coupled with the other conservation equations. In the present study, all three diffuse-interface methods are used in conjunction with a four-equation, multicomponent mixture model, in which pressure and temperature equilibria are assumed among the various phases. The primary objective of this work is to compare these three methods in terms of their ability to: maintain constant interface thickness throughout the simulation; conserve mass, momentum, and energy; and maintain accurate interface shape for long-time integration. The second objective of this work is to consistently extend these methods to model interfaces between solid materials with strength. To assess and compare the methods, they are used to simulate a wide variety of problems, including (1) advection of an air bubble in water, (2) shock interaction with a helium bubble in air, (3) shock interaction and the collapse of an air bubble in water, and (4) Richtmyer–Meshkov instability of a copper–aluminum interface. The current work focuses on comparing these methods in the limit of relatively coarse grid resolution, which illustrates the true performance of these methods. In conclusion, this is because it is rarely practical to use hundreds of grid points to resolve a single bubble or drop in large-scale simulations of engineering interest.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

gLaSDI: Parametric physics-informed greedy latent space dynamics identification

A parametric adaptive physics-informed greedy Latent Space Dynamics Identification (gLaSDI) method is proposed for accurate, efficient, and robust data-driven reduced-order modeling of high-dimensional nonlinear dynamical systems. In the proposed gLaSDI framework, an autoencoder discovers intrinsic nonlinear latent representations of high-dimensional data, while dynamics identification (DI) models capture local latent-space dynamics. Here, an interactive training algorithm is adopted for the autoencoder and local DI models, which enables identification of simple latent-space dynamics and enhances accuracy and efficiency of data-driven reduced-order modeling. To maximize and accelerate the exploration of the parameter space for the optimal model performance, an adaptive greedy sampling algorithm integrated with a physics-informed residual-based error indicator and random-subset evaluation is introduced to search for the optimal training samples on the fly. Further, to exploit local latent-space dynamics captured by the local DI models for an improved modeling accuracy with a minimum number of local DI models in the parameter space, a -nearest neighbor convex interpolation scheme is employed. The effectiveness of the proposed framework is demonstrated by modeling various nonlinear dynamical problems, including Burgers equations, nonlinear heat conduction, and radial advection. The proposed adaptive greedy sampling outperforms the conventional predefined uniform sampling in terms of accuracy. Compared with the high-fidelity models, gLaSDI achieves 17 to 2,658× speed-up with 1 to 5% relative errors.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Dyn$\mathrm{AMO}$: Multi-agent reinforcement learning for dynamic anticipatory mesh optimization with applications to hyperbolic conservation laws

Here we introduce DynAMO, a reinforcement learning paradigm for Dynamic Anticipatory Mesh Optimization. Adaptive mesh refinement is an effective tool for optimizing computational cost and solution accuracy in numerical methods for partial differential equations. However, traditional adaptive mesh refinement approaches for time-dependent problems typically rely only on instantaneous error indicators to guide adaptivity. As a result, standard strategies often require frequent remeshing to maintain accuracy. In the DynAMO approach, multi-agent reinforcement learning is used to discover new local refinement policies that can anticipate and respond to future solution states by producing meshes that deliver more accurate solutions for longer time intervals. By applying DynAMO to discontinuous Galerkin methods for the linear advection and compressible Euler equations in two dimensions, we demonstrate that this new mesh refinement paradigm can outperform conventional threshold-based strategies while also generalizing to different mesh sizes, remeshing and simulation times, and initial conditions.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Anti-symmetric and positivity preserving formulation of a spectral method for Vlasov-Poisson equations

We analyze the anti-symmetric properties of a spectral discretization for the one-dimensional Vlasov-Poisson equations. The discretization is based on a spectral expansion in velocity with the symmetrically weighted Hermite basis functions, central finite differencing in space, and an implicit Runge Kutta integrator in time. The proposed discretization preserves the anti-symmetric structure of the advection operator in the Vlasov equation, resulting in a stable numerical method. We apply such discretization to two formulations: the canonical Vlasov-Poisson equations and their continuously transformed square-root representation. The latter preserves the positivity of the particle distribution function. We derive analytically the conservation properties of both formulations, including particle number, momentum, and energy, which are verified numerically on the following benchmark problems: manufactured solution, linear and nonlinear Landau damping, two-stream instability, bump-on-tail instability, and ion-acoustic wave.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Generative AI models for learning flow maps of stochastic dynamical systems in bounded domains

Simulating stochastic differential equations (SDEs) in bounded domains, presents significant computational challenges due to particle exit phenomena, which requires accurate modeling of interior stochastic dynamics and boundary interactions. Despite the success of machine learning-based methods in learning SDEs, existing learning methods are not applicable to SDEs in bounded domains because they cannot accurately capture the particle exit dynamics. We present a unified hybrid data-driven approach that combines a conditional diffusion model with an exit prediction neural network to capture both interior stochastic dynamics and boundary exit phenomena. Our ML model consists of two major components: a neural network that learns exit probabilities using binary cross-entropy loss with rigorous convergence guarantees, and a training-free diffusion model that generates state transitions for non-exiting particles using closed-form score functions. The two components are integrated through a probabilistic sampling algorithm that determines particle exit at each time step and generates appropriate state transitions. Here, the performance of the proposed approach is demonstrated via three test cases: a one-dimensional simplified problem for theoretical verification, a two-dimensional advection-diffusion problem in a bounded domain, and a three-dimensional problem of interest to magnetically confined fusion plasmas.

Bounded domains↗