arXiv subjects

Ehsan Roohi

Publications and source records attributed to Ehsan Roohi.

At least 19 recordsLinked to original sources

arXiv2026

Task-preserving neural segmentation of overlapping shocks and vortex cores in compressible flows

Shock fronts and vortex cores often coexist and overlap in compressible flows, where walls, wakes and shear layers also produce strong gradients. Refining a network to detect one structure can therefore degrade its prediction of the other without revealing the loss in the optimized score. We present a task-preserving formulation for simultaneous shock and vortex-core segmentation. The experiments use two solvers and include supersonic diamond-airfoil flows at several incidences and Reynolds numbers, together with circular- and elliptical-cylinder flows. A shared primitive encoder feeds separate shock and vortex decoders with independent sigmoid outputs, allowing the two classes to overlap. Adaptation is confined to the relevant branch: zero-initialized adapters supply rotational diagnostics only to the vortex decoder, while corrected shock supervision updates only the shock decoder. All dependencies of the protected output remain fixed, and bitwise equality is verified on every evaluation field. Compression and conservation-jump (Rankine--Hugoniot) signatures provide weak shock supervision; rotation and topology provide vortex candidates. Analytical oblique-shock rays, Billig's bow-shock correlation and an isentropic vortex supply references independent of these labels. Under the same corrected-target budget, the restricted model and a capacity-matched shared-decoder U-Net obtain comparable shock agreement. Their airfoil vortex-core Dice overlap scores, however, are 0.83 and 0.08, respectively. A soft retention penalty recovers most of the U-Net's lost core agreement. The frozen shock-adapted models locate the tested analytical oblique-shock rays within 0.003 chord. An additional branch identifies expanding-flow regions, which are distinguished from centred Prandtl--Meyer expansion fans through comparison with ideal shock--expansion theory.

physics.flu-dyn↗

arXiv2026

Transport fidelity and domain of validity of compact Gaussian kinetic representations for rarefied flows

Compact representations of rarefied flows must retain nonequilibrium transport information while identifying their range of validity. We investigate a common localized-Gaussian strategy for discrete-velocity-method (DVM) states in monatomic normal shocks and lid-driven cavities. The strategy is specialized to the available kinetic state: a positive phase-space mixture represents shock distributions and regenerates their moment hierarchy by quadrature, whereas a shared-support physical-space map represents 20 cavity fields. Localized support, continuous evaluation, transport fidelity, and coefficient-count accounting therefore provide the common structure across the two benchmarks. For separately fitted Mach-3 and Mach-5 shocks, the method gives sub-percent errors in conserved quantities and approximately 1--2\% errors in transport and higher-order moments. At the same 4608-coefficient budget, the tested multilinear grids produce 89--98\% errors in these nonequilibrium quantities. For both cavity cases, the Gaussian map also outperforms matched bilinear and singular-value-decomposition baselines, reducing maximum errors by factors of approximately 7--24. In the Mach-conditioned tests, a correspondence-preserving local basis reduces the withheld Mach-6 distribution error from $42.86\pm5.40\%$ to $11.45\pm0.94\%$ at fixed storage, while its transport errors remain 30--40\%; a normalized-coordinate guard rejects Mach 12 outside the training range. Independent grid studies confirm that these trends are not dominated by DVM discretization error. The results establish localized Gaussian representations as storage-efficient transport-fidelity maps for fitted kinetic states and provide quantitative acceptance criteria for parametric use.

physics.flu-dyn↗

arXiv2026

Bulk-to-Wall Observability in Rarefied Hypersonic Flow: Moment Limits and Incident Half-Range Sufficiency

Wall traction in a rarefied gas is a half-range functional of molecules arriving at and leaving a surface, whereas hybrid solvers, moment methods, and learned wall models often transmit only finite full-range moments. We determine which directional information is lost and what restores the wall functional using direct simulation Monte Carlo (DSMC) of Mach-6 flow over three triangular-protrusion orientations. Output-specialized neural networks interpolate a 57-condition DSMC database. A distinct ExtraTrees regression holds learner capacity, auxiliary features, train/test split, and seeds fixed while comparing the primitive state $S_0$, the momentum-flux-augmented state $S_1$, and the heat-flux-augmented state $S_2$. Adding the momentum-flux tensor $P_{ij}$ reduces aggregate pressure error by 31\% but does not make signed shear transferable. An analytic null-space construction supplies the mechanism: strictly positive distributions can share all full-range moments through degree three while producing different pressure and opposite signed shear because the wall kernel selects the incident half space. A finite-distance off-wall ExtraTrees state $S_{\mathrm{off}}$ shows that partial directionality is useful but representation-dependent. Finally, a parameter-free kinetic reconstruction combines the incident half-range wall-arrival state $S_{\mathrm{HR}}$ with the prescribed diffuse kernel and agrees with both a same-window DSMC tally sharing the incident events and a separate 40,000-step DSMC wall-tally window. The resulting design principle is direct: a rarefied wall closure must preserve the incident normal--tangential correlations required by the target load rather than merely adding higher full-range moments.

physics.flu-dyn↗

arXiv2026

Geometry-native machine learning reconstruction of DSMC moment fields with support monitoring

Direct simulation Monte Carlo (DSMC) resolves rarefied-gas dynamics without a constitutive closure, but finite-sample estimates of macroscopic moments converge at markedly different rates. We develop a non-intrusive, geometry-native machine learning reconstruction of the retained two-dimensional moment hierarchy: number density, two velocity components, translational temperature, three pressure-tensor components, and two heat-flux components. From three sampling blocks, the estimator corrects a structured prior learned from development data with a bounded term computed from the current observation, while preserving additive-moment consistency and the measured zero-frequency content. In cavity development tests, the final observation-conditioned estimator, whose prior is a trained MambaIR restoration network, reduces transverse-heat-flux error to 0.658 and 0.672 times that of a ten-block direct average at two rarefied conditions. For a hypersonic cylinder, a cylinder-centred estimator is fixed before evaluation on six new observation/reference pairs. It improves both global transverse heat flux and near-wall normal heat flux in every pair; the ratios of arithmetic-mean normalised root-mean-square errors (NRMSEs) are 0.846 and 0.793, and the Holm-adjusted one-sided exact probabilities are 0.03125.

physics.data-an↗

arXiv2026

Noise-separated evidence for a slow collective displacement in a rarefied hypersonic bow-shock layer

Time-resolved direct simulation Monte Carlo (DSMC) fields are used to test whether a detached rarefied hypersonic bow shock contains a slow collective displacement that can be separated from correlated particle-sampling fluctuations. Mach-10 rotationally relaxing nitrogen flow over a circular cylinder is analysed for diameter-based Knudsen number $0.01\leq \KnD\leq1$, where $\KnD=λ_\infty/D$, $λ_\infty$ is the freestream mean free path and $D$ is the cylinder diameter. A density half-jump front is extracted on body-normal rays, unsupported solid-side points are excluded, and temporal coarse graining is performed before feature extraction. Persistent and sampling covariance components are compared using a penalized composite-fit score, design-scale cross-validation, block resampling, synthetic controls and complementary full-field matched filters. Corrected field proper orthogonal decomposition (POD) is high rank at every Knudsen number, yet a weak, same-signed angular displacement is resolved at $\KnD=0.01$ and $0.025$. Independent random-seed and simulator-particle-loading repeats recover the angular shape and relaxation time while the raw sampling variance changes with loading. Across the two resolved states the mean density layer broadens by $82\%$, while the angular shapes remain strongly aligned. Density and pressure recover the marker motion most strongly; the reduced Mach-number and translational-temperature participation at $\KnD=0.025$ is evidence consistent with moment-selective weakening, although observable-dependent signal-to-noise remains a possible contributor. The signal is interpreted as a low-pass bow-layer response embedded in broadband kinetic fluctuations, not as a newly discovered discrete oscillation or a demonstrated linear instability. The higher-Knudsen records are not sufficiently sensitive to establish physical disappearance.

physics.flu-dyn↗

arXiv2026

Cross-stream pressure support and the limits of scalar relaxation in rarefied Poiseuille flow

The weak wall-normal pressure variation in pressure-driven rarefied Poiseuille flow is a stringent test of higher-order constitutive models: it is almost invisible in the total-pressure norm, yet it is generated by anisotropic molecular stress. A tangent-form nonlinear coupled constitutive relation (NCCR) reproduces its convex topology, but the physical reason for its quantitative success remains unresolved. We ask whether the constitutive stress relation and reduced streamwise forcing are independently accurate or whether their effects compensate. A direct simulation Monte Carlo (DSMC) campaign is analysed using two-dimensional momentum budgets, a pressure-error norm based on the transverse signal, a matched-outlet-Knudsen comparison and componentwise tests of the pre-elimination NCCR balance. The non-equilibrium wall-normal stress over-supports the measured pressure defect, while streamwise transport of shear stress supplies an opposing correction. The state map, momentum budgets and forcing diagnostics show that neither outlet Knudsen nor outlet Mach number alone organises the pressure amplitude; along the fixed-ratio sequence, rarefaction is accompanied by larger changes in the constitutive diagnostics than in pressure amplitude. The DSMC-inferred stress relation departs from the fixed reduced coefficient, and even the best common scalar closes the dominant shear component far more accurately than the normal components that carry the pressure field. Correcting the coefficient alone can therefore worsen the reconstruction, whereas restoring omitted streamwise-momentum terms reduces the amplitude bias in strongly accelerated cases. The reduced law can remain accurate through stress--momentum compensation, showing that agreement of a weak non-equilibrium observable need not imply correct internal closure mechanics.

physics.flu-dyn↗

arXiv2026

Gaussian kinetic representations of rarefied nonequilibrium flows

Compact representations of rarefied flows must preserve kinetic observables, not only smooth macroscopic fields. We introduce Gaussian kinetic representations for discrete velocity method (DVM)-Shakhov solutions of normal shocks and a lid-driven cavity. A positive log-density phase-space model reconstructs shock velocity distribution functions (VDFs) and their moments, while a moment-field model compresses wall-bounded cavity structure. Log-density training recovers heat flux, stress, and third- and fourth-order shock moments without explicit moment supervision; the cavity representation gives a compact continuous wall-transport map.

physics.flu-dyn↗

arXiv2026

Accelerating Kinetic Fokker-Planck Simulations via a GPU-Native Deep Neural Network Surrogate: Application to Rarefied Internal and Hypersonic External Flows

Particle-based Fokker--Planck (FP) models provide an efficient kinetic alternative to direct simulation Monte Carlo (DSMC) in slip and early transitional gas flow regimes, but advanced cubic-FP closures require repeated cell-wise moment evaluation and small dense linear solves. This work develops and validates a GPU-native neural surrogate that replaces the deterministic cubic-FP closure calculation inside the particle simulation loop. The trained weights are evaluated directly with batched \texttt{CuPy} operations, avoiding CPU--GPU transfers during online deployment. The validation emphasizes quantitative evidence: component-level runtime profiles, break-even cost analysis including offline costs, conservation and stability diagnostics, particle-per-cell sensitivity, a direct time-averaged coefficient audit, and covariance-based entropy-proxy fidelity checks. The Couette case is retained as a compact, dimensionless verification problem, while the main internal-flow validation is a 2D lid-driven cavity tested by complete simulation conditions, including unseen moderately rarefied cases at nominal $Kn=0.5$ and $Kn=1.0$. For the hypersonic cylinder, a particle-moment covariance-based entropy-fidelity audit is performed on the front stagnation line and in the cell-centered near-wall gas layer. The same deployed neural $C/Γ$ closure used for the cylinder flow fields closely reproduces the equilibrium and Gaussian kinetic entropy profiles over the reported front-line and near-wall gas bins; these profiles are used as a relatively exact-FP/ML-FP audit. The study establishes GPU-native learned closure as a practical route to accelerating cubic-FP rarefied-flow solvers, delivering substantial online speedups while retaining the macroscopic, high-order, and entropy-proxy structure of the reference kinetic model.

physics.comp-ph↗

arXiv2026

Machine learning for rarefied gas transport in vacuum and micro/nano systems: promise, pitfalls, and a verification agenda

Machine learning is beginning to influence rarefied-gas modeling at multiple levels, including equation-solving, operator learning, learned collision physics, moment closures, direct simulation Monte Carlo (DSMC) field surrogates, and gas--surface models. This Perspective argues that the central challenge is not demonstration-level success, but trustworthy use under realistic deployment conditions: multiregime Knudsen behavior, stochastic DSMC labels, sharp nonequilibrium structures, uncertain gas--surface interaction, and scarce direct experimental anchors. I classify the main method families by what is learned, distinguish soft physics penalties from structure-preserving designs, and propose evaluation standards based on extrapolation tests, noise-aware metrics, end-to-end cost accounting, and a three-level validation hierarchy. Most current evidence is solver-facing: it demonstrates surrogate fidelity to a teacher solver more often than direct physical fidelity to experiment. The aim is not to dismiss ML for rarefied and vacuum-related gas transport, but to separate what is already credible from what remains provisional, and to define a reporting standard that makes future claims auditable.

physics.flu-dyn↗

arXiv2026

Anti-Fourier heat flux does not certify the fourth-order closure state of a rarefied cavity

Cold-to-hot heat transfer in rarefied cavities is usually treated as a signature of Fourier-law failure. Here it is used to ask whether a correct anti-Fourier heat-flux field certifies the flux-side fourth-order closure state. In a two-dimensional monatomic flow, the heat-flux hierarchy observes the divergence of the composite R26-level tensor $A_{ij}=R^{\cl}_{ij}+Δδ_{ij}/3$, not the tensorial fourth-order anisotropy $R^{\cl}_{ij}$ and scalar fourth-order excess $Δ$ separately. Unlike the one-dimensional shock problem, the null space is not a single algebraic direction: it is the function space of divergence-free symmetric tensor fields, including an exactly invisible out-of-plane channel $A_{zz}$. DSMC data for argon lid-driven cavities show that the size of the anti-Fourier region is strongly regime dependent: it is suppressed when the lid speed is increased from $100$ to $200\,\mathrm{m\,s^{-1}}$, but enlarged when the Knudsen number is increased from $0.05$ to $0.10$. In all cases, the anti-Fourier channel is primarily tensorial, while scalar-excess effects remain a smaller local modulation. Hidden Airy and out-of-plane states, scaled relative to the measured RMS composite tensor, change $R^{\cl}$ and $Δ$ by order-one amounts while leaving the in-plane heat-flux observable below the seed-to-seed statistical resolution, or exactly unchanged for the $A_{zz}$ mode. These shifted states satisfy necessary scalar Cauchy and contracted fourth-order Gram-positivity checks. Thus anti-Fourier heat-flux agreement is a physical validation target, but it is not a certificate of full R26-level closure recovery.

physics.flu-dyn↗

arXiv2026

Closure-channel identifiability and two-channel recovery in monatomic kinetic normal shocks

Residual agreement in a kinetic or moment equation does not automatically identify every higher-order closure variable entering a nonequilibrium shock. We formulate this issue as an observability problem for the fourth-order closure content of monatomic normal shocks and follow it through a hierarchy of collision models and diagnostics. The kinematic part of the result is independent of the collision operator: the one-dimensional heat-flux budget observes the projected fourth-order channel $S=R^{\cl}_{xx}+Δ/3$, not the tensorial R26-level moment $R^{\cl}_{xx}$ separately from the scalar fourth-order excess $Δ$. The observation map therefore has a one-dimensional null space, so a heat-flux residual can be small while the split between tensorial anisotropy and isotropic tail intensity remains wrong. A DVM-consistent scalar-excess budget supplies the missing channel and gives the two-channel reconstruction $R^{\cl}_{xx}=S-Δ/3$ without direct $R^{\cl}_{xx}$ data. Across BGK shocks at Mach 2--5, this reduces the active-zone $R^{\cl}_{xx}$ error from about $63$--$64\%$ to $2.4$--$4.1\%$. Sparse scalar-excess interpolation is used only as an information-reduction test: a representative 24-probe operating point gives $R^{\cl}_{xx}$ errors below $4.5\%$, and below $4.7\%$ with $1\%$ probe noise. Collision-model diagnostics then separate the invariant observation channel from the model-dependent source law. Shakhov changes the heat-flux relaxation to the correct Prandtl number but is neutral in the even $|\boldsymbol c|^4$ scalar-excess source; a direct discrete Shakhov channel check recovers $S$, $Δ$ and $R^{\cl}_{xx}$ with errors $6.4\times10^{-4}$, $2.1\times10^{-7}$ and $1.0\times10^{-3}$, respectively.

astro-ph.HE↗

arXiv2026

Tail observability and fourth-order closure recovery in physics-informed neural networks for Bhatnagar-Gross-Krook normal shocks

Closure-level accuracy in neural kinetic shock solvers is not guaranteed by accurate density, velocity and temperature profiles, because the relevant observables are velocity-weighted projections of the nonequilibrium distribution. We study this observability problem for one-dimensional Bhatnagar--Gross--Krook (BGK) shock waves using a positive macro--micro physics-informed neural network (PINN) in which the distribution is represented as a local Maxwellian multiplied by a bounded exponential correction. Independent discrete-velocity method (DVM) references are used for validation. Shock-tube tests show that sparse joint anchoring of heat flux and normal stress stabilises the primary nonequilibrium layer, whereas residual-only, macro-only and single-moment variants fail in distinct ways. In a stationary Mach-2 normal shock, a flux-locked compact model recovers $ρ$, $u_x$, $T$, $q_x$, $σ_{xx}$ and $m_{xxx}^{cl}$, but leaves $R_{xx}^{cl}$ with order-unity error. DVM diagnostics show that $R_{xx}^{cl}$ is controlled by a sign-changing, tail-weighted cancellation weakly observed by lower moments. A shock-local closure correction aligned with this missing projection reduces the relative $R_{xx}^{cl}$ error to $1.12\times10^{-1}$ while preserving the lower moments. A common-initialisation ablation shows that optional distribution-function probe losses are diagnostic rather than constitutive. A supplementary DVM--PINN comparison for the scalar fourth-order excess $Δ$ shows that the obstruction is anisotropic, sign-changing tail weighting rather than fourth-order polynomial degree alone.

physics.flu-dyn↗

arXiv2026

Transport-preserving neural ab initio scattering kernels for rarefied binary gas mixtures

Neural surrogates for molecular scattering provide a route to continuously evaluable and differentiable direct simulation Monte Carlo (DSMC) collision kernels, but a small pointwise deflection-angle error is not sufficient evidence that a learned map is kinetically reliable. Diffusion, viscosity, representative collision rates, angular redistribution, and mixture relaxation are nonlinear functionals of the same scattering measure. We therefore develop a multiscale validation framework for neural ab initio scattering kernels that combines angular regression, transport cross sections, Ohr-style representative quantities, cumulative angular measures, Fourier spectral content, impact-grid and angular-noise robustness, loss-ablation diagnostics, and three solver-level DSMC mixture tests. The framework is demonstrated on a refined argon--argon Jäger table and on helium--argon ab initio EPAPS data of Sharipov and Benites represented by a neural equal-area scattering surrogate. For He--Ar over $\Er/\kb\ge10~\mathrm{K}$, the surrogate preserves $\QD$, $\Qmu$, $\Qmu/\QD$, $\RCS$, and $\SigVSS$ within $0.75\%$, $1.37\%$, $0.84\%$, $1.21\%$, and $1.46\%$, respectively. The cumulative angular measure agrees within $1.43\%$, the median relative $L_2$ error of $χ(q)$ is $3.4\times10^{-3}$, and the high-mode spectral-energy ratio is essentially unbiased. The same neural He--Ar kernel is then embedded in periodic DSMC mixture problems that separately probe mass diffusion, momentum diffusion, and two-dimensional field-level mixing. A sinusoidal composition mode is reproduced over three independent realizations with a mean normalized-history error of $1.28\pm0.22\%$ and $D_{\NN}/D_{\EPAPS}=1.015\pm0.013$. A transverse shear wave is reproduced with a $1.58\%$ history error and $ν_{\NN}/ν_{\EPAPS}=0.989$.

physics.chem-ph↗

arXiv2026

Resolving Cryogenic and Hypersonic Rarefied Flows via Deep Learning-Accelerated Lennard-Jones DSMC

Integrating the physically realistic Lennard--Jones (LJ) potential into Direct Simulation Monte Carlo (DSMC) remains challenging because the long-range potential complicates collision-rate definition and makes repeated scattering-angle evaluation expensive. This study develops an LJ--DSMC framework built around two methodological advances and a transport-level validation of the resulting collision kernel. First, a generalized collision-selection treatment is formulated for Bird's DSMC algorithms (DSMC1, DSMC1S, and DS2V) through a Variable Effective Diameter (VED) model obtained from local Chapman--Enskog viscosity matching. This viscosity-consistent pair-selection model provides a finite DSMC collision-rate closure for the LJ potential and is validated in helium and argon normal shocks, cryogenic supersonic Couette flow, and hypersonic cylinder flows. The results show agreement with VHS in high-temperature repulsive regimes, but reveal clear LJ effects, including reduced shear stress and larger cryogenic wakes, when attractive forces become important. Second, the computational bottleneck of the accepted LJ binary-scattering step is removed by training a Deep Operator Network (DeepONet) to predict the LJ deflection angle from high-fidelity scattering data, replacing the numerical Matsumoto--Koura integral while preserving the standard elastic post-collision update. The surrogate gives a bulk mean wrapped-angle error of $1.6\times10^{-3}\,\mathrm{rad}$ and a 99th-percentile error of $9.9\times10^{-3}\,\mathrm{rad}$, accelerates the collision subroutine by 40\%, and reduces total wall time by 36\%. Finally, the same DeepONet--LJ scattering kernel is tested beyond viscosity-controlled flows through diffusion benchmarks.

physics.flu-dyn↗

arXiv2026

Prescribed Wall-Heat-Flux Control of Blockage and Impulse in a Rarefied Micro-Nozzle

Prescribed wall heat flux provides an active route for controlling rarefied micro-nozzle flows, but its effect is governed by the coupled wall--bulk thermal response rather than by the imposed flux alone. This work uses direct simulation Monte Carlo (DSMC) simulations to study nitrogen flow in a converging--diverging micro-nozzle with cooling, adiabatic, and heating applied on the diverging wall. The imposed heat flux is scaled by the inlet kinetic-energy flux, $E=0.5ρ_i U_i^3$, giving $Q_w/E$ from $-10.5\%$ to $97.3\%$; this range spans moderate cooling, weak-to-intermediate heating, and a near-unity thermal-forcing regime. Wall and mass-flux-weighted bulk temperature profiles, film-temperature-based Nusselt and local-viscosity Brinkman-type diagnostics, gradient-length Knudsen indicators, mass-flux thickness, thrust decomposition, and proper orthogonal decomposition (POD) of signed numerical schlieren are analyzed. The results show that heating creates strong wall--bulk stratification: the wall temperature exceeds five times the inlet value, while the bulk temperature responds more gradually. Cooling cases contain locations where $T_w-T_b$ changes sign, making the local Nusselt-type response singular; the raw singular behavior is retained for diagnosis and a validity mask is used only for comparative plotting. Heating contracts the effective mass-carrying core, increasing aerodynamic blockage and reducing mass flow rate. However, strong heating increases the specific impulse from $156$ s to $201$ s because thermal and pressure-thrust augmentation outweigh the mass-flow penalty. The internal compression feature evolves into a finite viscous--thermal compression zone, and its heat-flux-parametric response remains low-dimensional, with the first two POD modes capturing more than $97\%$ of the fluctuation energy.

physics.flu-dyn↗

arXiv2026

Rarefaction-induced inflation and similarity breakdown of hypersonic bow shocks over a circular cylinder

Rarefied hypersonic bow shocks over blunt bodies inflate as the Knudsen number increases, but it remains unclear whether this inflation is a simple shift and broadening of one common shock layer or a multi-scale change of the macroscopic and internal-energy fields. We address this question using direct simulation Monte Carlo (DSMC) data for Mach-10 flow over a circular cylinder in argon and nitrogen over $Kn_\infty \approx 0.01$--$1$, together with a Mach-number sweep at $Kn_\infty=0.01$. At low rarefaction, a ray-based density-gradient ridge gives a reproducible bow-shock location and agrees with an independent schlieren-based shock-wave-detection method. As $Kn_\infty$ increases, this ridge is replaced by a broad kinetic compression layer, so the high-Knudsen cases are analysed using profile-based standoff and thickness metrics rather than by imposing a visual shock line. The Knudsen- and Mach-number sweeps separate two mechanisms. At fixed $M_\infty$, the continuum normal-shock density ratio provides a useful low-rarefaction reference compression scale, whereas the measured standoff growth is governed primarily by the kinetic mean free path; the effective density thickness shows an intermediate minimum before increasing in the diffuse regime. At fixed low $Kn_\infty$, changing $M_\infty$ mainly changes compression strength and curvature, preserving a coherent attached-layer structure. Density-registered profiles and shock-attached proper orthogonal decomposition (POD) show that, within the present maximum-density-gradient registration, density becomes nearly rank one, whereas Mach number and thermal variables retain independent modal content. Rarefied bow-shock inflation is therefore a coupled compression--relaxation process, not a single-scale rescaling of a continuum-like shock.

physics.flu-dyn↗

arXiv2026

Shock-Centered Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows

We examine the structure of Direct Simulation Monte Carlo (DSMC)-resolved internal compression layers in rarefied micro-nozzle flows and show that their apparent parametric complexity is largely a registration and finite-thickness scaling effect. A density-gradient diagnostic identifies the compression-layer station $x_s$, while a jump-based thickness $δ_j=Δρ/\max|\partialρ/\partial x|$ defines a shock-centered coordinate $ξ_j=(x-x_s)/δ_j$. In physical coordinates, the leading proper orthogonal decomposition (POD) mode of the centerline density profiles captures only $83.33\%$ of the fluctuation energy, whereas the jump-scaled coordinate increases this value to $98.33\%$. A two-dimensional shock-window POD further confirms that this compactness is not a centerline artifact: in the registered $(ξ_j,η)$ frame, the first density mode captures $94.98\%$ and the first two modes capture $99.05\%$ of the fluctuation energy. The same region is identified by density-gradient and gradient-length Knudsen-number diagnostics, linking the reduced representation to localized short-gradient-length rarefaction rather than to shock motion alone. We then use this structure as an inductive bias in a shock-aligned Fusion--Deep Operator Network (DeepONet) surrogate for density, velocity components, temperature, Mach number, and pressure. For held-out back-pressure cases, density, temperature, and pressure errors remain below $6.8\%$, $4.3\%$, and $6.8\%$, respectively, and the hardest case reduces the shock-window mean error from $9.75\%$--$22.27\%$ for standard baselines to $4.51\%$. The results show that improved prediction follows from the reduced shock-centered structure of the DSMC fields rather than from network capacity alone.

physics.flu-dyn↗

arXiv2026

Physics Constrained Neural Collision Operators for Variable Hard Sphere Surrogates and Ab Initio Angle Prediction in Direct Simulation Monte Carlo

The Direct Simulation Monte Carlo (DSMC) method is the gold standard for non-equilibrium rarefied gas dynamics, yet its computational cost can be prohibitive, especially for near-continuum regimes and high-fidelity \emph{ab initio} potentials. This work develops a unified, physics-constrained neural-operator framework that accelerates DSMC while preserving physical invariants and stochasticity required for long-time kinetic simulations. First, we introduce a local neural collision kernel replacing the phenomenological Variable Hard Sphere (VHS) model. To overcome the variance suppression and artificial cooling inherent to purely deterministic regression surrogates, we augment inference with a physics-constrained stochastic layer. Controlled latent-noise injection restores thermal fluctuations, while cell-wise moment-matching strictly enforces momentum and kinetic-energy conservation. Remarkably, this operator exhibits zero-shot spatial and thermodynamic generalization: a model trained exclusively on 1D Couette flow accurately simulates a complex 2D lid-driven cavity, capturing high-order non-equilibrium moments without retraining.Second, to bypass the extreme cost of quantum-mechanical scattering, we develop a dedicated \emph{ab initio} neural operator for the Jäger interaction potential. Trained via a \emph{physics harvesting} strategy on large-scale collision pairs, it efficiently captures the high-energy scattering dynamics dominating hypersonic regimes. Validated on a Mach~10 rarefied argon flow over a cylinder, the framework reproduces transport behaviors and shock features with high fidelity, achieving an approximate 20\% cost reduction relative to direct numerical integration.

physics.comp-ph↗