ALT High-fidelity Reynolds-averaged Navier–Stokes (RANS) simulations remain a standard tool for aerodynamic analysis, yet each solve on an unstructured mesh is computationally expensive, making many-query tasks such as design exploration, optimization, and multi-condition evaluation costly. Neural operators provide mesh-flexible surrogates for mapping geometry and operating conditions to flow fields; however, in many existing architectures, global parameters such as the freestream state and design variables are concatenated with pointwise inputs, leaving their influence on intermediate features implicit. This paper proposes CoPiT, a Conditional Position-induced Transformer that builds on the Position-induced Transformer (PiT) as its geometric backbone and injects a global condition vector through multi-stage feature-wise linear modulation (FiLM), thereby making parametric modulation explicit while preserving geometry-based attention weights. The model is evaluated on two-dimensional AirfRA

ALT We present a coherent axion-electrodynamics extension of the OSIRIS particle-in-cell code and use it to identify and benchmark a parametric axion-photon instability supported by two equal counter-propagating electromagnetic pumps. The module evolves a cell-centered axion field together with a separately stored first-order electromagnetic response on the native staggered OSIRIS grid. Re-examining the previously proposed strictly co-linear branch shows that it is removed when the axion-Maxwell equations are reduced consistently. A closely related standing-wave geometry, however, supports a distinct Floquet instability. We derive the coupled Floquet problem for an equal-amplitude counter-propagating pump pair and obtain a reduced analytic growth rate and cutoff for the dominant long-wavelength envelope branch. For an axion mass-to-pump-frequency ratio of 0.06 and a per-beam vector-potential amplitude of 0.3, simulations at coupling strengths of 0.60, 0.80, and 1.00 reproduce both the grow

ALT We present an HLLD Riemann solver for a multicomponent hypoelastic diffuse-interface model of compressible fluid-solid interaction, with no separately computed interface and a deviatoric stress advanced by an objective hypoelastic rate law outside conservation-law form. The difficulty specific to this model is that the stress evolution is nonconservative and, unlike the familiar volume-fraction terms of Kapila-type models, cannot be left outside the Riemann solve once the shear waves are resolved. The shear coefficient ρ(G+τₓₓ) sets the impedance of the resolved shear waves and so belongs to their eigenstructure. Anchored HLLD carries it inside the solve by evaluating the HLLD fan twice at each face, anchored in turn to each adjacent cell-centered state, with every cell advancing from the flux anchored to its own state. HLL, HLLC, and anchored HLLD form a three-tier hierarchy of increasing wave resolution in one framework. We prove local structural properties: consistency at the recons

ALT This research explores how nanoparticle shapes affect the thermal behavior of nanofluid film boiling along a vertical cylinder, using a Continuous-Species-Transfer method within a Computational Multi-Fluid Dynamics framework. The behavior of nanoparticles in both liquid and vapor phases is modeled, accounting for Brownian motion and thermophoresis. A comprehensive two-dimensional axisymmetric analysis is conducted to investigate the effects of various Al2O3 nanoparticle shapes, including spheres, bricks, blades, cylinders, and platelets, on boiling heat transfer. The results demonstrate that nanoparticle shape has a minimal impact on deposition dynamics but significantly affects kinematic viscosity, particularly for platelet-shaped nanoparticles. Blade-shaped nanoparticles provide substantial enhancement of thermal transport, as indicated by pronounced temperature gradients and increased thermal conductivity. These nanoparticles also improve the Nusselt number, suggesting enhanced boil

ALT Regularized lattice Boltzmann methods improve numerical stability by projecting the nonequilibrium distribution onto its hydrodynamic second-order Hermite sector and filtering the remaining kinetic modes. We introduce a separate relaxation time for the complete complementary kinetic subspace. The resulting extended-regularized lattice Boltzmann method (E-RLBM) interpolates continuously between the Bhatnagar-Gross-Krook and regularized collision operators while retaining a two-rate implementation. A Chapman-Enskog expansion shows that the isothermal Navier-Stokes equations are recovered with kinematic viscosity ν=cₛ²(τ-Δt/2), independently of the kinetic relaxation time τₙₕ, whereas τₙₕ changes higher-order truncation errors. For linear transverse shear, its first effect is a fourth-derivative term whose coefficient depends on the direction of propagation relative to the lattice. This fourth-order coefficient is affine in τₙₕ. For linear shear on D2Q9 and τₙₕ between τ and Δt, it lies b

ALT ADER-DG numerical method with the LST-DG predictor, when used to solve hyperbolic equations with stiff source terms, exhibits properties characteristic of IMEX computational schemes. With increasing stiffness, characterized by the parameter z = νΔtⁿ < 0, the maximum of the Courant number CFLₘₐₓ of the ADER-DG numerical method increases. In the region of strong stiffness |z| ≫ 1, a linear increase in the Courant number CFLₘₐₓ(z) ∼ |z| occurs. In the region of small source terms |z| ≪ 1, the results CFLₘₐₓ(z) transform into known results for the problem CFLₘₐₓ(0) without source terms. In the transition region |z| ∼ 1, a range of insignificant decrease in the Courant number CFLₘₐₓ(z) is discovered. In the linear case, instability is violated precisely when one of the matrix eigenvalues reaches λ=-1, regardless of the phase θ of the numerical solution. A rigorous stability theory of the ADER-DG numerical method for stiff problems for arbitrary degree N of basis polynomials is constructed.

ALT Matrix-product-state (MPS) and quantized tensor-train (QTT) representations offer a promising framework for computational fluid dynamics, with logarithmic run time and memory scaling in mesh size when bond dimensions remain bounded. Existing MPS-based solvers are Eulerian: they compress velocity fields and enforce immersed-body boundary conditions through static masks or body-fitted coordinates. Moving or flexible bodies complicate this approach: deformation requires updating MPS masks every time step, while filamentary vorticity in high-Reynolds-number flows may resist low-rank compression. We propose a complementary approach: compress the Biot–Savart kernel rather than the flow state, evolve vorticity using Lagrangian vortex particles, and represent immersed bodies by bound vortex sheets on Lagrangian surface points. Our main theoretical result is a lifting theorem: QTT rank r of the kernel implies matrix-product-operator (MPO) rank at most 2ᵈ r for the corresponding convolution oper

ALT Machine-learning surrogates in computational science often require not only accurate predictions but also expectations, variances, conserved integrals, and normalization constants. Conventional neural networks, including Kolmogorov–Arnold networks (KANs), generally evaluate these quantities through Monte Carlo sampling or multidimensional quadrature, making repeated inference costly, particularly in high dimensions. We introduce KANs with Tractable Operators for Uncertainty and Constraints (TOUCKANs), whose finite-degree polynomial outer functions yield a decomposable sum–product representation. Under factorizing input measures, expectations and higher moments then reduce algebraically to deterministic recursions over one-dimensional leaf integrals. Independent and shared inner-block variants form a parameter-efficiency hierarchy, and a universal-approximation proof for its most restricted member extends to the complete class. The same deterministic operators allow conserved integrals

ALT We present DeHNSSo-v2, a major update of DeHNSSo-v1 (Westerbeek et al., Comput. Phys. Commun. 302, 2024), the open-source Delft Harmonic Navier-Stokes Solver for nonlinear stability analysis of shear flows. The new release adds a compressible formulation on general two-dimensional body-fitted geometries, automatic grid generation, linear-cost sparse assembly, reusable per-mode factorizations, and Newton pseudo-arclength continuation for high-amplitude nonlinear solutions. The curvilinear formulation preserves the fourth-order accuracy of the discretization on strongly distorted grids, and the compressible solver is confirmed to reproduce DeHNSSo-v1 in the incompressible limit. Validation spans published benchmarks for linear instability of compressible flat-plate boundary layers from Ma=0.5 to Ma=4.5, nonlinear oblique-mode breakdown at Ma=1.6, nonlinear swept-wing crossflow compared with direct numerical simulations, and linear Tollmien-Schlichting wave interaction with a modeled surf

ALT Deterministic solution of the phonon Boltzmann transport equation is costly for two reasons: the distribution depends on high-dimensional phase space, and source iteration converges slowly when scattering is frequent. We address both for the steady linearized gray Callaway model in two dimensions by combining proper generalized decomposition (PGD) with the general synthetic iterative scheme (GSIS). The distribution is a sum of products of a space–azimuth factor and a polar factor. This splitting is intrinsically low-rank: along each characteristic the polar angle only stretches the in-plane optical depth, so the rank is bounded, uniformly in the Knudsen numbers, by the numerical rank of the kernel exp(-τ/sinφ). PGD–GSIS updates the factors against a macroscopic source frozen within each alternating step and refreshed by the GSIS moment equations. A Fourier analysis shows that pure PGD, although implicit in the polar factor, moves macroscopic information only through lagged spatial swee

ALT Sparse regression methods for discovering governing partial differential equations (PDEs) from data are sensitive to observation noise and are not constrained to reproduce the data under forward integration. We address both limitations by performing weak-form discovery in the spatial discretization in which the PDE is solved, learned by differentiating through multistep rollouts anchored at the observed states. The new method, Weak-form Anchored Rollout for PDEs (WARP), produces a machine-learned PDE solver. In this work, we focus on systems amenable to a spectral Galerkin solver. Across eight benchmark fluid and plasma systems, including high-dimensional turbulent simulations, WARP produces numerically stable rollouts from new random initial conditions and substantially improves coefficient recovery, rollout accuracy, and statistical measures compared with a single-step weak-form SINDy baseline.

ALT Simulating high-pressure transcritical flows with phase change is critical for advanced propulsion, yet traditional first-principles approaches, vapor-liquid equilibrium (VLE) calculations, consume most of the runtime and frequently fail to converge. Standalone machine learning models introduce heavy evaluation overhead across large grids, while dynamic tabulation still relies on fragile iterative solvers. To resolve these limitations, this study introduces a hybrid In-Situ Adaptive Tabulation and Artificial Neural Network (ISAT-ANN) framework. A pre-trained ANN replaces the iterative solver during table expansion to guarantee crash-free operation, while ISAT enables rapid data retrieval via local linear interpolation. To eliminate parallel load imbalances, an O(N) greedy load-balancing algorithm redistributes computational tasks across cores. Coupled with Adaptive Mesh Refinement (AMR), the framework was validated on a Mach 5 shock-droplet interaction benchmark. It accurately captured

ALT Discovering governing partial differential equations (PDEs) from observed data is a central inverse problem in computational science and engineering: the goal is not only to predict trajectories, but to identify interpretable symbolic laws that can be analyzed and reused. Existing PDE discovery methods often depend on hand-designed libraries, accurate numerical derivatives, or per-equation symbolic search, making them fragile under sparse observations, noisy data, broad equation families, and unseen symbolic compositions. Here, we introduce FoundPDE, a pretrained data-to-symbol foundation model for PDE discovery. FoundPDE maps discretized spatio-temporal trajectories to symbolic equations with a transformer, uses Fourier and first-order spatial-derivative augmentation to expose complementary trajectory information, refines numerical coefficients, and supports downstream extension with improved generalization through few-shot fine-tuning and hierarchical discovery. On a clean in-domain

ALT At industrial scale the cost of resolvent analysis is set by the linear solves and the assembly and storage of the Jacobian. We present a matrix-free resolvent framework in the Reynolds-averaged Navier-Stokes solver ADflow: automatic differentiation supplies the action of the shifted Jacobian and its Hermitian transpose, preconditioned Krylov solves recycle subspaces across a Lanczos bidiagonalization, and every gain is certified by a backward error. It is applied to the NASA Common Research Model wing at Mach 0.85 and 4.2 degrees on three grid levels of 0.45, 3.6 and 28.8 million cells, the finest with 1.73x10⁸ complex unknowns, 2.3 times the largest reported resolvent computation. On the coarsest level an unstable buffet mode makes the gain peak a resonance; on the finer two the operator is stable and the peak, 1.33x10⁴ at omega = 6.4 and 3.0x10³ near omega = 7.7, is a pseudo-resonance of damped modes whose buffet cells travel outboard at about 0.3 times the free-stream speed. Refine

ALT Filtering by spatial convolution underlies coarse-graining and Large Eddy Simulation, the analysis of multiscale dynamics, and data processing across the sciences. Yet, as commonly practiced on the sphere, it violates a basic consistency requirement: commutation with differential operators, which is necessary for deriving coarse-grained dynamics and preserving the physics across lengthscales. We discuss the root of the problem, which is intrinsic to the curved geometry rather than being a result of metric terms, coordinate system, or numerical grid. A recently proposed generalized spherical convolution is, for a given scalar kernel, the unique linear operator commuting with the radial projection, divergence, and curl. Any consistent linear operator, be it spectral truncation, wavelet transform, diffusion, Green's-function inversion, or a machine-learned convolution, necessarily takes this form. From a simulation of an unstable jet, we demonstrate commutation to within numerical round-o

ALT High-accuracy computation of nonsmooth dynamics is a challenging problem in systems with multiple frictional contacts. This study proposes a general physics-informed neural network framework, termed the mixed leading variable physics-informed neural network (MLV-PINN). By using the governing equations and contact-friction laws as physical constraints, this framework provides common solution approaches for computing nonsmooth dynamics not only in discrete systems but also in continuum systems. Specifically, the network represents accelerations, normal contact forces and friction margins as independent outputs and determines them simultaneously, without first reducing the dynamics to discrete velocity-impulse complementary subproblems. A composite physics-informed loss is constructed from the equations of motion in their original form, contact-friction complementary conditions and a friction-margin consistency relation. To improve stick-slip state identification during PINN optimisation,

ALT For deeper understanding of quantum non-local correlations a new path integral real-time quantum dynamics approach has been developed and applied to the Monte Carlo simulation of the decoherence of pair entangled states in many-body systems in the framework of the “replica trick”. Calculations have been carried out for the Heisenberg-Wigner path integral representation of the entangled state correlation function (ESCF) in the modified unified electron gas model as example. The Wiener-Khinchin transformation of ESCF has been applied to random paths in path integral allowing for the Monte Carlo simulation of ESCF. Presented results include the spin-resolved radial distribution functions, ESCFs and estimations of the decoherence time of the entangled electron pairs due to thermalization and interparticle interaction.

ALT Bone scaffolds must reconcile a macroscale mechanical response with microscale geometric feasibility, yet conventional approaches to their design restrict attainable constitutive properties. This work presents a concurrent two-scale topology optimization framework; a conditional rectified flow generates periodic lattice microstructures, which are then refined in latent space by exact finite-element homogenization sensitivities. The resulting unit-cell geometries and their spatial assignments are jointly optimized under mechanical and feature-size constraints. In a distal rabbit femur benchmark, all eight flow-started refinements produce printable cells with maximum relative errors under 1% across six prescribed engineering moduli. Constructing the implant from a single tiled cell reproduces intact whole-femur compliance within 0.1% and regional strain energy within 0.35% under four loading conditions. In human femoral reconstruction, multiscale concurrent optimization produces a cortic

ALT We develop a Unified Interface Neural Network (UINN) framework for elliptic interface problems with discontinuous coefficients. A single shared network provides a unified representation of the solution in both subdomains, while a projection–correction construction embeds the solution and flux jump conditions directly into the neural trial space. This design aligns with the classical numerical principle of incorporating interfacial physics into the approximation basis to construct interface-unfitted numerical methods. The jump conditions are therefore satisfied exactly for any network parameters. Compared with methods based on separate phase networks and numerical formulations with interface penalty terms, UINN provides a unified representation with exact enforcement of interfacial jump conditions and interface-penalty-free optimization. Those features streamline the numerical formulations and can enhance training robustness. Numerical experiments on smooth interfaces at modestly large

ALT We present and validate an Implicit Monte Carlo (IMC) radiation-transport solver in the open-source, mesh-agnostic storm library, coupled to the moving-mesh hydrodynamics code rich in three-dimensional Voronoi tessellations. The solver is multigroup, or continuous in frequency, throughout; it transforms photon packets exactly between the comoving and laboratory frames, books every exchange with the material as a laboratory four-momentum so that the IMC path conserves energy to roundoff, formulates the Fleck factor in the fluid's proper time, and accelerates optically thick cells with multigroup Discrete Diffusion Monte Carlo (DDMC) behind an emissivity-preserving interface. We tested the solver on a broad suite of benchmark problems, and it performed well on all of them. The solver is built on the MPI-parallel Monte Carlo framework of storm, which scales to 13,440 cores.