ALT Finite-volume and discontinuous Galerkin methods update cells using the space-time flux integral over their faces, which typically depends on the solutions to local Riemann problems. In the multidimensional Riemann problem setting, this integral is difficult to evaluate exactly because of complex wave interactions. In this work, we show that the exact space-time flux integral is a polynomial in the time step and face dimensions. This motivates a learning-based approach, as only the mapping from the initial states to the polynomial coefficients needs to be learned. We propose a structure-preserving, data-informed Riemann solver framework that uses a neural network trained on high-resolution simulation data to learn this mapping. Key structural properties, including consistency and symmetry, are enforced by construction. Provided that the high-resolution simulations converge to the exact flux integrals and the network accurately predicts the coefficients, this framework yields near-exact

ALT Algorithm design tailored to graphics processing units (GPUs) can substantially improve the efficiency of computational fluid dynamics (CFD) simulations. Efforts to adapt CFD solvers to GPUs often focus on spatial discretization, while time advancement commonly relies on multistage Runge–Kutta (RK) methods. However, these RK methods require repeated residual evaluations and full-domain operations, increasing the cost of compressible-flow direct numerical simulation (DNS). To reduce this overhead, we develop a local arbitrary high-order derivatives (ADER) finite-difference method that couples a compact ten-point quadratic predictor to a conservative central corrector through operator matching. With two quadrature nodes, one Picard correction, and selective dissipation, smooth convective tests recover third-order convergence under fixed-CFL refinement and near-seventh-order spatial behavior when background spatial error dominates. Temporal states remain kernel-local, and halo communicati

ALT The stress tensor resolved in wavevector qvec and time t, σαβ(qvec,t), gives access to the elastic moduli of amorphous solids as a function of the probed length scale, and to the long-range stress correlations that distinguish an amorphous solid from a liquid. Its evaluation requires the contribution of every interacting pair and therefore an interface to the force loop of the molecular dynamics code. In the current work, we present: i) an optimized implementation of the LAMMPS module for calculating σαβ(qvec,t), in which trigonometric functions are calculated only for the basic wavevectors and, in addition, all the relevant wavevectors are supplied as an explicit list rather than generated as a full grid, so that only the wavevectors of interest are computed and stored, and ii) a validation protocol for the code illustrated for a two-dimensional polydisperse Lennard-Jones (2DpLJ) glass-forming liquid. Based on these technical achievements we elucidated how the affine moduli for the 2D

ALT This paper presents a novel framework for simulating load-transfer mechanisms in nanocomposites reinforced by thin, stiff, and prestressed reinforcements, such as, e.g., nanosheets or nanoplatelets. The reinforcements are modeled as open material surfaces treated as membranes endowed with their own elastic properties and residual surface tension; the matrix is assumed to be isotropic elastic. In the two-dimensional plane-strain setting considered here, each material surface is represented by a sufficiently smooth curve of otherwise arbitrary shape. The theoretical part of the framework is based on the Gurtin–Murdoch theory in which the surfaces are represented by traction jumps across them. The elastic fields in the matrix are exactly expressed by the integral representations written in terms of the unknown traction jumps that are functions of the second-order derivatives of the displacements. The computational part is based on the isogeometric boundary element method (IGABEM) that uti

ALT This work develops a differentiable finite element framework based on an intrinsic cohesive-zone formulation for identifying traction-separation laws from global force-displacement histories and spatially sparse strain measurements. The framework employs physics-constrained neural networks to represent flexible, thermodynamically structured cohesive laws, with sensitivities computed through automatic differentiation and a discrete adjoint that accounts for the history-dependent evolution of interfacial damage. To enable identification of spatially heterogeneous cohesive behavior, we extend learned constitutive priors to irreversible interfacial damage by constructing a shared, low-dimensional family of cohesive laws from representative traction-separation histories. This representation exploits common constitutive structure and parameter sharing to reduce the number of unknowns and regularize the inverse problem, while allowing local cohesive behavior to vary spatially through latent c

ALT The Discrete Element Method (DEM) is an indispensable tool for modeling and understanding the basic mechanical behaviors of (dry) granular media, a class of disordered material systems of significant interest to multiple scientific domains from (geo-)physics to (chemical) engineering. At the core of all present DEM frameworks is a phenomenological friction law–commonly chosen to be of the Amontons-Coulomb type–that models the frictional interaction among constituent grains. Here, inspired by research in the tribology community, we present an alternative, fundamentally different framework, termed surface-roughness-based DEM (SR-DEM), in which contact friction is handled in a more physics-based manner. In this framework, instead of using a friction law, we explicitly resolve the surface topography of each grain and let friction emerge from collective frictionless interactions of surface asperities. In essence, we trade phenomenology for physics at the cost of an increased computational d

ALT We develop an uncertainty-aware surrogate modeling approach for coupling an atomistic kinetic Monte Carlo (KMC) surface-chemistry solver with a continuum multi-species fluid dynamics solver across disparate physical length and time scales. The surrogate model predicts boundary mass fluxes for six species and their uncertainties, which the continuum solver monitors to automatically trigger additional KMC simulations when new training data are needed. This enables efficient multiscale coupling and maintains a user-specified level of accuracy. We demonstrate the approach for reactive halide-perovskite vapor deposition, which involves a multi-species vapor jet impinging on a reactive substrate. The KMC solver uses a DFT-calibrated energetics model that we construct as part of this work and provides net deposition and desorption rates for six species. With a conservative uncertainty threshold, the surrogate-coupled approach reproduces cumulative mass fluxes of the directly coupled approach

ALT This paper presents an efficient quantum spectral-Galerkin method for constant-coefficient second-order linear elliptic equations. The method employs a boundary-adapted Jacobi tensor-product basis that incorporates the boundary condition into the approximation space and produces Galerkin systems with polynomially bounded condition numbers and sparsity. For analytic solutions satisfying a suitable uniform regularity condition, spectral convergence allows the normalized Galerkin coefficient state to be prepared with complexity poly(d,log(1/ε)), where d is the spatial dimension and ε is the error tolerance, under standard sparse-access and state-preparation assumptions. At the state-preparation level, this improves the precision dependence over fixed-order finite-difference and finite-element discretizations. We further show how to estimate prescribed linear functionals of the solution, with an additional O(1/ε) factor arising from norm and inner-product estimation.

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