Papers

Neural surrogates can substantially accelerate computer-aided engineering (CAE) workflows, but their use in design requires uncertainty estimates that remain meaningful across varying geometries, spatial prediction fields, and engineering quantities of interest. We investigate how established uncertainty quantification (UQ) approaches behave when adapted to geometry-conditioned neural surrogates. We compare one closed-form and two sampling-based approaches-a Gaussian process (GP)-based method, concrete Monte Carlo (MC) dropout, and deep ensembles-and evaluate them on three large, industry-relevant CAE datasets for external aerodynamics and crash dynamics. We examine whether predicted uncertainties have credible magnitudes, identify locations with larger prediction errors, respond to unfamiliar inputs, and remain informative for derived engineering quantities. On the DrivAerStar dataset, where all three methods are compared, each generally assigns higher uncertainty to locations with larger prediction errors, and validation-based rescaling brings interval coverage close to nominal on a disjoint in-distribution test set. Results on AirFRANS and automotive crash also show useful error ranking and interval estimates, but the relative performance of the methods changes with the dataset and evaluation criterion. UQ methods and evaluation metrics should therefore be selected based on the intended downstream CAE decision.

Inspired by the recent progress in the simulation of tight-binding Hamiltonians on large lattices using tensor networks, we introduce a systematic matrix product operator (MPO) construction for single-particle Hamiltonians on recursively structured lattices. Taking advantage of this recursive structure, we encode the lattice geometry in a finite-state automaton and, adapting ideas from Abelian-symmetric tensor networks, obtain an exact and analytical MPO representation of the Hamiltonian, where the number of tensors grows logarithmically with the system size and the bond dimension is set by the number of automaton states. Several examples demonstrate the generality of the framework: regular lattices, fractals, Cayley trees, hyperbolic lattices, and one- and two-dimensional Fibonacci quasicrystals. Combined with the kernel polynomial method, these MPO representations enable large-scale calculations of spectral properties without explicitly constructing the full Hamiltonian. This provides a unified route to the exploration of electronic properties across a broad class of lattices at exponentially large system sizes.

We present a deep-learning surrogate for the Earth matter effect on solar neutrinos. The model uses a residual convolutional network conditioned on the solar neutrino oscillation parameters and is trained on numerical solutions computed over a grid of parameter values. It predicts the Earth-induced transition probabilities across neutrino energy and zenith angle, providing a fast approximation to the direct numerical calculation. For the reference electron-neutrino survival probability, the surrogate achieves a pointwise relative accuracy of approximately $2\%$ and a speed-up of about a factor of 60 in a laptop-CPU test. Since the network learns only the Earth-crossing propagation, it can be applied without retraining to new-physics scenarios that leave this propagation unchanged. The surrogate can also be retrained using alternative numerical implementations or extended parameter sets, providing a flexible and computationally efficient approach for solar-neutrino analyses. The code and simulation data are publicly available at \href{https://github.com/AI-Driven-HEP/NuMatterSurrogate}{\faGithub}.

A ghost-point immersed boundary method is coupled with auxiliary differential equations to impose a locally-reacting impedance condition on a wall that does not conform to a Cartesian grid, in the framework of the linearized Euler equations. The ghost-point reconstruction follows the normal-stencil approach: an elliptical least squares cloud of fluid nodes is used to build a high-order polynomial along the local wall normal, which is then extrapolated onto the ghost points by one-dimensional La grange interpolation. The impedance, modeled as a massspringdamper oscillator, is advanced in time through two auxiliary state variables per ghost point, coupled to the reconstruction at every RungeKutta stage. The method is validated against exact and semi-analytical references on a flat immersed wall, a cylindrical wall reflecting an acoustic pulse, and a cylinder scattering a harmonic monopole. Convergence orders ranging from about three on the curved wall to about four and a half on the flat wall are measured, and a cross-check against an exact harmonic reference shows that a persistent offset observed against a semi-analytical reference is a property of that ref erence rather than of the coupled solver. A spectral stability analysis of the linearized semi-discrete operator further shows that the normal-stencil reconstruction reduces, without eliminating, a known instability that occurs when the immersed wall becomes tangent to the grid.

We report the first calculation of the lowest-known energy configuration for $N=100\,000$ classical point charges confined to a disk and interacting via the $1/r$ Coulomb potential - a system size never before achieved for the Thomson problem in a disk, more than doubling the previous record of $N=40\,886$ reported by Amore and Zarate. An adaptive defect-targeting subdomain optimization strategy yields an approximately linear growth of the wall-clock time per cycle with $N$; for $N=100\,000$ a single $24$-core CPU workstation without GPU acceleration required $\approx31$ hours. The energy $E_{\min}=7.80466624157\times10^{9}$ deviates from the standard empirical asymptotic expansion by only $2.525\times10^{-7}$. We demonstrate that this remarkable agreement provides a stringent test of the rigorous next-order asymptotic theory for Riesz interactions, while the residual deviation is consistent with an $O(N^{4/3})$ boundary-layer correction whose absence from the standard fitting basis biases the empirical $N^{3/2}$ coefficient away from its exact crystalline value, thereby tying the deviation to the two-dimensional crystallization conjecture. Bond-orientational order analysis reveals a polycrystalline bulk threaded by radial grain boundaries, establishing a new benchmark for two-dimensional Coulomb systems.

Molecular properties govern how molecules interact with one another or external fields. Accurate molecular properties are essential for constructing intermolecular interaction models, and to achieve high accuracy we need to go beyond leading-order (dipolar) terms. This work presents CCSD(T) references for 73 small non-spin-polarized molecules for molecular dipole and quadrupole moments, and dipole-dipole and quadrupole-quadrupole polarizabilities. Using these results, we provide a holistic performance analysis of molecular properties computed with HF, MP2, CCSD, and a wide range of density-functional methods. Additionally, we investigate in detail what levels of basis sets are required to simultaneously describe all properties in the data set. The best-performing density functionals for all four properties are the asymptotically cor- rected hybrid GGAs B97-3-AC, closely followed by PBE0-AC. Surprisingly, modern meta- GGAs and range-separated functionals perform inconsistently, with large errors in the quadrupo- lar properties. These results have direct implications for methods for intermolecular interac- tions, such as symmetry-adapted perturbation theory based on density functional theory, or for the quality of properties and interactions in machine-learning datasets. Finally, for DFT methods, the Jensen aug-pcseg-2 basis set is a computationally efficient alternative to more established basis sets, but for generating correlated references, third-row elements benefit from core polarization, and double augmentation is strictly necessary for quadrupole-quadrupole polarizabilities.

The Volumetric Neutron Source (VNS) tokamak is a proposed fusion reactor for testing components under fusion neutron irradiation, and has potential use for radioisotope production. The VNS geometry is modeled in the Serpent 2.2.2 and OpenMC 0.15.2 neutronics codes. Coupled neutron-photon simulations compared fluxes, spectra, and selected reaction rates in the blanket and vacuum vessel. Good agreement was found overall, with the largest difference found in (n, 2n) reactions. On an HPC cluster, Serpent 2 was found to have shorter computation time in coupled simulations, while OpenMC was faster in neutron only simulations. Radioisotope production yields were simulated in Serpent 2.2.2 for capsule and Cobalt plate irradiation facilities. Results indicate potential for large volume production of 99Mo, 131I, 225Ac, 177Lu, 192Ir, 64Cu, 67Cu, 161Tb, and 153Sm while 203Pb indicates lower potential. 100Mo and LEU target heating was calculated, suggesting the LEU target mass or the cooling may need adjustment. Optimized 60Co production yielded 1.2 GBq/mg and 100,000 TBq after a 3-year irradiation period. Sensitivity to plant outage for 99Mo, 131I, 177Lu, and 60Co was simulated, suggesting irradiation can be restarted for the same isotope loading and demonstrated long-lived 60Co to be robust to long plant dwell-time.

The enormous recorded data at high-energy physics (HEP) colliders make the accurate identification of physics objects a bottleneck in disentangling event topologies, where machine learning has become a standard tool for jet tagging. In this work, we examine whether Vision-Language Models (VLMs) can provide a common interface for structured jet analysis from a single physics-informed image. Each JetClass jet becomes a 224x224 RGB image with four panels encoding p_T flow of all constituents; charged-hadron, neutral-hadron, and electromagnetic composition; p_T-weighted impact-parameter significances with displaced-track multiplicity; and signed-track p_T densities with local p_T^k-weighted jet-charge asymmetry. Four open VLMs are adapted with low-rank adaptation (LoRA) for class classification across QCD, Higgs, W/Z, and top jets, six-field attribute prediction, and cross-panel consistency with replaced-panel localization, evaluated on 24000 balanced JetClass test jets. Ablations identify the impact-parameter lifetime signature of heavy-flavor tagging as dominant, with jet charge separating the nearly mass-degenerate hadronic W and Z. Zero-shot recall stays near chance (3.33%-10.57%), once adapted, Task 1 Macro recall grows monotonically with training size, and Gemma4-E4B reaches 75.05% (74.87% F_1), 93.31% Task 2 field-mean, and 99.88%/99.75% binary/localization recall. Reallocating budget toward W/Z jets raises Zqq recall by up to 9.83 points at near-constant Macro recall. Transfer to broader-topology JetClass-II and real-data Aspen Open Jets (probing the simulation-to-data gap) is retained: with 3000 target jets, Task 1 recall exceeds 70% on JetClass-II and every Task 2/3 metric exceeds 92%. Thus rasterizing energy flow, species, displacement, and jet charge, with parameter-efficient adaptation, supports jet analysis through one instruction-conditioned interface for future collider data.

Astronomical maps made with different tracers are not expected to have identical morphology. Excitation, optical depth, chemistry, radiation, and ISM phase alter the response of a tracer, and the resulting differences can depend on both position and spatial scale. We propose scale-vector alignment, a scale-aware method based on Constrained Diffusion Decomposition (CDD). CDD decomposes an image into localized scale components; at each position, their amplitudes define a scale vector that describes how the measured intensity is distributed over spatial scale. We define the pixel-wise similarity $\Spix(x,y)$ as the normalized alignment of two local scale vectors. The normalization removes the overall amplitude, so $\Spix$ compares relative scale composition rather than absolute flux. We also define the scale-wise similarity $\Sscale(l)$ by comparing the two CDD component maps at each spatial scale. Spatial shifts are used to construct an empirical shifted reference distribution for $\Spix$. In Orion~A, the tracer with the highest similarity to the dust-derived column-density map changes from $^{12}$CO to $^{13}$CO to C$^{18}$O toward higher column density. In NGC~6334I(N), the line–continuum similarity decreases locally around the brightest compact structures, where radiative-transfer effects can alter the observed line morphology. In NGC~3627, CO is most similar to 21~$\mu$m emission, and $\Sscale$ reaches its maximum at an intermediate sub-kpc scale. The method measures where two tracers have similar multiscale structure and at which scales their spatial distributions agree. The implementation is publicly available at https://github.com/meng-ke/Scale-Vector-Alignment.

Fine-grained, subcell-level dissipation control is essential for achieving robust high-order discontinuous Galerkin (DG) simulations of nonlinear hyperbolic systems in under-resolved regimes while preserving accuracy. This paper proposes a subcell-refined entropy-residual-driven limiting strategy for DG on Legendre-Gauss-Lobatto nodes. The limiter introduces only nearest-neighbor pairwise dissipation within each element, with closed-form coefficients that supply the minimal dissipation required to restore the element entropy inequality. The strategy is a diagonal, locally stable approximation of classical entropy-stable methods, and a generalized subcell framework reveals split-form DG and residual-distribution-based entropy correction schemes as particular choices of the limiting coefficients. For the Euler equations, a physically consistent jump operator separately models thermal and shear entropy production while preserving velocity and pressure equilibrium; a subcell refinement of the Zhang-Shu positivity limiter ensures pointwise positivity. Extensive numerical tests confirm that the scheme maintains optimal high-order accuracy, strictly enforces entropy dissipation, and significantly reduces the difficulty of a posteriori positivity-preserving procedures.

This paper proposes a novel discretely entropy conserving/stable flux reconstruction (FR) scheme for nonlinear conservation laws. The scheme combines a hybridized split-form differential operator with a generalized entropy projection, enabling discrete entropy conservation for arbitrary nodal distributions and arbitrary correction functions without modifying the original quadrature weights. The formulation is built directly upon the classical FR framework and is shown to preserve conservation properties while achieving entropy conservation in the semi-discrete sense. Numerical experiments using the isentropic vortex problem confirm the theoretically predicted accuracy and demonstrate robust entropy behavior with entropy-dissipative interface fluxes.

Nonequilibrium flow and transport problems are inherently multiscale. Kinetic theory provides a fundamental physical basis for describing such phenomena, since it connects microscopic transport and interaction processes with emergent macroscopic behavior across regimes. In many situations, however, continuum descriptions lose validity in parts of the domain, whereas fully resolved kinetic descriptions become prohibitively expensive when numerical resolution remains tied to the smallest collision scales. Over the past two decades, a broad class of multiscale kinetic methods has therefore been developed to bridge rarefied, transitional, and continuum regimes in gas dynamics and other carrier-based transport systems. Existing reviews have clarified important parts of this field, including general numerical methods for kinetic equations, asymptotic-preserving methodology, and specific method families. This review adopts a different perspective by examining the subject through four interacting layers: numerical methods, computational strategies, asymptotic properties, and framework-level formulations. It surveys the main developments along these lines and emphasizes the common principles that connect them, including transport-interaction coupling, asymptotic consistency, scale-adaptive representation, and scale-dependent physical description. From this perspective, multiscale kinetic computation has evolved into a broader transport methodology for nonequilibrium systems across scales.

Relaxor ferroelectrics retain crystalline order while exhibiting glass-like dielectric and thermal responses. Using atomistic models trained on first-principles data, we investigate these responses in the prototypical relaxor Pb(Mg_{1/3}Nb_{2/3})O_3 (PMN). Compositional disorder couples elastic motion to electric polarization, producing a continuum of polar vibrational excitations, unlike the discrete polar optical modes of conventional ferroelectric PbTiO_3. The simulations qualitatively reproduce the temperature dependence of the low-frequency susceptibility, while the calculated far-infrared spectra agree closely with experiments. At low frequencies, disorder in PMN generates a boson peak comprising excess phonon-like modes and quasi-localized excitations. The latter exhibit a quartic frequency dependence of their density of states and pronounced anharmonicity, as in structural glasses. These excess modes account for PMN's anomalous behavior in the specific heat for temperature higher than 5 K. These results connect the dielectric, optical, and thermal anomalies of a crystalline relaxor through its disorder-induced polar excitation spectrum.

Interbasin exchange through the Indo-Pacific gateway supplies salt to the Atlantic and is widely invoked as a control on the stability of the Atlantic overturning circulation. We ask whether that control can act on the equilibrium structure of a conceptual thermohaline model. A closed five-box model with an exact salt invariant is constructed, comprising North Atlantic, upper-limb, Indian, Pacific, and deep reservoirs, with the return flow split between a warm route through the Indian reservoir and a cold route, together with an Indonesian Throughflow branch and an Agulhas retroflection. Adding the steady-state budgets of the gateway reservoirs shows that every internal exchange cancels, so the salt they export to the Atlantic is fixed by the net Atlantic freshwater export alone. This holds independently of the warm-route fraction, the throughflow, the retroflection, and how the export is apportioned among gateway reservoirs; across a parameter sweep the largest departure is of order ten to the minus eleven. The gateway therefore enters as a purely additive forcing and cannot renormalize the salt-advection feedback. Replacing the discrete transit lag by a gamma memory kernel leaves the equilibria unchanged but yields a closed-form threshold for oscillatory instability depending only on kernel shape. Broad memory is strongly stabilizing, and a discrete lag is the least stable member of the family. Because the instantaneous feedback vanishes at the fold, oscillatory instability always precedes the saddle-node, over an interval widening more than tenfold as memory sharpens. Gateways therefore appear to act on transient rather than equilibrium dynamics

Whether an initially crack-free heterostructure fails at its interface or within an adjoining phase is controlled by the relative cohesion of competing atomic planes, but how interfacial chemistry, crystallographic orientation, and intermixing reshape this competition remains unclear. Here, we combine density functional theory (DFT) with a fine-tuned atomistic foundation model to resolve tensile fracture in coherent diamond/cubic boron nitride (cBN) heterostructures. The resulting potential reproduces independent DFT tensile responses, including an unseen (001) interface orientation. Interfacial termination, orientation, and diffusion-induced intermixing jointly determine fracture resistance and fracture-plane selection. C-N-bonded (111) and C-B-bonded (001) remain interface-controlled throughout the investigated intermixing range, whereas pristine C-B-bonded (111) fractures at a neighboring B-N plane inside cBN because the interface is more strongly bound. Increasing the diffusion fraction from 0 to 50.0% causes a nonlinear decrease in fracture strength from 50.3 to 15.8 GPa and drives a bulk-to-interface transition through three regimes: cBN fracture up to 4.86%, configuration-dependent competition between 7.6 and 10.1%, and interfacial fracture at 12.5% and above. Atom-resolved stress fields and DFT separation energetics show that this transition is associated with stress relocation and a reversal in the relative cohesion of competing planes, while electron localization analysis connects the cohesion hierarchy to termination- and orientation-dependent bonding. These results establish an atomistic framework for controlling fracture resistance and fracture pathways in strongly bonded heterostructures.

We employ equation-driven, physics-constrained deep learning to solve the fixed-boundary Grad-Shafranov (GS) equilibrium problem, constructing axisymmetric magnetohydrodynamic equilibria with tokamak-relevant characteristics. Equilibria across linear (Solov'ev) and nonlinear profile functions are constructed using Physics-Informed Kolmogorov-Arnold Networks (KANs) that approximate GS solutions while satisfying appropriate boundary conditions. A highly nonlinear pressure profile recreating high-confinement mode phenomenology, such as pressure pedestals and significant bootstrap current components, is also considered. To enable efficient convergence, guided training schemes are employed, specifically homotopy-based continuation curriculum learning and transfer learning via pretrained networks. While computing nonlinear equilibria employing standard Multi-Layer Perceptrons under unguided physics-informed training remains an elusive or computationally inefficient task, our framework overcomes this limitation. Specifically, we demonstrate that the combination of three key elements, namely KAN architecture, guided training schemes, and the self-scaled Broyden optimization method, enables stable, efficient, and accurate equilibrium computation with simultaneous profile parameter identification in view of equilibrium constraints.

This study examines the impact of processing conditions, such as thermalprocessing, on the resulting microstructure and mechanical properties. Spe-cial emphasis is placed on microstructural features obtained from three-dimensional phase-field simulations, which provide detailed insights into bai-nite morphology, phase distribution and retained austenite content. Thesesimulated microstructures are correlated with changes in yield strength undermultiaxial load, as represented in the yield surface of the material. The re-sults demonstrate that optimized processing routes can refine the microstruc-ture, enhance mechanical properties and significantly alter the yield surfacecharacteristics. These findings provide valuable insights for the design andapplication of bainitic steels, as well as for the development of predictivemodels linking process-structure-property relationships.

We investigate spin-dependent transport in a non-collinear helical antiferromagnet in the presence of spin-orbit coupling within a tight-binding framework. Using the Landauer-Büttiker formalism, we analyze the generation of spin polarization arising from the combined effects of the helical magnetic texture and spin-orbit interaction. We find that finite spin polarization can be generated simultaneously along the $\hat{x}$, $\hat{y}$, and $\hat{z}$-directions, in contrast to the predominantly single-axis spin polarization commonly observed in conventional spin-filtering systems. The multidirectional spin polarization originates from the symmetry breaking introduced by the non-collinear magnetic order. We further show that the spin polarization is modified significantly in the presence of spin-orbit coupling and it has strong dependence on the parameters associated with the helical system. In particular, long-range hopping significantly enhances the spin-filtering effect, leading to large spin polarization components along all three spatial directions.

NLO simulations are essential for LHC physics analyses but are expensive, as they are not only slow but also lead to negative weights, which imply the need to simulate much larger samples of events. Folding is a powerful technique to reduce negative weights but is itself expensive. In this paper I propose “vectorized folding” as a new idea to speed up these calculations using SIMD and GPUs, and I present its CUDACPP-based implementation for MG5aMC in MadVfold, including its extension for unfolded NLO event generation. Preliminary results show overall speedups around 6x to 9x with folding and 3x without it. This work is based on a test-centric, LLM-assisted software development process.

We present a machine-learning-accelerated plasma simulation scheme that combines learned time jumps with ordinary physics evolution. A neural network corrects a low-cost physics forecast over multiple time steps, while the original solver reconstructs the state and advances it between jumps through short reanchoring intervals. The scheme is implemented in PASCHEN-1D, a one-dimensional drift-diffusion-Poisson solver, achieving up to $4.70 \times$ CPU rollout speedup relative to the ordinary solver for nanosecond pulsed nitrogen discharges. The simulations capture pre-breakdown evolution, rapid sheath formation, expansion and collapse under pulsed-voltage excitation, and post-pulse afterglow. Bulk densities and electric fields agree closely with the ordinary-solver reference, while cathode sheath width, gap voltage, and discharge current reproduce the principal temporal features. The largest spatial discrepancies occur in the cathode sheath during fast transients. A sweep of the physics-reanchoring duration reveals a trade-off between accuracy, acceleration, and numerical stability over the tested 500 ns simulation interval. A model trained on simulations with 1000 grid points also shows useful transfer to 500- and 1500-point meshes without retraining. These results demonstrate a practical route to accelerating plasma simulations by augmenting an established physics solver with machine learning.

Unstable thermal stratification modifies near-wall momentum and heat transport, causing the mean velocity profile to depart from the classical logarithmic law and complicating wall modelling for turbulent mixed convection. We develop a buoyancy-modified logarithmic-quadratic wall model for incompressible Poiseuille–Rayleigh–Bénard flow. The model combines an approximately linear relation between the near-wall mean temperature and mean streamwise velocity with a thermally modified mean-gradient representation inspired by mixing-length scaling. A priori assessments using wall quantities from the direct numerical simulation (DNS) database show that the calibrated wall law reconstructs near-wall velocity and wall-function-equivalent eddy-viscosity profiles. We implement the wall model in wall-modelled large-eddy simulations (WMLES) at friction Reynolds numbers up to $Re_\tau\approx6000$ and Rayleigh numbers up to $Ra=10^{10}$. For cases with DNS reference profiles at $Ra=10^8$ and $10^9$, the maximum pointwise absolute relative errors are $3.6\%$ for the mean velocity and $1.9\%$ for the mean temperature. For cases with available DNS global-transport data, the maximum relative deviations in the Nusselt number $Nu$ and skin-friction coefficient $C_f$ are $11.7\%$ and $15.9\%$, respectively. The WMLES reduces the mesh count by factors of approximately $195$–$542$ relative to the corresponding DNS meshes. For the $Ra=10^{10}$ and $Ri_b=0.1$ case, extrapolation of reference DNS resolution strategies gives a mesh count of order $10^{11}$, approximately three orders of magnitude larger than the present WMLES mesh count. We also examine how the balance between shear and buoyancy reorganises flow structure, and we identify signatures consistent with the coexistence of streamwise-elongated motions resembling very-large-scale motions and buoyancy-associated streamwise rolls.

Recently, a hybrid qudit-qubit algorithm [1] was presented for solving the integer programming problem with a polynomial quantum advantage. In this work, we investigate the algorithm [1] to understand the role of qudits ($d$-dimensional quantum system) by conducting a comparative resource analysis with its qubit-only implementation and the classical simulability of the algorithm by exploring the entanglement structure. The resource analysis part is performed in terms of logical gate counts, and fault-tolerant physical resources, including non-Clifford gates. The hybrid qudit-qubit implementation has a more compact structure of the unitary operators as opposed to its qubit-only simulation which reduces the logical and fault-tolerant resource requirements. Two example problems, one with qutrits ($d=3$) and the other with ququint ($d=5$), when contrasted with their qubit-only implementation, within a simplified fault-tolerant resource model, showed $\sim 180 \times $ and $\sim 2220\times$ fewer total resource count, respectively. For the entanglement study, volume-law-like entropy growth and signatures of multi-partite entanglement is observed leading to increasing difficulty in the classical simulation of the algorithm. The algorithm generates synergistic tri-partite entanglement even for a quadratic problem, revealing that the algorithmic structure itself can generate higher-order entanglement in the system independent of the problem.

Hybrid physics-machine-learning solvers improve under-resolved simulations by embedding trainable corrections into the time integration. During autoregressive inference, repeated solver-model interactions can amplify small errors, motivating multi-timestep solver-in-the-loop training. However, production solvers rarely expose the derivatives needed to backpropagate through such rollouts. We introduce Diff-NekRS, a scalable differentiable framework that embeds neural corrections directly in the GPU-accelerated NekRS incompressible-flow solver. NekRS computes the authoritative forward trajectory, a manually implemented exact discrete adjoint differentiates the supported fully discrete timestep, and LibTorch supplies neural vector-Jacobian products and parameter gradients. End-to-end Taylor and centered finite-difference tests verify the assembled gradient for two-dimensional cylinder flow (2Dcyl) and the three-dimensional Taylor-Green vortex (3DTGV) across five horizons and 12-1,020 MPI ranks. At 1,020 ranks, optimizer-enabled post-setup training updates retain 54.5%-78.0% and 80.7%-81.9% weak-scaling efficiency for 2Dcyl and 3DTGV, respectively. In 200-step autoregressive inference, the M = 50 model reduces the three-seed median terminal relative L2 velocity error by 59.2% for 2Dcyl and 12.1% for 3DTGV relative to the uncorrected coarse-grid P = 2 baseline, and retains wall-clock speedups of 5.38x and 2.49x, respectively, relative to the corresponding P = 7 configurations for equal simulated-time intervals. These results establish a verified and scalable path for multi-timestep solver-in-the-loop training that improves coarse-grid trajectory accuracy while retaining a speed advantage over the high-order reference

The dynamics of interacting dipole skyrmion chains in a weak pinning landscape is studied through numerical solutions of the stochastic Thiele equation. Chains of different lengths with periodic boundary conditions are driven across quenched attractive pinning sites under different magnetic fields. A clear threshold spin current is identified as the critical depinning force. Three main results emerge: (i) for chains of 50 skyrmions or more, the depinning threshold is independent of chain length and remains close to one third of that of an isolated skyrmion. (ii) The transition rounding is only partly thermal: the width changes from w = 0.334 +/- 0.004 decades at T = 0 to 0.633 +/- 0.002 at 300 K, while the intrinsic Larkin correlation length remains about 2.6 bonds below kBT ~ V0/25. (iii) The width is nearly unchanged up to kBT ~ 0.14 V0, but increases almost fourfold by kBT ~ 0.23 V0, mainly through broadening of the creep regime. It is independent of chain length, ruling out finite-size rounding. Increasing the field from 30 to 40 mT changes the transition shape, widening its core by 26% while shortening the creep tails. For chains of about 200 skyrmions, depinning proceeds through a sequence of internal deformations - growth of the Larkin length and roughness, transient bond stretching, and subsequent recovery of mobility and Hall angle. These collective effects are relevant for skyrmion-based devices in which chains, rather than isolated textures, act as information carriers.

The Stokes-flow hydrodynamics of an irregular microparticle is encoded by its grand resistance matrix, a 6x6 tensor whose translational and rotational blocks (A and C) govern settling, diffusion, and orientational transport. Empirical drag correlations compress these tensors to a single scalar, discarding drag's orientation dependence and the rotational response. We present an SO(3)-equivariant neural network that predicts the full symmetric positive-definite A and C blocks from a particle's spherical-harmonic surface representation, equivariant by construction to floating-point precision. Trained on 1.1x10^5 random shapes from near-spherical to very rough, with a sealed test set of 18,000, it achieves 1.4% and 2.7% mean relative error on the two blocks while evaluating each shape 4-5 orders of magnitude faster than the regularised-Stokeslet solver that generated its labels. A spectral-convergence study confirms the representation is faithful: truncating a shape at spherical-harmonic degree 15 changes its resistance by a median of 0.14% (translation) and 0.38% (rotation), while the training shapes, generated band-limited at degree 15, carry no truncation error. Across 1.16x10^6 orientation-sampled settling, rotation and diffusion events, the surrogate reveals lateral drift up to 11 deg, rotational misalignment up to 46 deg, and shape-induced diffusion spreads of 30% (translational) and 2.4x (rotational), all identically zero under any scalar or spheroid reduction. Even the orientation-averaged scalar friction the correlations target, accurate to 1.7-2.8% (median; 2.2-3.2% mean), carries no tensor orientation, whereas the surrogate reproduces that scalar to ~1% while supplying the full anisotropic tensors. A fast, equivariant tensor surrogate can replace both solver and scalar approximation in atmospheric dust transport, microplastic fate and colloidal Brownian dynamics.

We investigate the coupling dependence of ballistic energy transport and the emergent spin dynamics in an integrable Hermitian three-state chain that connects a clock interaction to a highly degenerate flag limit. By constructing a regular $R$-matrix to establish a globally conserved energy current, we analytically evaluate its full variance to obtain the exact, strictly positive leading high-temperature coefficient of the thermal Drude weight and the ballistic growth rate of the energy-correlation second moment. In the strong-coupling limit, the degeneracy is lifted by virtual transitions of a delocalized third-color spectator state, which generates an effective spin-$1/2$ XXZ Hamiltonian with anisotropy $\Delta = -1/2$ and fundamentally selects the all-active two-color sector as the true ground state. For periodic boundaries, this virtual spectator motion introduces a positive length-changing XXZ supercharge squared that, for $L\ge4$, strictly annihilates all states within a finite, length-independent energy interval above the ground state. Consequently, we rigorously prove that the full periodic effective theory perfectly replicates the exact low-energy XXZ spectrum, including all state multiplicities, as well as its macroscopic bulk free-energy density.

Physics-Informed Neural Networks (PINNs) provide a mesh-free framework for solving partial differential equations but often struggle with sharp gradients and shock-dominated solutions. Extended Physics-Informed Neural Networks (XPINNs) address this challenge through domain decomposition; however, the effects of decomposition design, overlap, and local network capacity on solution accuracy remain insufficiently characterized. This work presents a systematic assessment of domain decomposition configurations for XPINNs applied to the one-dimensional viscous Burgers equation ($\nu=0.01/\pi$). We compare a standard PINN, a conventional XPINN, a shock-focused XPINN with increased network capacity in the shock-containing subdomain, and overlapping XPINNs with different overlap widths. All configurations are trained using a common protocol based on Adam, L-BFGS refinement, and ten Residual-based Adaptive Refinement (RAR) cycles. Performance is evaluated against a reference solution using global and shock-region relative $L_2$ and $L_\infty$ errors, maximum PDE residuals, and interface continuity errors. The results show that decomposition design strongly affects XPINN accuracy and shock resolution. Among the overlapping configurations, the smallest overlap provides the best accuracy, while larger overlaps degrade performance. The shock-focused XPINN achieves the lowest overall solution errors, indicating that increased local network capacity can provide greater benefit than increasing overlap alone. RAR produces the largest improvements during early refinement stages, followed by increasingly non-monotonic changes in accuracy. These findings highlight the importance of jointly considering decomposition, interface coupling, network capacity, and adaptive refinement for shock-dominated problems.

The persistence of beta-blockers like atenolol in aquatic environments necessitates efficient remediation strategies, such as enzymatic biodegradation. This study employs reactive molecular dynamics (rMD) simulations to investigate the initial degradation steps of atenolol by the oxidoreductase 9CL6 ammonia monooxygenase. Using the ReaxFF reactive forcefield within a simulated aqueous environment, the degradation processes were modeled at 300 K and 350 K over 6.5 nanoseconds. Results indicate initial degradation rates of 24% at 300 K and 18% at 350 K, with each enzyme molecule degrading approximately 20 atenolol molecules before reaching a saturation point. Mass spectrum analysis reveals the primary formation of C8 and C6 fragments at both temperatures. However, at 300 K, additional intermediate fragments (C1, C3, C11, C13) are observed, which are completely bypassed at the higher temperature of 350 K. Furthermore, increasing the temperature to 350 K accelerates the initial degradation phase from 2 ns to 0.5 ns, despite yielding a slightly lower overall degradation rate. Ultimately, these atomistic insights provide a foundational computational methodology for predicting biodegradation rates and pathways of pharmaceutical contaminants at the molecular scale.

In the realm of material analysis, identifying different material phases is of key importance. Artificial intelligence in the form of neural networks provides a very fast and, once trained, computationally inexpensive method for analysing large amounts of image data, like the sets of diffraction patterns generated during four-dimensional scanning transmission electron microscopy (4DSTEM) dataset acquisition. In this work, we train multiple network architectures on images of this type to distinguish between the phases of LiNiO2 and NiO, an important and challenging distinction in the lithium-ion battery community, since the formation of NiO limits battery capacity. We test both classical convolutional neural networks (CNNs) and different forms of vision transformers (ViTs). Our networks are trained on synthetic images and tested on experimentally recorded diffraction patterns. Additionally, we also investigate the decision-making of our networks using the GradCAM method. We test our networks on both synthetic as well as experimental diffraction patterns. Our networks exhibit very robust results, especially when dealing with highly varying data, an area where traditional template-matching methods typically struggle.

We present TubeLab, a browser-based acoustic simulator and inverse design tool for wind instrument bores without tone holes. The direct problem is solved by a Transfer Matrix Method. Inverse design - finding a bore correction that shifts selected resonance frequencies toward specified musical targets - is formulated as a Tikhonov-regularized least-squares problem whose Jacobian is computed by a single adjoint backward pass per mode. Modes whose frequencies must be preserved are handled by a saddle-point formulation that enforces hard equality constraints regardless of the regularization strength. Resonance frequencies agree with state-of-the-art finite-element calculations to within 1.21 cent over eleven geometries and 132 mode pairs. Experimental validation against tap-tone measurements of 16 numerical control-machined didgeridoos spanning six distinct bore designs yields 9.6 cent RMS deviation over 189 matched mode pairs. Replicate specimens of the same nominal bore disagree with each other by 4.5 cent RMS, so about 36% of the residual variance is fabrication scatter.