Papers

We present e3j, a fast Euclid-equivariance backend for geometric deep learning applications with JAX bindings for GPU and TPU. Leveraging both optimized CUDA and Pallas kernels and algorithmic improvements, the library achieves state-of-the-art throughput and runtime on both forward and backward paths. On a machine learning interatomic potential (MLIP) use case, it outperforms established backends, measuring up to 34% speed-up over cuEquivariance on water box NPT simulation using MACE, while remaining fully open source. E3j achieves over 80% efficiency over the H100 maximum memory bandwidth on tensor product operations, and in many cases more than doubles throughput of message passing convolutions forward compared to previously available backends. In addition, with the release of dedicated Pallas TPU kernel, e3j opens the possibility of large scale equivariant deep learning workloads on TPU architectures, which has so far been difficult to achieve. Our benchmarks show that e3j also achieves over 80% of a TPUv6e memory bandwidth, up to one order of magnitude more than e3nn-jax. The library is available on GitHub, PyPI and is released under an open source Apache 2.0 license.

The Solar Wind Charge Exchange (SWCX) mechanism, where X-rays can be generated through interactions between heavy, highly charged solar wind ions and neutral atoms, offers an opportunity to observe the large-scale transfers of energy and momentum through the Sun-Earth system. In this study, we simulate SWCX signatures from Earth's outer boundaries using Gorgon global magnetohydrodynamic (MHD) simulations combined with kinetic particle-based simulations which we call the X-ray Imaging of the Magnetosphere (XIM) framework. The XIM-predicted emissivities agree with the predictions of the MHD model, producing enhanced emissions from the magnetosheath and cusp regions, but several differences are apparent. Compared with MHD, XIM shows enhanced structuring in the magnetosheath and notable enhanced emissions along the magnetopause associated with betatron acceleration. The results also evidence species-specific spatial variations, which are shown to vary compared to anticipated relative abundances in the solar wind and ion-specific properties. These simulations provide new insights into the underlying dynamics of SWCX at the Earth's outer boundaries, which can be used to understand what might be observed using X-ray observatories in space, such as the recently launched SMILE mission.

Motivated by biological systems and my previous studies of quorum sensing with density-enhanced motility, I study a model of density-enhanced size and motility, in which both particle size and motility increase when the local density (over a distance larger than particle diameter) exceeds the global density. The emergent structures along different size ratios are spots, holes, bands and labyrinths controlled by several distinct observations. First, the characteristic pattern length scale is controlled by the sensing radius and remains approximately independent of the size ratio. Second, the total area occupied by the particles decreases with increasing size ratio. Third, the active fraction barely depends on the size ratio. These results demonstrate how both particle size and motility can couple microscopic regulation to large-scale pattern formation. I conclude by discussing possible extensions of the model.

Interatomic potentials are central tools in the atomistic modeling of materials. The atomic cluster expansion (ACE) parameterizes such potentials from ab initio data, conventionally encoding the chemical degrees of freedom with a one-hot representation that yields chemically stratified models. The alternative chemical representations used in on-lattice configurational cluster expansions have not been assessed for interatomic potentials. Here we revisit the multicomponent ACE for an arbitrary chemical site basis. We then establish an exact analytical mapping between a fitted linear ACE and the average-atom potential that describes a perfectly random alloy. We benchmark potentials built on the occupational, Chebyshev, and conventional ACE bases against solute binding and vacancy formation energies in Mg-Nd, and against the mixing enthalpies of the Mo-Nb and Cr-W solid solutions. When training data are scarce, the occupational basis converges fastest and offers the best control over targeted material properties, while the conventional and Chebyshev bases face challenges in reproducing these properties. The occupational basis likewise yields the most reliable average-atom description of disordered alloy thermodynamics. In the large-data limit the three bases perform identically. The chemical basis is therefore a design choice that governs data efficiency. Its explicit treatment opens a route to average-atom potentials for the thermodynamic, mechanical, and kinetic properties of concentrated alloys.

Many process engineering applications hold a gas-liquid interface stationary inside a structured solid by a controlled pressure difference. Gas diffusion electrodes (GDEs) are one such case, where the interface separates the liquid electrolyte from the gaseous reactant. Maintaining it is particularly challenging in organic electrosynthesis, where low surface tensions lower the admissible pressures throughout and small contact angles leave the electrode with little margin against flooding. Here, we quantify how the shape, wettability, and three-dimensional topology of a structured medium set this window, using phase-field simulations of the Cahn-Hilliard-Navier-Stokes equations. Each geometry is characterised by its Laplace pressure curve, which yields both the maximum admissible pressure difference and the stiffness of the interface against pressure fluctuations. For single flat orifices at constant open area, elongating the opening from an aspect ratio of one to six raises the admissible pressure difference by 40 % and the stiffness by a factor of 3.3. Comparison with slits of equal width shows that this gain originates entirely from the reduced opening width. Sheared, diamond shaped openings are markedly less effective. In woven meshes, the wettability displaces the operating window several times as far as it stretches it. A less wetting surface therefore buys flooding margin largely at the expense of breakthrough margin, whereas the geometric route, established here for flat openings, widens the window itself. From these results we derive design rules for structured gas-liquid contactors and improved GDE architectures for organic electrosynthesis.

Artificial intelligence increasingly demands computing architectures capable of adaptive representation, temporal information processing, and robust operation under uncertainty. However, conventional photonic neural architectures typically rely on predefined computational operations and separate functional modules, limiting the ability of physical systems to exploit their intrinsic dynamics for intelligence. Here, we demonstrate a monolithically integrated active photonic neural network (APNN) that harnesses driven-dissipative criticality as a physical computational resource. By balancing optical excitation and dissipation, the system operates near a critical regime where weak input-dependent variations are amplified into separable representations while stable attractor dynamics are preserved. The APNN integrates an optoelectronic nonlinear array and a reconfigurable symmetric optical coupling matrix on a silicon photonic chip, enabling recurrent physical computation within a compact closed loop. We demonstrate nonlinear classification with 95.2% accuracy using only 100 training samples and 44 trainable parameters. And it remains robust at an ultralow signal-to-noise ratio of -30 dB. Beyond static recognition, the same driven-dissipative dynamics enable long-range temporal feature extraction from electrocardiogram signals and associative recovery of corrupted patterns through attractor-based relaxation. These results establish driven-dissipative criticality as a unified mechanism for representation enhancement, temporal information retention, and error-resilient computation, providing a pathway toward scalable photonic systems in which intelligence emerges from intrinsic physical dynamics.

Floquet theory provides insight into the inversion of time-dependent Kohn-Sham density functional theory. Specifically, mathematical derivations show that the fundamental frequencies of a time-dependent wavefunction solution are the leading-order harmonics for the TD-KS state. Numerical tests of the resulting ansatz in 1D and 3D for atomic and molecular cases demonstrate its utility. In particular, low $L_{2}$ errors in the time-dependent density and longitudinal current were found, even though currents were not an explicit optimization objective. In all, the proposed inversion ansatz provides exchange-correlation potentials from time-dependent wavefunctions, is highly interpretable, and may significantly help in the development of nonadiabatic density functionals.

We implement the machine-learned Skala exchange-correlation (XC) functional natively in CP2K using its Gaussian and plane-wave (GPW) and Gaussian and augmented-plane-wave (GAPW) methods. A joint one-centre reconstruction of density, density gradients, and kinetic-energy density before functional evaluation preserves mixed gradient terms and nonlocal couplings between smooth and atom-local contributions in all-electron and pseudopotential calculations. An XC-specific GAPW representation resolves rapidly varying local contributions on atom-centred grids, reducing plane-wave requirements for pseudopotential calculations. The implementation includes Brillouin-zone sampling and point-group symmetry reduction. With sufficiently flexible orbital bases, it retains the molecular benchmark accuracy of our earlier GauXC formulation. All-electron Skala-D3(BJ) calculations yield a mean absolute error (MAE) of 1.54 kJ mol$^{-1}$ against diffusion Monte Carlo for crystalline CO$_2$, NH$_3$, and urea, spanning dispersion, quadrupolar electrostatics, and hydrogen bonding. For all thirteen DMC-ICE13 phases, the MAEs are 1.16 kJ mol$^{-1}$ for absolute lattice energies and 0.82 kJ mol$^{-1}$ for the twelve relative energies to ice Ih. At fixed experimental geometries, all-electron/mixed-core calculations give a band-gap MAE of 0.43 eV on a 15-material set, substantially below commonly used semilocal functionals and comparable to widely used hybrid functionals. The LC10 benchmark nevertheless reveals systematically underestimated equilibrium lattice constants, indicating structural overbinding. This framework connects molecular Skala to condensed-phase electronic structure and enables future development using periodic many-body reference data.

We present a first-quantization, all-electron, full-potential Kohn-Sham density functional theory method for quantum computers, based on a classically optimized quantum-circuit eigensolver for the self-consistent field (SCF) eigenproblems in any orthonormal basis. The plane-wave-orthonormalized-orbital (PWOO) basis combines plane waves with atomic orbitals (AOs) orthonormalized against them and one another. The eigensolver has a dual-basis form: after full-basis bootstrap steps, it solves each SCF step in a contracted basis of $K$ functions ($\lceil\log_2 K\rceil$ qubits), updated in the full basis when the residual outside it exceeds a threshold. For an H$_8$ chain (SVWN, $K=8$), the state-vector-emulated SCF agrees with classical calculations within 0.02 mHa for 32768 plane waves and PWOO bases up to cc-pVTZ; contraction changes these PWOO energies by at most 5.7 $\mu$Ha. With emulated shot noise, the STO-3G PWOO SCF converges near the noise-free fixed point. On IonQ Forte-1, three-qubit-register readout reproduces the noise-free PWOO-AO energy difference within one standard deviation.

Cloud computing and high-performance computing (HPC) typically follow different paradigms: cloud services are often orchestrated using Kubernetes, whereas HPC workloads are managed through batch schedulers such as Slurm. Growing demand for shared computational resources increases the need for interoperability between these environments. This study uses Podman as a user-accessible tool to benchmark quantum chemistry software distributed as precompiled executables. Containerized and on-system execution are compared across CPU-optimized builds and multiple compute nodes, without additional network optimizations. The results demonstrate that performance depends on software compilation, startup overhead, and execution configuration. Container preparation can dominate short-task workflows, while long-running calculations require monitoring of computational progress. These findings highlight the importance of workload-specific benchmarking and user-level monitoring when deploying scientific applications in containers on HPC systems.

Modeling spatiotemporal coupling is a key challenge in building physical intelligence across scales, from microscopic to macroscopic. Existing models capture such structure broadly through physics-motivated dynamical formulations or learning-motivated architectures. The former provide stronger priors but may constrain flexibility, whereas the latter are more flexible but leave the spatiotemporal coupling largely implicit. We therefore seek an approach that combines flexible learning with an explicit geometric bias for jointly modeling time and space. To this end, we propose Minkowski Positional Encoding (MinkowskiPE), which uses joint temporal and spatial coordinates to parameterize Lorentz transformations applied to query and key features. With MinkowskiPE, the query-key attention score depends on position only through the relative spacetime displacement between the two tokens and is therefore invariant to global translation of the coordinates. This paradigm retains the standard dot-product attention interface and remains compatible with efficient attention implementations. We evaluate MinkowskiPE on microscopic molecular dynamics and macroscopic video prediction tasks, achieving the best results on all nine multi-trajectory molecular evaluations and reducing KTH video-prediction MSE by 9.9% relative to the best baseline while using roughly one-tenth as many parameters.

De novo crystal generation (DNG) models decide where to search in composition space and how to generate structures with one set of weights. We argue that discovery is better served by separating the two. A crystal structure prediction (CSP) model is a physical prior that should be improved by likelihood training, while rewards, including novelty measured against the search's own history, should act on a search over compositions. We introduce ANCHOR, a GRPO composition policy trained with multi-objective rewards around a frozen CSP model, and continuous adaptive novelty (CAN), a graded novelty score against known structures and a growing discovery history. Using the frozen CSP model as a fixed ruler under one evaluator, we test where adaptation should act. Replacing DNG compositions with ANCHOR's policy on the same CSP backbone raises MSUN from 11.4% to 47.6% and SUN from 1.1% to 22.1% at 99.9% formula uniqueness. Fine-tuning DNG models directly on the same rewards instead moves their composition marginal without raising their on-hull fraction. We show that KL-regularized fine-tuning of a DNG model can only reweight chemistry the pretrained model already supports by a bounded factor, while unregularized DNG fine-tunes move toward known or less stable chemistry. Even a stability-only reward routed into ANCHOR's CSP backbone roughly halves SUN relative to the frozen backbone, whereas likelihood training on structures found during search can improve a CSP backbone. Under MatterGen's evaluation pipeline, ANCHOR raises state-of-the-art MSUN from 29.2% to 41.3%, transfers without retraining to two further CSP backbones, and reaches 47.1% after distillation into Crystalite-CSP. As with any model optimised against a potential, its on-hull rate depends on that potential.

Quadratically nonlinear systems driven by additive noise arise throughout science and engineering, both as stochastic dynamical systems in their own right and as reduced-order models (ROMs) of turbulent flows. We propose stochastic physics-constrained operator inference (SPOpInf), a non-intrusive method that learns a stochastic differential equation, i.e., a quadratic–linear drift and a diffusion amplitude, from data. Unlike operator inference (OpInf), which fits a deterministic drift by least squares, SPOpInf maximizes an Euler–Maruyama increment likelihood in which the residual covariance is itself an unknown, so the deterministic and stochastic components are calibrated jointly; it enforces the energy-preserving quadratic structure exactly, through linear equality constraints imposed inside the optimization; and it works in an upper-triangular parametrization that removes the structural non-identifiability of the full quadratic tensor. The resulting optimization is solved by an expectation–maximization (EM)-based iterative learning algorithm that updates the drift coefficients and the noise levels in turn: each iteration requires only an inexpensive weighted least-squares solve for the drift and a residual-variance update for the noise. With five stochastic benchmark systems that show intermittency and chaos, SPOpInf recovers the deterministic operators more accurately than OpInf, satisfies the imposed constraints to machine precision, accurately estimates the noise amplitudes, and reproduces long-time statistics. Applied to a stochastic Burgers equation and a quasi-geostrophic double-gyre flow, the same estimator yields non-intrusive stochastic ROMs that remain stable over long times where unconstrained alternatives blow up.

Criticality in the Ising model is conventionally generated by Hamiltonian dynamics and controlled by temperature. Here we show that critical like behavior can emerge in an Ising system whose dynamics is completely independent of the Ising Hamiltonian and contains no temperature like parameter. We introduce an adaptive cluster dynamics in which spin connectivity is controlled by a local quiet time variable, the time elapsed since a spin was last updated. The Ising Hamiltonian enters only as an observable characterizing the resulting configurations. As the parameter $\alpha$, controlling the connectivity strength, is varied, the system undergoes spontaneous symmetry breaking accompanied by strong collective fluctuations. The cluster size distribution develops an extended power law regime, terminated by a small finite size hump at the largest scales, while the Ising energy exhibits a singular response to the variation of $\alpha$. These results show that memory dependent connectivity alone can generate collective critical behavior, revealing a route to nonequilibrium criticality without energy based dynamics.

Whether orthogonalising the moment basis changes a central-moment lattice Boltzmann scheme is decided by the geometry of the velocity set. The basis enters the collision only through the conjugate $\mathit{T}^{-1} \Lambda \mathit{T}$, so two bases related by a constant matrix $\mathit{A}$ define exactly the same scheme if and only if $[\Lambda,\mathit{A}]_{ij}=\mathit{A}_{ij}(\lambda_i-\lambda_j)$ vanishes, and on physical states only its columns for the non-conserved moments matter. We prove that on lattices with velocities in $\{0,\pm1\}^d$ and symmetric weights orthogonalisation reaches the shear moments only through the face and body diagonals: whatever the orthogonalisation, the shear rate is free on D2Q9 and D3Q15, whereas on D3Q19 and D3Q27 the scheme changes whenever the fourth-order moments do not relax at the shear rate. On rectangular lattices, where the symmetry is broken, an independent bulk rate yields an orthogonal counterpart that does not share the transport coefficients of the published scheme, which is itself orthogonal in the inner product of the rest equilibrium up to the one relaxation entry that consistency requires. Where the formulations differ but share their hydrodynamics, a basis orthogonal in the inner product of the rest equilibrium, which guarantees linear stability at rest, was never less robust in the least stable flow direction by more than a few per cent, often much more robust, and the more accurate against a Taylor-Green DNS. Computed through the non-orthogonal transforms with a conjugated relaxation matrix, it costs at most $2\%$ more on D3Q27.

The fission matrix (FM) method recasts neutron transport in matrix form, enabling fast, interpolation-based reactor calculations from a pre-computed database of Monte Carlo-derived coefficients. Propagation of the underlying Monte Carlo statistical uncertainty to the FM eigenvalue and eigenvector is rarely rigorous: prior approaches assume independent coefficients without testing this against their actual covariance. This work derives a full-covariance Delta-method framework for propagating uncertainty to keff and the fission source, and evaluates it with two cheaper alternatives, a diagonal-covariance approximation and direct resampling of the FM coefficients, using an OpenMC model of the JSI TRIGA Mark-II reactor. For the all-rods-out case, these three estimators and an empirical benchmark of 100 independent Monte Carlo runs agree within 5.7% for keff and 1% for the fission source. The sign of the diagonal approximation's bias flips between the two statistics levels, so it must be checked case by case. With a global fixed-source FM generation strategy, the diagonal, resampling, and independent-run estimators agree within about 2% and lie roughly 10% below the full-covariance estimate, a gap attributed to covariance sampling noise. The large off-diagonal covariance is nearly symmetric and mostly cancels when propagated, rather than being small or negative as previously assumed. For the FM control-rod interpolation and combination strategy (FM-CRd), keff matches an exact perturbed reference within 60 pcm (about two standard deviations) and the fission source within 0.7%, while the diagonal and resampling estimators agree closely and are conservative by about a factor of two. Given this and the prohibitive memory cost of the full covariance, the diagonal Delta method is recommended as the practical default, with the full covariance reserved for one-time characterization of a system.

We present GEM (Ghost Embedding Method), an open-source software package written in Python for computing equilibrium properties of strongly correlated electronic systems within the ghost-Gutzwiller approximation method. GEM provides a computationally efficient framework for studying multi-orbital lattice models. It supports zero- and finite-temperature calculations and symmetry broken phases. It is integrated with the TRIQS ecosystem, providing tools for model construction, self-consistent solution, and evaluation of physical observables. We first detail the method's theoretical formulation, then we present the software architecture, and finally we introduce some practical workflow, which also validates the implementation against established results. In particular, we illustrate the capabilities of GEM through multiorbital and finite-temperature applications and discuss its computational cost relative to more demanding quantum embedding approaches.

Improvised explosives used for fishing on shallow Indonesian reefs shatter coral skeleton, yet the damage they cause has been described largely through empirical radii and ecological surveys. We formulate an idealized model of how free gas held within a coral canopy modifies the shock loading that such a charge delivers to skeletal plates. The canopy is treated as a relaxed bubbly mixture whose shock impedance follows from the conservation of mass and momentum, and the reef is represented as a layered column of water, canopy, skeletal plate, and canopy struck at normal incidence. Three closed-form results emerge. Above a crossover pressure set by the void fraction and the stiffness of seawater, the canopy becomes nearly transparent to the shock. The impulse transmitted through any lossless layered stack is independent of the canopy, so gas redistributes the pulse in time without changing its total push. A plate carries tension after reflection from its lower face only when the canopy impedance falls below a threshold fixed by the plate thickness and the pulse duration, which defines a critical thickness. For a one-kilogram charge directly overhead, a gas-rich canopy more than triples the standoff at which a twelve-centimeter plate spalls while shortening the standoff at which it is crushed. A prescribed daily cycle of photosynthetic gas makes the same charge markedly more damaging at noon than at night. Bubble dynamics show that the canopy does not reach equilibrium within the pulse, so the results are best read as upper bounds.

Carleman linearization represents nonlinear lattice Boltzmann collision dynamics in a form amenable to quantum block encoding, but low postselection probabilities in existing population-space encodings make coherent multi-step evolution exponentially unlikely to succeed. We present a quantum Carleman lattice Boltzmann scheme based on the multi-relaxation-time collision operator in a weighted Hermite moment basis. In this basis, the lifted collision operator separates into small coupled blocks whose norm exceeds unity because of the coupling between conserved and relaxing modes. This block structure enables a norm-attaining block encoding with a single-step success probability close to unity. Crucially, scaling the pair sector for a prescribed evolution horizon makes the combined encoding and sector-selection overhead grow polynomially rather than exponentially with the number of steps. For a hundred-step evolution, the resulting complete-run success probability exceeds that of population-space encodings by orders of magnitude. Over horizons of several tens of steps, the truncated dynamics reproduces the nonlinearly generated modes of a benchmark flow to within a few percent. We verify the combined preparation, evolution and readout protocol as a single unitary circuit and give a complete gate-level resource estimate for extracting a nonlinear observable of the benchmark flow from a coherent Carleman evolution. The block structure of conserved and relaxing modes holds equally on three-dimensional lattices and provides a constructive route to norm-attaining encodings for lattice Boltzmann models with quadratic equilibria.

Verifying a numerical algorithm in a large scientific simulation framework is challenging: the framework is too big to model-check, and the unit tests exercise only sampled inputs. We report a case study in which we developed a new cloud-in-cell (CIC) deposition algorithm for Flash-X, a large-scale multiphysics simulation framework, keeping the CIVL model checker in the development loop. Rather than verify the algorithm within Flash-X's hefty infrastructure, we extract only the interfaces that the algorithm needs into a small, self-contained C model, which abstracts away implementation details of the Flash-X infrastructure that are unrelated to the new algorithm. The new algorithm is then built and checked within this C model. The CIVL model checker enables verification of the required physical properties of the CIC deposition algorithm using symbolic values for the particle positions. It proves two physical properties—mass conservation and the deposition location—for the continuum of admissible positions in the simulation domain. CIVL also verifies the algorithm's memory safety and freedom from MPI deadlocks and data race conditions over all rank distributions within specified bounds. Writing the verifying properties first and continuously checking them at each stage of the bottom-up prototyping workflow turned CIVL into a design guardrail that greatly increased confidence in the extended algorithm. During our case study, CIVL surfaced a concurrency defect in the algorithm that our random-seed-based tests failed to exercise. This paper shows our workflow, with the goal of helping readers understand its benefits, cost, and tradeoffs compared with testing.

A point-defect cavity side-coupled to a line-defect waveguide in a two-dimensional photonic crystal of silicon rods in water is studied with plane-wave expansion and finite-difference time-domain computations. The defect-rod radius tunes the resonance continuously within the band gap, as first-order perturbation theory predicts, whereas the quality factor changes in discrete steps set by the number of lattice rows between cavity and guide; displacing the defect rod by up to a tenth of a period changes it by less than 7 percent. Each added row multiplies the quality factor by a factor that follows, without an adjustable parameter, from the decay of the evanescent Bloch channel of the bulk crystal that is phase-matched to the guided mode; the channel at zero wavevector along the guide predicts little more than half that factor. Two biases of a finite computational domain, leakage across the cladding and a standing wave set up by reflections at the ends of the truncated guide, lower the per-row factor and change the quality factor by up to a factor of two if left uncorrected. Scaled to 1550 nm the design gives a sensitivity of 634 nm per refractive index unit, which perturbation theory reproduces, and the linewidth agrees with that of a transmission spectrum normalized to a cavity-free reference. Absorption by water caps the quality factor near 9200 and limits the useful number of barrier rows. The guided mode lies inside the light cone, so a slab of finite height needs a different guide.

Density functional theory (DFT) strikes a practical balance between accuracy and computational cost in many problems of computational chemistry and materials science. However, many DFT calculations are limited by fixed atom-centered basis sets, which dictate how accuracy and cost scale with system size. We propose Gaussian Splatting for Density Functional Theory (GS-DFT), which represents molecular orbitals as a cloud of Gaussians whose positions, shapes, and mixing coefficients are optimized jointly by gradient descent to minimize the energy without training data. Conceptually, GS-DFT is 3D Gaussian splatting with the renderer replaced by quantum mechanics. We introduce two key solver components: adaptive density fitting with screening for efficient evaluation of two-electron integrals, and a regularized differentiable orthogonalization of the molecular orbitals. Empirically, the optimized basis reaches the accuracy of the largest conventional basis sets with a fraction of the parameters, converging systematically in energy, density, and nuclear forces. At equal parameter count, it captures the stretched-bond and anion physics that fixed bases only recover with specialized basis augmentation. The resulting solver exhibits quadratic peak memory scaling in the cloud size, allowing us to simulate systems of up to 2,742 atoms (10,406 electrons) without any modifications at triple-zeta scale using a single four-GPU node.

We present a parallel strategy for the study of the vortex-induced vibrations (VIV) of a rigid, massless cylinder mounted on translational springs, in two and three dimensions. Without mass or damping, its motion is governed solely by the fluid forces and the spring restoring force, and is an immediate response to the flow. We focus on low spring stiffness, yielding high reduced velocity and maximal oscillation amplitude. A monolithic finite element method in an arbitrary Lagrangian-Eulerian framework with implicit time stepping is proposed, solving the fluid flow, cylinder dynamics, and mesh motion simultaneously. Mesh movement is modelled with a linear elastic pseudo-solid with variable Lamé coefficients, and the no-slip condition on the cylinder is enforced with a Lagrange multiplier coupled to the position degrees of freedom; three strategies are explored to enforce this force-position coupling in a distributed framework. To the best of our knowledge, this work is the first to propose a distributed solver for three-dimensional fluid-structure interaction at zero mass ratio. The solver is verified with manufactured solutions, and exhibits second-order accuracy in time. A numerical study of two- and three-dimensional VIV for Reynolds numbers from 100 to 300 reproduces the VIV responses obtained in previous two-dimensional studies, and predicts nonperiodic 3D oscillations starting at $Re = 300$. Using the direct solver MUMPS, the proposed method scales to up to 768 compute cores.

Polymers are widely used as functional insulating materials, but predicting their dielectric behavior is challenging because multiple mechanisms, acting across different spatial and temporal scales, contribute to their response. In polyethylene (PE), one of the most common polymers, electronic, atomic, and mesoscale dynamics must all be considered. In this work, semicrystalline models of polyethylene were developed and investigated using a multiscale approach. Quantum simulations were employed to describe electronic and vibrational contributions to the dielectric response, while classical molecular dynamics simulations captured the behavior of polymer chains at room temperature and frequencies down to the 10-100 MHz range. The study focuses on the impact of radio-oxidation defects on the dielectric properties of polyethylene. Quantum calculations reveal how electronic and vibrational contributions depend on the local atomic environment surrounding these defects. Comparison with molecular dynamics results highlights the influence of temperature on the static dielectric constant. Structural analyses further assess the effect of each defect type on PE crystallinity. Analysis of dipolar correlation functions shows that different defects interact with one another and with the polymer matrix in distinct ways, affecting permittivity and dielectric loss peaks. For all defect types, defect-defect interactions provide the largest contribution to dielectric response. While most oxidized groups exhibit positive coupling with the PE matrix, alcohol defects display a negative cross-correlation, partially offsetting their impact on the dielectric properties. Our results also show that ketone groups produce the largest dielectric loss between the defects studied.

Scientific data span heterogeneous structures, including coordinates, networks, surfaces, volumes and fields, yet their topology can be quantified within a common framework through graph connectivity, cycle structure, genus and spatial embedding. Graph- and homology-based summaries do not determine spatial embedding, while standard knot and link polynomials require extensions to accommodate branching graphs. Here, we introduce KnottedGraph, a computational framework that converts such scientific representations to knotted graphs that retain graph connectivity and spatial embedding together. It constructs projected diagrams and PD codes, enabling various topological analyses, including Yamada-polynomial evaluation for topological classification. For scalable exact evaluation, it combines partial resolutions that leave the same unresolved connections and optimizes their processing order; the resulting algorithm is verified against published topological invariants of knotted graphs with up to 500 crossings. This scalability enables us to introduce an LLM-assisted mathematical-discovery methodology, in which computational topological data generated across knotted-graph families are used to identify candidate closed-form formulas. With this approach, we identify analytical Yamada-polynomials for generic graph motif families exhibiting Abelian and non-Abelian word sequences. Together, these scalable capabilities make knotted-graph topology computationally accessible across scientific domains, enabling large-scale classification and introducing a route from topological data to LLM-assisted AI4Math discovery.

This study derives the asymptotic conditions under which the massless stretched string formulation is valid for the equivalent dynamics of the inertial string carrying a moving point mass. Consequently, the governing equation under such conditions can be written as a singularly perturbed partial differential equation when the inertia of the string is included. When the inertia of the string is ignored, the governing equation reduces to a non-homogeneous hypergeometric ordinary differential equation governing the transverse motion of the moving mass. This hypergeometric equation has a discontinuous solution at the terminating boundary known as the trajectory paradox. However, numerically solving the actual equation yields a continuous solution with a rapid variation near the boundary. The complete solution resembles the inner solution as well, whereas the hypergeometric ordinary differential equation leads to an outer solution, revealing that the trajectory paradox is a boundary layer.

The emergence of autonomous laboratories motivates rapid conversion of experimental data into reliable atomistic models on time-scales compatible with closed-loop optimization. Here we develop an energetically driven structure matching framework for analysis during ongoing total X-ray scattering experiments. Using data from gold nanoparticles, we match against idealized spherical, octahedral, decahedral, and icosahedral geometries, their machine-learned interatomic potential (MLIP)-relaxed structures, and molecular dynamics (MD) ensembles. Idealized models are fast to generate but can misassign morphology and systematically underestimate size by neglecting surface relaxation, strain, and thermal disorder. MLIP relaxation markedly improves both, while MD ensemble averaging agrees best with experiment. We therefore introduce a hierarchical workflow combining rapid idealized screening with targeted MLIP and MD refinement of top candidates, delivering improved structural feedback without interrupting autonomous operation. This framework provides a route towards autonomous campaigns in which the target structure itself can be updated in response to the evolving energy landscape of structures compatible with the experimental data.

Representation learning, or featurization, of mean-field Bloch states provides an important route for incorporating electronic information into machine-learning models of first-principles condensed-phase systems. A challenge in representing Bloch states is the gauge redundancy of each state. In this work, we propose to address this issue by explicitly incorporating gauge equivariance in the machine-learning framework. We develop a $U(1)$-equivariant autoencoder that compresses the plane-wave-basis Bloch states obtained from density functional theory into a low-dimensional latent representation. We achieve an average overlap of 0.970 between original wavefunctions and the reconstructions from a 64-dimensional latent space using a dataset of two-dimensional insulators. We further show that $U(1)$ equivariance endows the latent space with physically meaningful structures, including smoothness and topological information. Finally, we present a proof-of-principle application in which the latent representations are used to predict the off-diagonal elements of the $GW$ self energy matrix, and demonstrate the importance of enforcing gauge equivariance in the prediction.

This study conducts a systematic hyperparameter search across five deep learning architectures, DLinear, LSTM, PatchTST, ResAttLstm, and Mamba2, and nine context lengths (1-168 h) for single-station significant wave height (Hs) forecasting on NDBC buoy 41009, followed by re-evaluation of the best configurations on a 47-buoy, 37-year corpus. The five families converge to a common performance level on the multi-buoy evaluation (between-family SD = 0.0014 m^2, 0.8% of the grand mean), a spread dwarfed by the 4.83x cross-dataset MSE shift between buoy corpora. All multi-buoy trials beat persistence (mean skill +0.062), but no architecture consistently outperforms the others. On the single-buoy experiment, skill peaks at 12-24 h where five trials fall below persistence, per-family Q4/Q3 test MSE ratios range from 2.4 to 2.6, and deep models underperform persistence for the most extreme 1% of waves. These findings are consistent with the interpretation that persistence already captures the dominant linear-inertial signal in univariate Hs, and that architecture engineering under this univariate input setting has reached diminishing returns: cross-buoy variance, not model class, dominates forecast error. Future work should prioritise atmospheric covariates, zero-shot cross-buoy transfer, and decomposition of Hs into swell and wind-sea components. By establishing a rigorous reference baseline for what univariate Hs models can and cannot achieve, this study provides a benchmark against which future multivariate and physics-informed approaches can be calibrated, and offers practical guidance for lightweight buoy-level forecasting in mid-latitude storm-dominated and swell-mixed environments.

Physics-informed neural networks (PINNs) often converge to inaccurate solutions for conservation laws with shocks, because uniformly distributed collocation points undersample localized features and let the residual be dominated by regions that are already well resolved. We propose a feature-tracking PINN (FT-PINN) in which the solution network is defined on a fixed reference domain and composed with a diffeomorphic deformation map from a parameterized nonlinear manifold. The deformation and solution-network parameters are trained jointly by minimizing the pulled-back conservation-law residual. This lets collocation points concentrate along features of essentially arbitrary geometry, including curved, oblique, and merging shocks, without prior knowledge of their locations. The framework is agnostic to the choice of parameterization. Boundary preservation is enforced exactly through a tangential projection of the displacement, and folding is discouraged by a one-sided penalty on the Jacobian determinant. On four test problems (space-time viscous Burgers with merging shocks, a decelerating Burgers shock, the space-time Euler shock tube, and steady 2D Euler regular shock reflection), FT-PINN resolves shocks at their correct locations with a limited collocation budget. A vanilla PINN with the same architecture, budget, and training either misplaces the shocks or fails to form them.