Papers

We present Transient PULSE, a software package that numerically implements a previously developed source-to-detector framework for transient ultralight bosonic signals from astrophysical bursts. Predicting these signals relies on connecting the source emission spectrum to its evolution during propagation and the resulting observables at a terrestrial detector. The package discretizes a user supplied energy spectrum into momentum modes, propagates them through a specified matter density profile and constructs the time-frequency energy density distribution at Earth, accounting for dispersion and in-medium screening effects. This treatment accommodates non-Gaussian source spectra and provides inputs for detector specific analyses. A complementary analytical module estimates coupling sensitivities, arrival time delays and screening thresholds from parameterized source and detector properties.

Widely used methods for identifying crystal structure in atomistic simulations are limited in practice to a handful of simple structures, leaving many important crystalline systems without automated classification techniques. Voronoi topology analysis offers a route to classifying arbitrary crystalline and defect environments, but realizing this potential first requires enumerating the Voronoi cell topologies that can arise under thermal perturbation of a structure of interest. We present an algorithm that deterministically enumerates all Voronoi cell topologies arising from generic infinitesimal perturbations of an arbitrary crystal structure, producing structural classifiers that extend automated identification to general crystalline systems. We demonstrate the approach on several structures of general interest.

We introduce Lambda-ABF-OPES+ ($\text{LAO+}$), a multi-replica framework for absolute binding free energy (ABFE) calculations that accelerates both the alchemical transformation and the slow “orthogonal” motions coupled to it. At the core of $\text{LAO+}$ is a partitioned $\lambda$-dynamics scheme that concentrates sampling on the abrupt rehydration of the binding pocket, the main bottleneck of ligand decoupling, while Hamiltonian replica exchange relays configurations along the entire alchemical path. This drives a fourfold gain in convergence speed for the rate-limiting leg over our previous $\text{LAO}$ method, which was itself up to ninefold faster than Lambda-ABF, an overall gain of up to $\sim$36-fold. Applied to 28 protein–ligand complexes across five targets, $\text{LAO+}$ achieves a root-mean-square error of 0.83~kcal~mol$^{-1}$ and a correlation of 0.87 with experiment from only 63~ns of sampling per ligand. Moreover, dedicated reservoir replicas accelerate any slow degree of freedom that can be described by a collective variable. We demonstrate this by recovering hidden protein and ligand conformational states, for example in T4 lysozyme, BRD4 and JNK1. Together, these advances make accurate ABFE calculations practical for drug discovery.

Advances in polymer synthesis and computational modeling are expanding the block-copolymer architecture space accessible for phase-behavior design. Machine learning can accelerate this exploration, yet a common representation capable of learning across diverse chain topologies remains lacking. Here, we present a graph neural network (GNN) representation of acyclic AB multiblock architectures, tested by random-phase approximation (RPA) instability prediction. Each chain is represented as a graph, enabling a common model to learn across diverse topologies. This representation, which organizes RPA-related information, retains predictive capability when extrapolated to architectures with more blocks and demonstrates its potential for reuse across tasks through transfer to instability-wavenumber prediction. By effectively linking block-copolymer chain architecture to field-theoretic response, this graph representation not only reconstructs stability-limit curves but also provides a practical route for future self-consistent field theory exploration of ordered phase space across complex topologies.

We present a novel method which combines the invertibility of the differential filter of Germano, with convolutional networks to accelerate plasma turbulence simulations. Rather than learning the mapping from coarse-grid LES fields to fine-grid DNS, the proposed method learns the mapping from coarse LES fields to the differential-filtered DNS fields. We then use the inverse of Germano's filter to reconstruct the fine-scale details and hence calculate exactly the nonlinear terms in the governing equations and subgrid-scale terms in the LES equations. The method is tested on the 2D Hasegawa-Wakatani (HW) and modified Hasegawa-Wakatani (mHW) plasma turbulence models at $256^2$ and $512^2$ DNS resolutions using 2, 4 and 8 times smaller LES grids in each direction. We compare the model with DNS results on energy, enstrophy, spectra, probability distributions, poloidal and radial fluxes and computational cost. Validation extends to 1000 simulation time units for HW and 100 for mHW, whose faster dynamics lead toward laminarization. For the $256^2$ cases, the finer LES meshes preserve several integral and spectral features, whereas the coarsest mesh yields unphysical behavior. In contrast, for the $512^2$ cases, even the coarsest LES mesh preserves the turbulent character of the flow and maintains acceptable statistics for both the HW and mHW models. Moreover, we show how our methodology is superior to traditional algebraic numerical LES models, which traditionally fail to capture important design features. Finally, benchmarks show an MPI task-time reductions of 4.82–49.45, with a maximum wall-clock speedup of $1.55\times$ when compared to full CPU socket.

Repeated high-fidelity state and gradient evaluations make large-scale PDE-constrained optimization computationally expensive. Reduced-order modeling provides a natural way to reduce the cost of these repeated high-dimensional computations. However, existing reduced-order modeling approaches often rely on converged high-fidelity states for model construction or updating, while their reduced spaces may lose accuracy as the design moves beyond the region represented by the available data. To address these limitations, we present Reduced-order Trajectory-based Optimization (RETO), an online framework that constructs local reduced-order models (ROMs) directly from unconverged primal solver trajectories. Each local ROM is built from snapshots collected during a finite number of high-fidelity primal iterations, without requiring full-order convergence, and supports multiple low-cost state evaluations, adjoint-based gradient evaluations, and design updates. New solver trajectories are generated at updated design points to reconstruct the local ROM and continue the optimization. Across three distinct PDE-constrained optimization problems, RETO achieves solution quality comparable to that of full-order optimization, with speedups of approximately 8 to 22 times in cases without discontinuities in the state fields. Even in the transonic inverse-design case involving moving shocks, RETO retains an approximately threefold speedup. The transonic results further show that the online local ROM progressively captures evolving shock-related flow features as new primal solver trajectories are incorporated. These results demonstrate the value of unconverged primal solver trajectories as an online information source for reduced-order optimization, allowing the reduced basis to evolve with the design rather than requiring a basis that covers the entire design space in advance.

Rapid prediction of pressure-driven flow in microfluidic porous media is important for experimental design, tracer-test interpretation, and digital-twin development for subsurface energy and critical mineral applications. High-fidelity simulations resolve geometry-controlled flow but are computationally expensive across large geometry ensembles. Here, we introduce GeONet, a Geometry-Encoded Operator Network that predicts steady-state pressure fields by jointly representing material properties, spatial coordinates, and solid–void geometry. GeONet extends the Branch–Trunk architecture with a dedicated Leaf Network encoding the binary domain mask through multiscale features. The Branch Network represents porosity and permeability, the Trunk Network combines coordinates with local geometric descriptors and random Fourier features, and a gated DeepMixer integrates these representations to predict pressure. GeONet was trained and evaluated using 5,000 PFLOTRAN simulations of heterogeneous Reduced Complexity Platform domains, comprising nearly 30 TB of data. Comparisons with pore-scale Stokes solutions across three geometries yielded Pearson correlations of 0.987–0.991 and $R^2$ values of 0.974–0.982, supporting PFLOTRAN as reference data. Under matched partitions and two-stage hyperparameter optimization, GeONet substantially outperformed a boundary-condition-aware DeepONet baseline. Across three held-out domains, GeONet achieved NRMSE of 0.0381–0.0500, MAPE of 1.76–2.59%, and $R^2$ of 0.9673–0.9822, versus 0.1483–0.2040, 7.81–10.45%, and 0.5658–0.7126 for DeepONet, respectively. On three additional unseen geometries, GeONet achieved NRMSE of 0.0448–0.0676 and $R^2$ of 0.9511–0.9770. These results demonstrate improved accuracy, pressure-range preservation, and cross-geometry generalization through explicit geometry encoding.

Velocity space discretization is a primary source of computational cost in deterministic methods for multiscale gas flows. A fixed velocity grid often retains redundant kinetic degrees of freedom (DOFs), particularly under near equilibrium conditions. To address this issue, this work develops a nonequilibrium-capturing formulation based on the unified gas kinetic scheme (UGKS), in which the number of kinetic DOFs adapts locally to the degree of nonequilibrium. A discrete orthogonal basis is constructed for numerical implementation, and the velocity distribution function is decomposed into an analytical local equilibrium and a basis expanded nonequilibrium component. The retained, locally adapted DOFs are evolved directly, substantially lowering computational overhead while preserving the discrete conservation of mass, momentum, and energy, as well as accurately capturing nonequilibrium states. The formulation retains the core multiscale coupling of molecular transport and collision inherent to UGKS, providing explicit and implicit schemes for unsteady and steady flows, respectively. Numerical tests across a wide range of flow speeds and rarefaction regimes (from continuum to highly rarefied) demonstrate close agreement with benchmark solutions. For unsteady flows, the explicit scheme achieves speedups of 12.64 to 58.50 over the standard UGKS. In steady state tests, only about $2\%$ of the original kinetic DOFs are required in continuum regions, accelerating each implicit iteration by a factor of 33.87. Even in the most rarefied cases, the scheme captures nonequilibrium behavior using only about $27\%$ of the original DOFs.

Planck-mean absorption coefficients of pure gases are calculated from line-by-line integrations of HITEMP and ExoMol spectra up to 5000 K for use in high-enthalpy radiative heat transfer simulations. The dataset extends beyond conventional combustion products, including high-temperature radicals, nitrogen-bearing species, soot precursors, metal oxides, metal hydrides, and halides: AlF, AlH, AlO, BH, C2, C2H2, CH, CH4, CN, CO, CO2, H2O, HBO, HCN, HF, MgH, MgO, N2O, NO, NO2, OH, SiO, TiH, TiO. New calculations are validated against historical correlations for overlapping species, demonstrating good agreement over their applicable temperature ranges. Strong visible opacities result in large Planck-mean absorption coefficients for many of the considered species, highlighting the need to account for their radiative contribution in extreme environments. A brute-force search over several candidate functional forms is performed to provide a common set of coefficients, establishing a standardized framework that can be easily integrated into production solvers and extended as additional high-temperature line lists become available.

This work extends the Deep Energy Method to phase-field modelling of ductile fracture in elasto-plastic solids. Its key contribution is an incremental DEM-based formulation that couples history-dependent J2 plasticity and plasticity-dependent fracture toughness with separate energy-optimised displacement and phase-field representations. The formulation combines the second-order Ambrosio-Tortorelli phase-field fracture model with small-strain J2 plasticity and linear isotropic hardening. A volumetric-deviatoric split defines the elastic crack-driving energy, while accumulated equivalent plastic strain governs the degradation of local fracture toughness. Plastic internal variables are updated locally through radial return. The reduced energy is minimised alternately with respect to the displacement and phase fields, represented by a ReZero residual neural network and spatially localised Gaussian radial basis functions with trainable centres, respectively. This split addresses the diffuse phase-field profiles observed in preliminary calculations with a shared global network. Alternating optimisation is combined with transfer learning to reuse trainable parameters and optimiser states across loading increments, while the converged constitutive history is carried forward separately at quadrature points. The numerical results demonstrate close agreement with finite-element reference solutions in predicting force-displacement responses, energy evolution, plastic deformation and crack propagation. The framework captures the main features of ductile fracture, although accuracy becomes more sensitive to loading increments near abrupt fracture events.

Bayesian inversion is widely used in engineering applications, including material characterisation, structural damage identification, and medical diagnostics. These inverse problems are typically ill-posed, because localised variations in material properties must be inferred from noisy observations, and they are computationally intensive, since they often require many evaluations of a high-fidelity forward solver. Quantum computing has recently attracted considerable interest, partly because some near-term algorithms are feasible on NISQ hardware. In particular, PQC combined with classical optimisation enable a hybrid quantum-classical surrogate model. A central obstacle to applying such circuits to inversion is that the discretised parameter and response fields are far too high-dimensional to be embedded in a near-term quantum register. In this work we propose a quantum-assisted latent surrogate model for the Bayesian inversion of inhomogeneous material properties, in which latent compression bridges these high-dimensional fields and the small registers accessible to near-term circuits. The low intrinsic dimensional structure of the spatially varying conductivity and potential fields is exploited by reducing the conductivity through PCA and the response through a convolutional autoencoder. A PQC is then trained to map the latent conductivity to the latent response, and stochastic variational inference is performed entirely in latent space. The methodology is demonstrated on one- and two-dimensional inverse problems under both informative and non-informative priors. We further evaluate the model on IonQ simulator and Rigetti Cepheus-1-108Q, and use a lightweight learned denoising stage that recovers the noiseless accuracy to within a small residual. (The abstract has been shortened to meet arXiv's 1,920-character limit. For the full Abstract, please download the full Article.)

In this work, we develop a unified theoretical framework that constructs Bell-shaped Gaussian quadratures for deterministic Boltzmann solvers. The proposed framework establishes a general class of bell-shaped weight functions together with the corresponding integral transformations, revealing the common mathematical structure underlying existing generalized Gaussian quadratures. Based on this framework, a unified procedure for constructing discrete velocity sets is developed by combining radial quadratures with appropriate directional quadratures in different velocity-space dimensions. Several existing generalized Gaussian quadratures are naturally recovered as special cases, while the proposed framework provides a systematic route for constructing new quadrature rules based on different bell-shaped weight functions. Extensive benchmark simulations over a broad range of flow regimes demonstrate that the proposed framework achieves high integration accuracy and computational efficiency with significantly fewer discrete velocities than conventional quadrature strategies. Overall, the proposed framework not only unifies existing generalized Gaussian quadratures under a common mathematical foundation but also establishes a general design principle for the systematic development of efficient velocity-space quadratures in deterministic Boltzmann solvers.

Cu-C materials and interfaces are central to diamond thermal management, metallization, graphene growth and carbon-coating technologies, but atomistic simulations across these applications require a potential that describes metallic Cu, diverse carbon bonding, heterogeneous Cu-C interactions and close atomic encounters. Here we develop NEP-CuC, a transferable neuroevolution potential trained on a dataset of 2,727 uniformly relabelled configurations selected from a heterogeneous Cu-C candidate pool. Disagreement within an ensemble of five independently trained models provides an internal indicator of model sensitivity. A Ziegler-Biersack-Littmark (ZBL) correction describes short-range nuclear repulsion, while a runtime D3(BJ) correction supplements dispersion-sensitive calculations. Tests on source-derived held-out and independent external datasets, together with structural, elastic, defect, interfacial, vibrational and finite-temperature transport benchmarks, establish broad but property-dependent physical fidelity across elemental Cu, diverse carbon environments and heterogeneous Cu-C configurations. Large-scale simulations of amorphous-carbon formation and orientation-dependent shock compression of Cu further test transferability under strongly non-equilibrium conditions. For Cu/diamond interfaces, the same potential describes deposition, annealing and tensile response: preparation history leaves persistent differences in interphase structure, while the mean peak nominal tensile stress at 500 K decreases from $12.35\pm0.71$ to $6.65\pm0.98$ GPa as the incident Cu energy during the initial deposition stage increases from 1 to 50 eV. NEP-CuC provides an atomistic framework for linking processing, interfacial structure and physical response across Cu-C systems, with direct relevance to Cu/diamond thermal-management interfaces, diamond metallization and non-equilibrium Cu-C processing.

Magnetic racetrack memory requires localized carriers that combine rapid motion, resistance to perturbations and a detectable signal. Here we show how a 360{\deg} domain wall in a hollow ferromagnetic tube combines these properties within a single continuous magnetic shell. Two successive magnetization reversals form a bound object whose surrounding domains point in the same direction. Analytical energetics and micromagnetic simulations establish its finite separation, recovery from tested perturbations and current driven transport without microscopic Dzyaloshinskii-Moriya interaction or a maintaining field. The texture's winding resists unwinding while radial rotation carries an energy cost, providing a specific control over stability. Relative rotation of the constituent spins accounts quantitatively for additional displacement during current onset. The wall supports motion at hundreds of metres per second, with transient velocities approaching one kilometre per second at stronger drive. A prepared seven-bit pattern retains its carriers and local readout contrast after pulsed transport and recovery. Curved-track and differential-current tests identify radial stiffness and drive uniformity as controls for intact motion. These results establish a physical basis for fast, locally distinguishable tubular magnetic bits and identify a continuous switching pathway that can be targeted by tailored excitation.

Kohn-Sham density-functional theory is expensive because it needs orbitals that extend over the whole system. For insulators this can be avoided by using only the diagonal of the one-electron resolvent, $g(\mathbf{r},z)=\langle\mathbf{r}|(z-\hat h)^{-1}|\mathbf{r}\rangle$, at a few complex energies $z$. We call the scheme local-resolvent density-functional theory (LRes-DFT). The density and the band energy are linear in $g$, so neither orbitals nor a kinetic-energy functional are needed. The complex energies are $M$ equally spaced points on a circle that encloses the occupied levels, offset by half a spacing so that no point lies on the real axis. Summing the resolvent over them is equivalent to occupying each level with $1/(1+u^M)$, where $u$ is the level's energy measured from the circle's center in units of its radius. This is a smooth step that is near 1 inside the circle and near 0 outside, and it stays between 0 and 1 for every $M$. If the circle moves with the chemical potential, forces at fixed electron number are exact. Gauss-Legendre and Zolotarev rules need fewer points when the gap is small. In three dimensions we use eigenpairs of small windows around each molecule instead of resolvents. This is divide-and-conquer (DC) with a different occupation function, and it is as accurate as DC with Fermi-Dirac occupations. For H$_2$ molecular crystals of up to 1024 electrons it agrees with Kohn-Sham to $2.5\times10^{-7}$ Ha per electron. On one core it is slower than dense diagonalization below about 500 electrons and 3.5 times faster at 1024 electrons. It loses accuracy for disordered or compressed systems and for diffuse basis functions.

Although machine learning potentials (MLPs) generalize across configurational and chemical compound spaces, their accuracy is commonly believed to be limited by their training methods, with improvements beyond this limit achieved so far only by refitting to experimental observables. In this Perspective, we argue that MLPs can also be made more accurate than their training methods non-empirically by generalizing across a third space, that of quantum-chemical methods. We propose routes to method-transferable MLPs that predict at unseen methods, with working implementations in both density-functional and wavefunction-based theories showing that they can be more accurate than any of their training methods. Aiming beyond the accuracy of the training methods could also make universal MLPs more accurate than single-method models, even when the method-transferable MLPs remain less accurate than those QM methods. Method-transferable MLPs will shape the construction of training datasets and the evaluation of models, pushing the accuracy limits of chemical simulations.

We introduce STRUCTURES-P, a machine-learned all-electron orbital-free density functional for periodic CHNO systems. Electrostatics are evaluated analytically in an atom-centered Gaussian basis, while an equivariant network learns the kinetic and exchange-correlation energy from energies and gradients of non-ground-state densities. Minimizing the functional from a superposition of atomic densities recovers the Kohn-Sham ground state: on held-out crystals, the density error falls from 6.7% to 0.4% of the electron count and the energy error reaches 0.25 mHa per atom, half that of a same-architecture interatomic potential. A single functional can be trained for both isolated molecules and periodic systems, and the model generalizes to larger unit cells. It largely preserves relative-energy rankings and reproduces convex-hull vertices on the tested H-N composition slice. Together, these results demonstrate the viability of machine-learned all-electron orbital-free DFT for variational density optimization and energy evaluation in fixed-geometry solids.

Immersed-boundary methods avoid body-fitted meshes, but the energy or entropy stability of the underlying flow discretisation does not automatically extend to the immersed treatment. This manuscript analyses the volume-penalised compressible Navier–Stokes equations for both energy and entropy stability, on the continuous and semi-discrete levels, and integrates the isolated source exactly in time. The source is formulated as a one-parameter family indexed by $\theta$, whose momentum component relaxes the fluid velocity towards the prescribed solid velocity; $\theta$ sets how much of the resulting kinetic-energy loss leaves the domain rather than being converted to internal energy. The two stability requirements impose opposing bounds on $\theta$, with dissipation of the relative total energy requiring $\theta\geq0$ and stability of the mathematical entropy requiring $\theta\leq1$. Where penalisation acts, both conditions are therefore satisfied if and only if $0\leq\theta\leq1$, and the symmetric value $\theta=1/2$ divides the kinetic-energy loss equally between the domain and the internal energy. We conclude that any entropy-stable split-form discontinuous Galerkin spectral element method remains semi-discretely entropy stable once the source is added at the collocation nodes, for stationary and prescribed moving bodies alike.

We present a Python-based program that combines maximally localized Wannier functions-based first-principles electronic structure with the nonequilibrium Green's function formalism to enable efficient simulations of scanning tunneling microscopy (STM). The workflow builds upon standard density functional theory packages to construct compact transport Hamiltonians that preserve the properties of realistic materials. Superconductivity is incorporated via an effective pairing potential within the Nambu-spinor formalism, while coupling to the STM tip and substrate electrodes is treated using the wide-band limit approximation. Within this formulation, transport quantities such as current-voltage characteristics and differential conductance are evaluated in a closed analytical form. This avoids explicit numerical energy integrations and enables rapid spectroscopic calculations over broad parameter spaces. The framework provides a unified and computationally efficient approach for modeling superconducting hybrid nanostructures with spin-orbit coupling, magnetic textures, and spin polarization. Representative applications in spin chains, two-dimensional and molecular magnets on a superconductor demonstrate its robust capabilities for both simple model systems and realistic ab initio molecular structures relevant to modern STM experiments.

Microscopic simulations resolve spatial patterns but are feasible only over small domains and short timescales, whereas bulk descriptions erase those patterns through spatial averaging. Mesoscopic fields preserve this spatial organisation, but their effective equations are known only for selected microscopic systems and scaling limits. We introduce Deep Mesoscopic Dynamics (DeepMesoD), which uses neural networks to learn an effective mesoscopic field equation from microscopic trajectories at a prescribed coarse-graining scale. For the nonconserved dissipative dynamics studied here, DeepMesoD learns the free-energy functional with a spatial interaction kernel and a state-dependent dissipation operator constrained by the fluctuation-dissipation relation. We first validate the construction in the Ising-Kac model, where the learned mesoscopic equation recovers the known hydrodynamic limit and rollouts remain stable far beyond the training horizon. We then treat two systems without closed-form mesoscopic descriptions. For a two-dimensional Heisenberg ferromagnet governed by atomistic spin dynamics, DeepMesoD learns a mesoscopic model whose predictions match atomistic references up to 1 ns, and a rollout with an unseen initial condition remains bounded up to 25 ns. For layered CrBr$_3$, the learned kernel captures the suppression and sign reversal of interlayer coupling at a stacking fault whose location and strength are not supplied as inputs. Controlled changes to the learned interaction show how fault number and placement shape multistep magnetic responses, complementing our magneto-photoluminescence measurements. Across the two atomistic systems, DeepMesoD achieves a three-to-four-order-of-magnitude reduction in wall-clock time compared with atomistic spin dynamics.

Noncollinear ferrimagnets combine a net magnetic moment with internal spin degrees of freedom, creating opportunities to couple magnetic, mechanical, thermal, and electronic responses. Using first-principles calculations, symmetry analysis, atomistic spin simulations, and transport modeling, we identify stable NbMnX$_2$ ($X$ = S, Se, Te) monolayers with noncollinear ferrimagnetic ground states and Curie temperatures up to 313 K. Competing exchange, Dzyaloshinskii–Moriya interactions, and magnetic anisotropy produce field-responsive canted states that couple strongly to the lattice and charge carriers. Magnetization rotation changes the elastic modulus of NbMnTe$_2$ by up to 36%, while lattice entropy substantially enhances the near-room-temperature magnetocaloric response of NbMnS$_2$ and NbMnSe$_2$. In NbMnSe$_2$, rotation restores a mirror-protected crossing, continuously closes an approximately 0.13 eV gap, and produces a conductivity-based anisotropic magnetoresistance ratio up to 10,000% at 100 K. The combined results establish noncollinear NbMnX$_2$ monolayers as a multifunctional platform for two-dimensional spintronics, nanomechanics, and thermal control.

Density-functional tight binding has yet to yield a transferable description of vanadium oxides; for the standard second-order construction and the tested cells, we demonstrate that two of its approximations deviate by electron volts and offset each other in the band-index centroid separation between the V 3d and O 2p bands: the neutral two-centre reference omits electron-volt environmental terms, whereas the Mulliken charge model assigns the compact V 3d shell less than half of the self-consistent potential shift observed in PBE. Instead, we build a tight-binding model where the reference Hamiltonian derives from superposed neutral atoms, the full PBE exchange-correlation potential and frozen-core orthogonality, without adjustable terms, and where the orbital-resolved charge response employs three screening factors obtained from PBE linear response and an unscreened Coulomb range. Relative to the primary PAW reference, the plane-wave Harris-Foulkes energy differences of VO2 are matched by the reference energy at fixed geometry and the stated numerical settings, with signed deviations of +2.6 meV/atom for M1 relative to rutile (an energy difference of 92 meV/atom) and +6.2 and -5.2 meV/atom under 3% volume compression and expansion; the charge response reproduces 14 of 22 fitted and 5 of 8 held-out matched PBE responses within one tolerance, and 28 of the 30 within twice the tolerance, and in rutile the fitted first-radial V 3d shift is -4.39 eV, 0.47 eV more negative than PBE's -3.92 eV, whereas the tested DFTB2 charge model gives -1.53 eV. The convexity of the spinless model at fixed geometry prevents it from spontaneously differentiating symmetry-equivalent sites under the symmetries respected by its implemented operators and sampling, so within this model such differentiation in the Magnéli phases must arise from electron-lattice coupling or an explicit spin or correlation term.

The clean-energy transition is driving unprecedented demand for metals, whose extraction is among the largest industrial sources of carbon emissions. Molten-salt electrolysis offers a path toward carbon-free production of aluminum, iron, titanium, and critical metals. However, corrosive operating conditions and complex, multicomponent feedstocks make experimental development costly and challenging. Here, we introduce a first-principles framework for constructing electrochemical phase diagrams of multicomponent systems to accelerate electrode and electrolyte design and guide the selection of compatible materials and operating conditions for electrochemical cells. We derive a grand potential that generates these diagrams at scale, and supply free energies using first-principles data obtained through a fine-tuned foundation machine-learned interatomic potential. For silicon in molten CaCl$_2$, the construction not only recovers the experimental diagram when using the first-principles framework on a limited set of structures, but also predicts further domains when extended to a larger set of crystal structures. Finally, we demonstrate the predictive power of the approach by screening ten alkali and alkaline-earth halide electrolytes for aluminum electrowinning. Three thermodynamic criteria identify NaF, where cryolite emerges as the stable aluminum-bearing phase, recovering the chemistry that Hall and Héroult established empirically in 1886. The framework provides a first-principles basis for selecting compatible electrodes, electrolytes, and operating conditions toward low-carbon metal production from complex source materials.

A key challenge in the design of next-generation colliders is predicting the effects of beam-beam interactions and using these predictions to optimize machine performance. Beam-beam interactions are characterized by strong focusing forces, radiative effects, and the generation of background particles. While analytical formulas provide insight into the dynamics of beam-beam interactions, these nonlinear, coupled effects are most accurately described with numerical methods. In this paper, we introduce the open-source particle-in-cell code WarpX as a modern tool for modeling the interaction point in future lepton colliders. WarpX provides high-performance execution on distributed GPU architectures within an open-source and actively maintained code base. We present convergence scans and benchmarks against the established beam-beam codes GUINEA-PIG (v1.2.2) and CAIN (v2.42) for luminosity spectra, photon emission, and secondary-particle production under a wide range of beam parameters corresponding to different collider concepts. Our results show that WarpX (v26.09) reproduces the benchmark beam-beam observables while enabling GPU-portable, extensible simulations. These results establish WarpX as a scalable platform for high-fidelity beam-beam modeling in future collider studies.

Topological boundary states offer a platform for guided-wave propagation within bulk bandgaps. Their propagation characteristics depend not only on the spectral extent of the states but also on their dispersion within the operating bandwidth. A nearly linear dispersion provides more uniform group velocity across frequency, whereas a reduced slope enables slow-wave propagation. Despite advances in inverse design of prescribed dispersion relations and topological dispersion tuning, application-oriented characteristics of boundary-state dispersion have rarely been direct inverse-design objectives. Here, we develop a supercell-enabled, surrogate-assisted framework for the inverse design of boundary-state dispersion in a phononic crystal with pseudomagnetic fields. Area-preserving anisotropic deformation shifts the local Dirac points, and independent variation of 21 rows within the supercell provides distributed control over the boundary-state branch. A constraint-preserving surrogate reconstructs the dispersion from an initial frequency and positive frequency increments, with first- and second-difference losses introduced to capture local slope and curvature. Coupled with a genetic algorithm, the framework targets two prescribed-bandwidth design tasks: highly linear dispersion and slow-wave dispersion. For the former, finite-element verification yields relative group-velocity variations of 0.142% to 1.183% over prescribed bandwidths of 4% to 6%. For slow-wave designs, mean group velocities of 190 to 385 m/s are obtained over bandwidths of 0.2% to 0.8% while satisfying a 5% group-velocity variation limit. These results establish boundary-state dispersion as a direct inverse-design target beyond conventional bandwidth optimization, opening a flexible route to group-velocity control through application-oriented dispersion engineering over prescribed relative bandwidths.

Machine learning surrogates of partial differential equations (PDEs) are commonly trained on data generated by numerical solvers. Therefore, the training data obey not the PDE but the modified equation of the numerical scheme, and the test loss, computed on data from the same solver, cannot distinguish a model that learned the physics from one that learned the discretization error. Here, we show that the difference is nevertheless visible in the trained model. We propose a suite of structure-preserving fidelity diagnostics, simple scores that measure whether a learned model respects one known property of the physics, such as a conserved quantity, a symmetry or a Hamiltonian structure, without access to the training data or the governing equation. Over five systems, the diagnostics track the error with respect to the true dynamics with a rank correlation of up to $0.94$, while the test loss is uncorrelated or anti-correlated with it. For the Burgers, Korteweg-de Vries and Navier-Stokes equations, the diagnostics separate numerical schemes that the test loss ranks as equivalent, including schemes of the same order. order.

Continuum gyrokinetic codes use structured, field-aligned grids on nested flux surfaces; particle-in-cell codes support unstructured meshes and open field lines but carry a statistical noise floor. We present a continuum drift-kinetic solver that occupies neither position: a semi-Lagrangian discontinuous Galerkin discretization on unstructured triangular poloidal planes extruded toroidally, whose parallel advance is a map along the exact field line in the flux-coordinate independent manner, so the mesh is never aligned with the field, with adiabatic electrons and a long-wavelength polarization field solve. Every operator is verified against an independently computed reference, from Landau damping to the geodesic-acoustic root and a linear ion-temperature-gradient eigenvalue problem, every measured rate within 4% except the geodesic-acoustic damping, within 12%. A linear toroidal ion-temperature-gradient demonstration on a canonical-Maxwellian equilibrium recovers a radially coherent mode whose growth rate, 0.065 c_s/a, is stationary in time. The collisionless zonal-flow residual is the one measurement still moving: it rises with poloidal refinement from 0.72 to 0.87 of the model's own orbit-quadrature prediction for the measured observable and has not converged. The solver is fully device resident, and every result is reproduced between CPU and GPU builds and across MPI process counts. The code, the data behind every table and an artifact description are in a public repository.

We present a method for enforcing exactly Dirichlet, Neumann, and Robin conditions on general triangular domains with arbitrarily curved boundaries. The algorithmic constructions developed here complements those in a previous work for general quadrilateral domains. Our method combines (i) the exact mapping between a general curved triangular domain and the standard triangle, (ii) TFC constrained expressions, and (iii) Barnhill transfinite interpolations, to provide explicit closed-form trial ansatze that mathematically satisfy the imposed boundary conditions exactly. Corner compatibility induced by the boundary conditions is pivotal, and enforcing exactly the imposed boundary conditions hinges on the exact enforcement of the induced compatibility constraints. The corner compatibility associated with the acute vertices of the standard triangle and the coupling between gradient components when the hypotenuse corresponds to a Neumann/Robin boundary pose particular challenges. Two strategies are critical to resolving these issues, by reformulating conditional corner constraints into equivalent unconditional forms and by introducing a separate TFC-style auxiliary edge construction together with an associated linear solve on the hypotenuse. We analyze the corner compatibility constraints and present formulations for the general form of functions that exactly satisfy the imposed Dirichlet, Neumann, or Robin conditions on curved triangular domains. The proposed method has been implemented using extreme learning machine type randomized neural networks for solving PDE problems. We present ample numerical experiments with linear/nonlinear PDE problems on a variety of domains with complex boundary geometries. Numerical results show that the current method has enforced the Dirichlet, Neumann, and Robin conditions on curved domain boundaries to the machine precision.

General-purpose molecular dynamics software supports diverse interatomic potentials and simulation requirements. Within a simulation stage, the loaded potential model and the required calculations typically remain fixed as the atomic configuration evolves. We present the Wisevolve Potential Engine (WPE), which uses this information from GPUMD to select and reuse a GPU execution policy tailored to the model and simulation stage. GPUMD retains simulation control and ownership of the simulation data. On a single NVIDIA RTX 5090, WPE-enabled GPUMD (GPUMD-WPE) achieves a median throughput of 109 million atom-step/s across 106 neuroevolution potential (NEP) workloads. For a 15.1-million-atom diamond Si system, it sustains 142 million atom-step/s. Relative to GPUMD, geometric-mean speedups are 3.49x across these NEP workloads, 3.61x across 16 workloads using NEP with dynamic charges (qNEP), 1.24x across 28 classical-potential workloads, and 10.5x across 56 path-integral molecular dynamics (PIMD) configurations. End-to-end calculations of water structure, lattice thermal conductivity, and PIMD thermal expansion show close agreement with corresponding GPUMD results and published simulation results. A separate 12.5-million-atom Cu shock-compression simulation demonstrates its applicability to large-scale nonequilibrium dynamics. These results support model- and stage-specific specialization as a practical way to accelerate GPU potential evaluation in general-purpose molecular dynamics workflows.

Small polarons, formed when excess electrons become localized through lattice distortions, play a critical role in charge transport, catalysis, and degradation processes in transition-metal (TM) oxides. Whether universal machine-learning interatomic potentials (uMLIPs), which lack explicit electronic degrees of freedom, can describe them remains unclear. Here, we investigate H-induced electron localization across a range of TM oxides using a geometric descriptor based on TM-O bond-length expansion (Z-score) to identify polaronic distortions. We find that uMLIPs exhibit varying degrees of electron localization, from delocalized states to metastable small polarons, with their behavior strongly dependent on the training data and treatment of electronic correlations. In particular, the absence of Hubbard U corrections for specific TM cations in the training data leads to electron delocalization, in contrast to DFT+U predictions. Although some uMLIPs reproduce polaron hopping barriers during coupled proton-polaron transfer, all of them fail to stabilize spatially separated polaron-donor configurations, instead favoring localization near the H dopant.