Papers

Kolmogorov-Arnold Networks (KANs), inspired by the Kolmogorov Arnold representation theorem, provide an interpretable alternative to multilayer perceptrons (MLPs) by using learnable activation functions on edges rather than fixed node activations. We propose a Physics-Informed Kolmogorov-Arnold Network (PI-KAN) framework for solving forward problem of viscoelastic fluid equations, which arise in many complex fluid dynamics applications and are characterized by strong nonlinear coupling between fluid fields. For viscoelastic fluid equations, we adopt the generalized hydrodynamic model, which is well established in the field of dusty plasma. To evaluate the performance of the proposed framework for viscoelastic fluid, we consider benchmark problem based on the Taylor-Green (TG) flow and a modified Taylor-Green flow. We systematically investigate the effects of different network architectures, hyperparameters, and collocation point distributions on the accuracy and convergence behavior of PI-KANs for the range of viscoelastic parameter ($\tau_m = 1$–$20$). We also study the impact of random seed initialization on training outcomes. The obtained results provide useful guidance for the design and implementation of physics-informed Kolmogorov-Arnold networks (PI-KANs) in solving viscoelastic fluid equations

We construct temperature-dependent deep potentials for sodium using finite-temperature DFT data obtained with the PBE, AM05, and $r^2$SCAN exchange-correlation functionals and investigate the thermophysical properties of sodium from room temperature to the critical region. The predicted critical parameters show a dependence on the exchange-correlation functional. The model based on the $r^2$SCAN functional gives a critical temperature $T_c=2.508(8)$ kK, density $\rho_c=0.203(4)$ g/cm$^{3}$, and pressure $P_c=0.249(6)$ kbar, in close agreement with the recommended values. This model is then used to reconstruct the normal-pressure and critical isobars and to calculate the enthalpy, heat capacities, thermal expansion coefficient, bulk moduli, Grüneisen parameter, and speed of sound. The calculated normal-pressure bcc density differs by only 0.06% from the experimental value. Direct solid-liquid coexistence simulations give a melting temperature of $346(2)$ K, 25 K below the recommended value, consistent with the sensitivity expected from meV/atom free-energy errors. Liquid-vapor coexistence simulations reproduce the binodal and yield a surface tension that approaches zero near the critical point. The calculated self-diffusion coefficient and shear viscosity extend the available transport-property data into the expanded-liquid and near-critical regions, where direct experimental information is sparse. We also demonstrate the thermodynamic consistency of the results by comparing the speed of sound obtained from direct acoustic simulations with that calculated from the equation of state.

We extend the Wigner-Eckart factorization of the spectral Boltzmann collision operator to polyatomic gases with continuous internal energy. Because internal energies are invariant under spatial rotations, the SO(3) reduction survives the Borgnakke-Larsen energy exchange, and the twelve-dimensional collision integral collapses onto a nine-dimensional kinematic core. The core splits into a sparse geometric tensor, evaluated exactly, and a dense physical tensor, integrated by singularity-resolving Gauss rules with an auxiliary Laplace representation of the fractional energy couplings. The quadrature attains near machine precision at the fractional exponents of real gases. The collision invariants are embedded exactly, preserving the translational-internal energy exchange. The factorization compresses the operator by three to nearly four orders of magnitude and accelerates its evaluation 40-fold over dense formulations. The method is validated against the exact monatomic limit, Landau-Teller relaxation, and an analytic frozen-channel Prandtl number, and it matches a published calibration of the same kernel for N2, CO, and H2.

We show that optimal control can turn the skyrmion Hall effect from a source of typically unwanted transverse motion into a mechanism for reducing Ohmic losses in skyrmion transport. We consider a pair of antiferromagnetically coupled skyrmions confined to a tubular geometry, where their relative transverse displacement becomes a periodic internal coordinate. The skyrmion Hall effect drives this coordinate, while finite interlayer coupling makes the resulting relation between applied current and longitudinal velocity nonlinear, allowing different current protocols to produce the same prescribed average velocity. We determine which of these protocols minimizes Joule heating. Depending on the interlayer coupling and spin-transfer-torque parameters, the optimal current is either constant, with the skyrmion pair maintaining a fixed relative position, or time dependent, with the pair undergoing periodic relative motion around the tube. In either case, the additional internal degree of freedom created by the skyrmion Hall effect and interlayer coupling enables skyrmion transport at a lower power than in the uncoupled limit.

Full-structure and sub-structure characteristic mode analysis (CMA) formulations are developed for composite metallic–dielectric nanostructures based on a coupled system of volume integral equations (VIE) and the hydrodynamic equation (HDE). In the full-structure CMA, the generalized eigenvalue equation (GEE) is constructed from the matrix of the complete coupled system, and the resulting characteristic currents describe the response of the entire composite nanostructure. In the sub-structure CMA, the GEE is constructed from a reduced system, derived from the coupled system by eliminating the dielectric-region unknowns, so that it is expressed only in terms of the metallic-region currents. This isolates the resonances of the metallic region while still incorporating the effect of the dielectric region through the reduced system. Because the reduced system has a smaller dimension, the sub-structure CMA is computationally more efficient than the full-structure CMA and, when the dielectric does not resonate in the frequency range of interest, identifies the same resonances. Both formulations are validated against extinction cross-section (ECS) results and are used to characterize how a dielectric environment reshapes the metallic resonances, including substrate-induced red-shifts and, for high-contrast substrates in direct contact, hybridized modal responses.

A unified gas-kinetic wave–particle method with Fokker–Planck collisions (UGKWP-FP) is developed for the Vlasov–Poisson–Fokker–Planck system. The collision operator is modeled by the Lenard–Bernstein operator, whose stochastic representation corresponds to the Ornstein–Uhlenbeck process in velocity space. To extend the UGKWP framework beyond the conventional Bhatnagar–Gross–Krook (BGK) collision model, the Fokker–Planck operator is decomposed into a nonstiff drift–diffusion contribution and a stiff thermalization contribution. The former is retained in the particle dynamics through a modified Ornstein–Uhlenbeck process, whereas the latter is represented by a BGK-type relaxation toward the local Maxwellian. This decomposition enables an adaptive wave–particle representation: the method follows stochastic particle dynamics in rarefied regimes and increasingly represents the rapidly equilibrating distribution by the analytical wave component as the continuum regime is approached. The modified friction coefficient is constructed to recover the original Fokker–Planck dynamics in the rarefied limit while preserving the hydrodynamic limit under strong collisions. Numerical experiments demonstrate that the proposed method captures velocity-space drift and diffusion, recovers the expected kinetic and continuum behavior across a range of Knudsen numbers, and reproduces the characteristic evolution of collisional plasma phenomena.

Amorphous solid-state electrolytes are attractive candidates for safe, high-energy-density all-solid-state batteries, yet their mechanical properties remain poorly understood from a computational perspective. Here, we investigate the elastic behavior of the recently discovered amorphous superionic Li-ion conductor LiTaCl$_6$ using density-functional-theory (DFT)-based methods, including unrelaxed static, relaxed static, and strain fluctuations from molecular dynamics (MD) simulations in the isobaric–isothermal (NPT) ensemble with DFT-trained machine-learning force fields (MLFFs). While the unrelaxed static method predicts a Young's modulus an order of magnitude higher than the experiment, the relaxed static method—commonly applied to crystalline electrolytes—still overestimates the modulus by more than 170%. In contrast, the MD approach using MLFFs yields a Young's modulus of $2.84 \pm 0.26$ GPa, which quantitatively agrees with the experimental value of $2.91 \pm 0.32$ GPa. Using the MLFF-MD approach, we further predict bulk modulus (4.44 GPa), shear modulus (1.02 GPa), and Poisson's ratio (0.39) for amorphous LiTaCl$_6$ and conclude that elastically it behaves like a soft polymer or gel. These results demonstrate that amorphous superionic materials possess some unique elastic properties and that, among the methods examined, only the MLFF-MD approach yields quantitative agreement with experiment, highlighting the necessity of a dynamical treatment to simulate their elastic response, consistent with recent findings for crystalline superionic conductors.

Efficient lead-free perovskite solar cells remain limited by inefficient charge transport and significant recombination losses. In this work, copper (Cu) doped nickel oxide (NiOx) is employed as the hole transport layer (HTL) in a formamidinium tin iodide (FASnI3) perovskite solar cell to improve hole extraction and suppress carrier losses. The optoelectronic response of the proposed device architecture is evaluated through a coupled numerical framework combining finite-difference time-domain (FDTD) optical simulations with finite element method (FEM)-based electrical modeling. Electrical analysis solves the Poisson equation together with the drift-diffusion and carrier continuity equations, while accounting for radiative, non-adiative, and interfacial recombination mechanisms. Systematic optimization of the thicknesses and doping concentrations of the constituent layers was performed to establish a high-performance device configuration. Following optimization of layer dimensions and carrier densities, the device achieved a power conversion efficiency (PCE) of 24.71%. Integrating an anti-reflection coating (ARC) effectively suppressed reflection losses, yielding a 5.47% relative enhancement in PCE. Consequently, the optimized device achieved a peak PCE of 26.06%, with a short-circuit current density (Jsc) of 28.98 mA/cm2, an open-circuit voltage (Voc) of 1.051 V, and a fill factor (FF) of 85.64%. These findings demonstrate that Cu-doped NiOx functions as a highly promising HTL to boost charge collection and maximize overall efficiency in lead-free FASnI3 solar cells.

Open quantum systems lose energy and phase coherence through different dissipative processes, but these processes can produce overlapping dynamical signatures. The Liouvillian spectrum summarizes how such a system relaxes, yet it is not obvious how much of that spectrum is needed to distinguish the underlying dissipation rates. We study this question for amplitude damping and dephasing in a six-qubit Lindblad model whose spectrum can be derived analytically. We retain only the slowest non-steady spectral modes and ask how many are required before each dissipative rate becomes recoverable. We show that population modes contain no dephasing information, which creates a lower bound of D = 2^n retained modes for uniform dephasing identifiability in the relevant rate regime. The measured recovery threshold reaches this bound at n = 4,5,6, while n = 3 remains above it. At n = 6, least squares achieves a mean joint absolute error of order 10^-9, compared with 4.355 x 10^-4 for four tabular learning methods. Robustness tests show that this advantage weakens when the spectra are perturbed and when a transverse field breaks the commuting structure. These results show that the amount and structure of retained spectral information can determine whether dissipative parameters are recoverable, independently of the estimator used. The present conclusions apply to noise-free simulator spectra rather than measurement-derived spectra.

We develop an entropy-stable and physical-constraint-preserving discontinuous Galerkin spectral element method for symmetry-reduced general-relativistic hydrodynamics on prescribed stationary spacetimes. Using a local orthonormal transformation, the fluid variables are expressed in a form for which the relativistic hydrodynamic algebra and the admissible set are independent of the spatial metric, while the spacetime geometry enters through stationary coefficients. This separation allows entropy-conservative special-relativistic fluxes to be combined with a compatible discretization of the geometric source terms. On affine tensor-product meshes, the resulting DGSEM is conservative and satisfies a semidiscrete entropy inequality, while the transformed variables provide a convex framework for physical-constraint preservation. For practical stabilization, we use a geometry-only causal speed that is sufficient for both classical local Lax–Friedrichs entropy dissipation and the physical-constraint-preserving Lax–Friedrichs splitting. The fully discrete method combines this stabilization with SSP Runge–Kutta time stepping, oscillation elimination, and conservative local-orthonormal-state scaling. Numerical experiments cover smooth and strongly shocked special-relativistic flows, an axisymmetric jet, stationary Michel accretion, Schwarzschild Bondi–Hoyle flow, and four Kerr accretion cases. The results demonstrate the designed high-order accuracy in smooth regimes and robust performance for demanding relativistic flows on curved stationary backgrounds.

We establish a uniform inf-sup stability estimate for the Scott-Vogelius finite element spaces on uniform Freudenthal tetrahedralizations of the unit cube for polynomial degrees k >= 4. This result completely settles the first conjecture of Farrell, Mitchell, and Scott for the critical degrees k = 4 and k = 5, complementing the known stability range for higher polynomial degrees. The main mathematical difficulties stem from the complex topological compatibility required at the singular vertices and the corresponding mean-value constraints across adjacent elements. We tackle these challenges by developing a unified barycentric skeleton-bubble calculus that explicitly constructs vertex jets, edge modes, and face transfers to globally route element means. The accompanying exact computations independently verify these finite-dimensional identities and provide reproducibility data.

In Nyström-collocation discretizations of the electric field integral equation (EFIE), the surface divergence acts on surface densities that may be discontinuous across patch boundaries, which degrades accuracy and convergence. We show that this not only affects the EFIE but every formulation in which the operator occurs, either in the equation itself or in the scattered field computation, and propose a high-order-accurate continuity-enforcing scheme for smooth surfaces as a remedy for the direct and indirect EFIEs, magnetic field integral equations (MFIEs), and regularized combined field integral equations (CFIEs) alike. The scheme comprises two ingredients: i) We show how to discretize the equations via a Chebyshev-based Nyström scheme, which admits closed quadrature rules. ii) Since unknowns and test vectors are in terms of patch-local curvilinear bases, continuity is enforced by a change of basis: we construct sparse mapping matrices assembled solely from the curvilinear geometry description. In doing so, we restore the accuracy of the EFIE such that it can be combined with the MFIEs with equal weights to form CFIEs. Numerical studies for the scattering from canonical and realistic geometries show that all considered formulations individually and combined benefit from the continuity enforcement in terms of better conditioning, reduced iterations of an iterative solver, and several more digits of accuracy in the scattered fields, despite reducing the total number of unknowns.

Experiments on superconducting cavities have found that under large RF fields the quality factor can improve with increasing field amplitude, a so-called “anti-Q slope.” We numerically solve the Bogoliubov-de Gennes equations at a superconducting surface in a parallel magnetic field, finding at large fields there are surface quasiparticle states with energies below the bulk superconducting gap that emerge and disappear as the field cycles. Modifying the standard two-fluid model, we introduce a “three”-fluid model where we partition the normal fluid to consider continuum and surface quasiparticle states separately. We compute dissipation in a semi-classical theory of conductivity, where we provide physical estimates of elastic scattering times of Bogoliubov quasiparticles with point-like impurities having potential strengths informed from complementary ab initio calculations of impurities in bulk niobium. We show, in this simple yet effective framework, how the relative scattering rates of surface and continuum quasiparticle states can play a role in producing an anti-Q slope while demonstrating how this model naturally includes a mechanism for turning the anti-Q slope on and off.

A protein's function follows from the structure it adopts, and in some cases which structure that is depends on the pathway taken. In programmable matter the target is fixed before assembly, and whatever else forms is treated as error. Here we show that pathways themselves form a design space. Using reinforcement learning, we fold model DNA-coated droplet chains into rigid two-dimensional geometries, uncovering two classes of pathways: downhill, in which bonds are only added, and detour, in which bonds are broken and remade before the target is reached: for some the only route that exists. Coarse-graining pathways by interactions gives experimentally realizable protocols. Some produce one geometry, others several: structures sharing a detour route can be cycled between, while those that coexist assemble into superstructures inaccessible to a uniform product. Function emerges from the pathways rather than being designed. Designing the process instead of the components could give colloidal materials that reconfigure on demand.

Computational models of blood flow are caught between fully resolved cell-based methods, which faithfully reproduce the dynamics of individual cells but are computationally prohibitive at vessel scale, and continuum models, scalable yet blind to particle motion. We present an unresolved, mesoscale computational fluid dynamics-discrete element method (CFD-DEM) model of platelet dynamics that bridges this gap and, coupled with an existing unresolved description of deformable red blood cells, moves closer to a scalable model of whole blood. Within this framework, implemented on the open source OpenFOAM-LIGGGHTS coupling, platelets are represented as rigid oblate particles advanced by orientation dependent drag, lift and hydrodynamic torque closures. The model is first validated against resolved simulations and experiments in cylindrical microvessels of diameter $100-200\,\mu m$, across wall shear rates $\dot{\gamma}=150-1650\,s^{-1}$ and hematocrit Ht $=10-20\%$ then used to characterize platelet margination. The model quantifies diffusion coefficient, CFL formation and their dependence on shear rate, Ht and channel size. In particular, platelet diffusivity grows with vessel size and shear rate, while remaining insensitive to Ht, whereas CFL thickens with shear rate and thins with Ht. We further show that even at this mesoscale level, the model remains sensitive to platelet shape: oblate platelets marginate faster and diffuse nearly an order of magnitude more than their spherical surrogates, reaching a comparable steady state distribution but along markedly different temporal paths. Together these results demonstrate that shape driven platelet dynamics can be recovered at a fraction of the cost of fully resolved methods.

Fourier neural operators (FNOs) provide an efficient framework for learning mappings between function spaces as they are, by construction, independent of the grid resolution at which they are trained and evaluated. However, FNOs are not independent of the periodic domain they are applied to: their discrete spectral weights are indexed by integer Fourier mode numbers, which correspond to physical wavevectors. When applied to a different domain, the same trained weights act at different wavevectors, and the FNO silently represents a different operator. This makes FNOs unsuitable for tasks where transfer across domains is crucial. We propose Euclidean Fourier neural operators~(EFNOs) as a domain-independent alternative to FNOs. By parameterizing the spectral kernel as a continuous function of the physical wavevector, the EFNO can learn operators that act consistently across periodic domains of varying shape and size. We evaluate the EFNO on a simple heat equation and on a practically relevant materials science task of learning exchange-correlation potentials across different crystal structures, and demonstrate that the EFNO is able to generalize to unseen grid sizes and domains.

State estimation in magnetohydrodynamic flows is critical for real-time monitoring of liquid metal blankets in tokamak fusion reactors. Due to the multiphysics nature of these phenomena, high-fidelity simulations are computationally prohibitive for real-time applications. This work investigates a data- driven Reduced Order Model framework: the Shallow Recurrent Decoder (SHRED) coupled with Principal Component Analysis, to map sparse temperature measurements to the full thermo-hydraulic system's state. The major contribution of this work lies in the two-parameter analysis of a fully three-dimensional domain representative of the DEMO breeding blanket configuration. Here, the flow is subjected to an external magnetic field varying in direction and intensity and is hindered by two cylinders acting as a water-cooling system, which impose a temperature boundary condition on their surfaces. This double-parametric magnetic variation induces nonlinear transitions in the flow dynamics, ranging from chaotic behavior at low magnetic field intensities to laminarized regimes at high intensities, characterized by the formation of asymmetric side layers at an inclination angle of 30 degrees. SHRED reconstruction maintains a mean relative error of approximately 5% for the temperature, pressure, and velocity fields. This accuracy is maintained across both weak and strong magnetic fields, ranging from 0.075 T to 0.300 T, and for inclination angles from 5 to 30 degrees, reflecting its dominant toroidal component. These errors are only slightly larger than the lower error bound dictated by low-rank truncation. The results establish SHRED as a reliable state estimator for complex and realistic engineering applications involving completely unseen parametric scenarios and validate it as an accurate real-time state estimation technique suitable for online monitoring and control of real facilities.

In this work, we develop a variational imaginary-time evolution (ITE) framework based on polynomial filtering, derived from an operator-level action principle, which yields an optimized non-unitary projector expressed as a polynomial in the Hamiltonian. Starting from a single-ancilla, first-order imaginary-time update defined by a Taylor expansion and Trotter-Suzuki (TS) decompositions, we show that replacing these approximations with alternative variational formulas substantially improves both accuracy and stability at larger time steps, leading to up to an order-of-magnitude enhancement in the final success probability. We further derive rigorous error bounds that depend only on static properties of the Hamiltonian, providing practical guidance for selecting the simulation time step. Benchmarks on the transverse-field Ising model demonstrate faster convergence to the ground-state energy and improved robustness compared to standard TS–Taylor ITE, highlighting variational polynomial filtering as a practical route to higher-fidelity ground-state preparation on near-term quantum devices.

We study quantum many-body effects in the long-wavelength optical response of confined electrons at finite temperatures. We simulate homogeneous electron gas confined in one dimension into a slab of nanoscale thickness. We demonstrate how the slab boundaries break down the ideal Drude response of free charge carriers, giving rise to scattering effects due to both the surfaces and quantum many-body interactions. We use a recent path-integral Monte Carlo (PIMC) approach developed in [Tiihonen et al. Phys. Rev. A 113, 053711] to quantify these effects in high accuracy. We perform phenomenological fits to Drude and Drude-Lorentz models parameters, manifesting various trends of the optical response with physical parameters like density and temperature, and numerical effects like finite size and the quantum statistics.

CeCrB$_4$ belongs to the family of MTB$_4$ ternary metal borides, some of whose magnetic phases have recently been identified as quantum spin dimers. Employing density functional theory within the GGA+$U$ framework, this work investigates the key ground-state properties of this system, including its ferromagnetic ground state, the mixed-valence nature of cerium, and the charge transfer from the cationic cerium–chromium layers to the anionic boron layers. In particular, we focus on elucidating the bonding mechanism within the structurally embedded Cr-Cr dimers. Specifically, we evaluate a previously proposed interpretation that the localized Cr $3d_{z^2}$ states are molecular-like bonding and antibonding states. The calculated dependence of the $3d_{z^2}$ electronic structure on the intra-dimer distance correlates with the level-splitting characteristics known for classical homonuclear diatomic molecules.

This research topic aims to explore and promote strategies for green computing in high-energy physics and astrophysics. The primary objectives include assessing current energy consumption patterns, identifying opportunities for resource optimization, and fostering cross-disciplinary collaborations to enhance sustainability. Key questions to be addressed include: What are the current energy demands in these fields? How can existing technologies be leveraged for more efficient resource usage? What synergies can be identified between high-energy and astrophysics projects to promote green computing?

We investigate the applicability of AAA rational approximation to scatterometry-related response functions of nanoscale gratings. A silicon line grating with material dispersion is considered. We compare the convergence of AAA rational approximation with that of cubic spline interpolation as the number of frequency samples is increased. The results demonstrate the potential of rational approximation, consistent with the pole structure of the considered response function arising from resonance effects of the grating.

Solving the non-gray Callaway phonon Boltzmann transport equation allows a dual-relaxation-time approximation of separate normal and resistive scatterings and resolving the mode-dependent spectrum. The conventional iterative scheme (CIS) for deterministic solutions avoids a monolithic phase-space inversion, but its collision-source iteration can become prohibitively slow at a large characteristic length of a material. Existing synthetic acceleration schemes address either non-gray single-relaxation models or gray dual-relaxation models, leaving mode-resolved dual-relaxation transport without a dedicated acceleration framework. We develop a general synthetic iterative scheme (GSIS) for the stationary, linearized, non-gray Callaway equation, where synthetic approximations for the normal-process pseudo-temperature and phonon drift velocity are provided by exact energy and quasi-momentum balance laws closed with first-order Chapman-Enskog constitutive relations and non-equilibrium terms evaluated from the kinetic solution. The resistive-process pseudo-temperature is retrieved from the two quantities. Each iteration couples an upwind nodal discontinuous Galerkin kinetic sweep and a hybridizable discontinuous Galerkin solution of the synthetic equations to achieve high-order spatial discretization. A branch- and frequency-resolved Fourier analysis identifies the deterioration of CIS and shows that the GSIS contraction factor remains bounded away from unity for the considered graphene material. Asymptotic analysis indicates that GSIS reduces to a consistent discretization of a Guyer-Krumhansl-like equation and Fourier's law of heat conduction in the hydrodynamic and diffusive limits, respectively.

Electronic-structure calculations require a finite representation of both the electronic wave functions and their Coulomb interaction. Conventional compact basis sets lead to a four-index interaction. Gausslet basis sets are one of a very small number of approaches that allow a much smaller two-index interaction, similar to a real-space grid, but with far fewer points. The continuing challenge in their development is reducing further the number of functions needed while maintaining high accuracy. Here we introduce projected q-shells (PQS), an improvement to the nested Cartesian gausslets of White and Lindsey. Their standard nesting construction divides a joining shell into disjoint faces, edges, and corners, reducing its polynomial completeness from order q to order q-2. PQS approximately restores the two lost orders. In terms of completeness, we prove that for an ideal, undistorted parent, the span of the PQS basis is equivalent to an overcomplete basis of overlapping patches. Coordinate distortions, which are always used in practice, harm this equivalence only slightly. The moment properties that allow two-index interactions also become inexact, even without distortion, but we show that the improvement in order more than makes up for this loss. For similar basis sizes, PQS gives smaller one-electron and interaction errors on small molecules, such as H2+, H2, and C2, than standard nesting. The improvement is largest for more compact bases with smaller q.

Sparsification via neglecting far-field coupling (S-NFC) enables fast full-wave radar-cross-section analysis of large-scale chaff clouds by retaining only significant local electromagnetic interactions. This letter further accelerates S-NFC by concatenating the retained off-diagonal interaction blocks associated with each receiving chaff element and applying a joint low-rank factorization with a shared receiving-side basis. Exact self interactions are preserved, while repeated chaff templates reuse precomputed lower–upper factorizations of the self-interaction blocks. The compressed formulation reduces retained-coupling storage and matrix–vector multiplication cost and also decreases the number of iterations required by the generalized conjugate residual solver. Numerical tests with 100,000 chaff elements demonstrate sub-$1\%$ complex-far-field error for low-rank approximations in sparse regimes and identify a practical self-only limit at sufficiently large mean spacing. For a one-million-chaff plume, the proposed compressed S-NFC achieves a $6.92\times$ end-to-end speedup over uncompressed S-NFC while storing only $6.60\%$ of the retained coupling, with a complex-far-field error of $0.253\%$.

Type-IV two-dimensional (2D) magnetism-a newly classified collinear magnetic phase featuring nonrelativistic spin degeneracy and spin-orbit-coupling-induced momentum-dependent spin splitting-extends the symmetry classification of collinear magnets, opening new opportunities for unconventional topological quantum states. Here, we reveal that the recently proposed two-dimensional type-IV 2D magnet MgCr$_2$O$_4$ hosts an intrinsic higher-order topological insulating phase, featuring $\mathcal{C}_{3z}$-protected corner states and a nontrivial rotational topological invariant of $\chi^{(3)}$ = $\{-2,4\}$ with a quantized fractional corner charge of $4e/3$. Spin-orbit coupling breaks the spin-degeneracy-enforcing symmetry $[C_{2}||M_z]$ while preserving the crystalline $\mathcal{C}_{3z}$ rotational symmetry that protects the higher-order topological phase, thereby enabling spin splitting to coexist with the nontrivial topology. Furthermore, the higher-order topological phase remains intact throughout a wide range of biaxial strains without band-gap closing and topological phase transition, demonstrating the robustness of the symmetry-protected topological state against external perturbations. Our work establishes a direct connection between type-IV magnetic system and higher-order topology, providing a new route for symmetry-engineered magnetic topological quantum states.

Physical systems are often modeled by solution operators that map input fields, parameters, geometries, or past states to steady or future physical states. Learning these maps is difficult, especially for time-dependent systems that must assimilate history and remain stable under autoregressive rollout. Many neural operators work best on regular, structured grids, while realistic simulations often require unstructured meshes or point clouds to resolve complex geometries; in such settings, grid-centric representations can lose accuracy. Graph neural operators handle these domains through message passing or spectral graph filtering, but pairwise edges do not directly capture group-wise couplings among mesh cells, local neighborhoods, or conservation volumes. We introduce the Hypergraph Adaptive waveLet Operator (HALO), which lifts the domain to a hypergraph and learns in its spectral wavelet domain. HALO avoids explicit hypergraph-Laplacian eigendecomposition through Chebyshev polynomial wavelet filters, giving localized spectral kernels at linear sparse-matrix cost. Its trainable dyadic wavelet scales are regularized toward tight-frame coverage, allowing the frequency response to adapt to each PDE while encouraging stable multi-scale spectral coverage. Across 2D and 3D benchmarks on structured and unstructured discretizations, HALO achieves best or near-best accuracy among frequency-, transformer-, DeepONet-, state-space-, and graph-based baselines and sustains stable multi-step rollouts. The same model scales to industrial aerodynamic geometries: on meshes of a few hundred thousand points it is on par with, or better than, the strongest fixed-discretization transformers, while remaining resolution-equivariant.

Variational Monte Carlo (VMC) calculations based on tensor networks (TN) have recently achieved competitive accuracy in ground-state calculations of strongly correlated spin and fermionic systems. However, existing tensor network VMC (TN-VMC) algorithms have not been formulated in a manner that can fully utilize GPU acceleration. We tackle the key missing ingredient, namely, the vectorized evaluation of tensor network amplitudes and tensor network operations. This ensures high GPU utilization by batching over computations with identical structure. In particular, we show how to achieve vectorization for the practically relevant case of abelian symmetric tensor networks (which includes fermionic tensor networks) by developing a “flat” tensor network formalism for block-sparse tensor representation and contraction. Using this, we construct a GPU-adapted symmetric TN-VMC workflow with batched tensor network computation. In the two-dimensional Fermi–Hubbard model, we demonstrate a GPU speedup of up to $300 \times$ over single core CPU implementations, for fermionic TN variational wavefunctions.

The LDA-1/2 method provides an efficient correction to semilocal density functional theory for improving ionization energies and band gaps, yet its application to molecular systems has remained limited. In this work, we present an all-electron finite-element implementation of LDA-1/2 within the NESSIE electronic-structure framework and apply it to the GW100 molecular benchmark set with systematically controllable numerical accuracy. The self-energy correction is constructed explicitly from neutral and half-ionized calculations for each molecule, avoiding the use of precomputed atomic correction potentials. The real-space finite-element formulation enables systematic convergence with respect to the discretization and provides a controlled assessment of LDA-1/2 performance. For the GW100 set, the present implementation yields a mean absolute error of 0.472 eV and a root-mean-square error of 0.645 eV relative to CCSD(T) reference ionization energies, substantially improving upon conventional LDA and the previously reported LAPW implementation of LDA-1/2, while achieving accuracy comparable to G0W0@PBE. Convergence tests show that third-order finite elements are sufficient to reach or approach chemical accuracy relative to higher-order calculations for the representative systems considered. The resulting corrected Hamiltonian also improves several lower lying valence states relative to LDA, although the improvement becomes less systematic away from the HOMO. This work provides accurate LDA-1/2 benchmark data for molecular systems and establishes a rigorous finite-element foundation for future molecular GW calculations.

I explore Conway's Game of Life (GoL) on six composite Archimedean lattices. On the Kagome lattice, on which small gliders and puffers appear particularly frequently across inputs, I use the output of a symmetry-constrained evolutionary search algorithm to construct a novel glider gun. The glider gun comprises four interacting bouncers and stably emits a small glider every 276th generation. Serving as an extension of classical GoL, I also propose cells with a phase degree of freedom and an associated local phase rule, which on the Kagome lattice is demonstrated to host phase-periodic gliders. This enables the possibility of phase-sensitive and interference-based computations.