Papers

For atomistic molecular dynamics simulations, we consider a recently developed hybrid coupling between the highly accurate machine learning (ML)-based atomic cluster expansion (ACE) interaction model and a less precise (but about 1-2 orders faster) EAM potential, in order to leverage the performance bottleneck of pure ML potentials in a parallel computing environment. This spatial-temporal adaptivity has the potential for a speedup of more than an order of magnitude, that would be lost without a dynamic load-balancing strategy that becomes critical due to fluctuating potential contributions. We compare the load-balancing strategies of LAMMPS with load-balancing methods provided by the library ALL in adaptive-precision EAM-ACE simulations of a copper nanoindentation. For a regular-grid domain decomposition, the modified tensor method of the ALL library, which conserves the simplicity and transferability of the tensor method, significantly reduces the imbalance factor of the force calculation from 3.0 to 1.7 compared to the native load-balancing method of LAMMPS. A nearly perfectly balanced system with an imbalance factor close to 1.0 can be reached by load balancing an irregular grid of domains with the recursive bisectioning method of LAMMPS and with ALL's histogram method for a staggered grid of domains. Load balancing a staggered grid with ALL is found to be significantly faster than load balancing an irregular grid with the bisectioning method of LAMMPS, but the communication costs during a regular timestep are lower for the irregular grid of domains, as a lower surface-by-volume ratio of the domains is reached. Furthermore, we suggest a strategy to find the ideal load-balancing frequency for adaptive-precision simulations.

Endovascular implants prevent intracranial aneurysm rupture by altering the mechanical and hemodynamic environment at the aneurysm neck. Yet many in silico workflows prescribe or reconstruct the post-deployment geometry before computing flow, leaving unresolved the mechanics that create the clinically relevant interface. Here we review braided intraluminal flow diverters, intrasaccular devices, and emerging flow-disruption concepts across deployment mechanics, inter-wire and wire-wall contact, superelasticity, wall apposition, pore geometry, computational fluid dynamics, and fluid-structure interaction. We connect these modeling choices to neck coverage, malapposition, migration, deformation, and durability, and distinguish established evidence from mechanistic inference and prospective hypotheses. We argue that model fidelity should match the clinical question: prescribed or fast placement may support screening, whereas questions of coverage, apposition, compaction, and migration benefit from mechanically plausible deployment states. An interface-resolved mechanics-to-flow framework, supported by measurable validation targets and standardized reporting, could improve device design and enable more reliable patient-specific treatment planning.

Phase-field trajectories governed by the Allen–Cahn equation determine the effective force $G=F'/\eps^2$, but not the free-energy potential $F$ and interfacial scale $\eps$ separately. We introduce surface-tension-calibrated Allen–Cahn identification (STAC), a two-step method that resolves this ambiguity using an independently supplied surface tension. First, space–time weak moments produce a linear inverse problem without differentiating the measured field. A Bernstein representation with positive coefficients enforces two stable pure phases and a single central energy maximum. Second, the surface tension fixes the remaining scale algebraically. We prove scale equivalence of the forward model, uniqueness of the calibrated pair within this class, and finite perturbation bounds that remain valid when the potential vanishes at the pure phases. Experiments with resolved synthetic phase fields separate the effects of the structural constraint, ridge regularization, and constitutive approximation error. Across 80 shared noisy records, unconstrained degree-five regression produces six potentials with an incorrect well structure. Positivity combined with ridge regularization eliminates these violations and reduces the mean force error from 8.70% to 5.66%. Lower-degree models are nevertheless more accurate in some tests, and an admissible law outside the positive Bernstein family shows how the constraint can introduce approximation bias. STAC thus recovers a structurally admissible, physically scaled potential while making explicit which information comes from the observed dynamics and which comes from the independent surface-tension datum.

Random-batch methods accelerate molecular dynamics by replacing full interaction sums with stochastic force estimators. In Langevin simulations, however, random-batch force errors can cause artificial heating and distort equilibrium and dynamical observables, especially for small batch sizes or under weak thermostat coupling. Moreover, the magnitude of these errors can vary across particles. We introduce moment-informed force rescaling for random-batch list (Mi-RBL) and random-batch Ewald (Mi-RBE) methods. A lagged average of each particle's sampled-force intensity sets an isotropic gain before the current batch is sampled, changing the random-batch force magnitude without changing its direction. The formal finite-time analysis quantifies the bias–variance tradeoff, and an estimate of the steady-state kinetic-temperature error predicts the scaling of the kinetic error with time step and thermostat friction. In the coexistence, binary-mixture, and electrolyte tests, Mi-RBL and Mi-RBE reduce kinetic errors and more closely reproduce the mean-square displacement, radial distribution function, and charge density profiles of the reference solutions. Mi-RBE also reduces the growth rate of the kinetic error with the time step by more than half and retains the predicted dependence on thermostat friction. The tested rescaling strength decreases with increasing batch size, and the particlewise update retains $O(N)$ complexity for fixed batch size.

The properties of water under high pressure and high temperature (HP-HT) are critical in multiple geochemical processes in deep Earth. Ab initio molecular dynamics (AIMD) is a promising approach to study water under extreme conditions without any empirical parameters. However, the accuracy of AIMD simulations is determined by the exchange-correlation (XC) functional including the dispersion correction used in density functional theory calculations. While van der Waals (vdW) interactions are well known to be critically important for water under ambient conditions, the influence of the dispersion correction on the properties of HP-HT water as found in Earth's mantle remains largely unexplored. To address this, we carried out AIMD simulations for supercritical water at 1, 5, and 10 GPa, and 1000 K. We compared PBE, PBE-D3, RPBE-D3, and SCAN functionals, where D3 means Grimme's D3 dispersion correction. We compared the structural, diffusion, and vibrational properties of water as computed with these XC functionals. Overall, the discrepancies between the functionals are reduced under extreme P-T conditions relative to ambient conditions. PBE and PBE-D3 exhibit higher proton-transfer rates than RPBE-D3 and SCAN, suggesting that while vdW interactions do not significantly affect the water structure under extreme conditions, the oxygen-hydrogen bond strength does influence proton transfer. Our results provide molecular-level insight into water in Earth's mantle and offer valuable guidance for selecting appropriate XC functionals in AIMD simulations of aqueous solutions under extreme conditions.

Medical images of soft tissues typically depict loaded configurations rather than true unloaded (stress-free) states, which can bias biomechanical simulations and inverse material identification. A gradient-based inverse finite element framework is presented that jointly reconstructs an effective unloaded reference geometry and estimates hyperelastic material parameters from two or more observed deformed configurations. The formulation is fully differentiable and leverages exact end-to-end gradients to enable unified, simultaneous optimization of geometry and constitutive parameters. The objective function combines a nodal-position misfit with a deformation-gradient-based mismatch term, improving robustness under large deformations. Benchmark studies quantify the influence of loading diversity and observation count and demonstrate reduced sensitivity to poor material initialization. Finally, application to an MRI-derived breast model shows accurate recovery of the unloaded configuration and constitutive parameters from multiple gravity-loaded states. The framework provides a unified and scalable tool for inverse biomechanics with potential applications in personalized modeling, elastography, and surgical planning.

In the simulation of conjugate magnetohydrodynamic (MHD) flows, where a moving conducting fluid dynamically interacts with bounding conducting walls under the influence of an externally imposed magnetic field, resolving the electrical conductivity transition across the fluid-solid interface introduces significant numerical challenges. In problems with high magnetic Reynolds numbers, it is required to solve the full magnetic induction formulation that has a curl-of-curl term for the magnetic diffusion, which is simplified to a divergence term in the original vector-valued lattice Boltzmann method (LBM). The resulting LBM scheme is valid for simulating fluid domains with a constant conductivity where its bounding solid walls are modelled using appropriate boundary conditions. The current study shows that this scheme is also valid for two-dimensional conjugate MHD simulations where the magnetic field component with non-zero gradients is perpendicular to the conductivity gradient. For general conjugate MHD simulations, we improve the LBM scheme by considering the difference between the curl-of-curl term and the simplified divergence form, which is treated as a source term in the LBM evolution algorithm and computed using an efficient LBM discretisation scheme. The improved LBM scheme automatically satisfies the required conjugate constraints at the fluid-solid interface as a volume integral inside two adjacent boundary layers. The accuracy of the improved LBM scheme is verified by piecewise analytical solutions in benchmark problems with an abrupt conductivity jump across the fluid-solid interface.

In the present study, the consistent and conservative Phase-Field method is extended to the six-equation model for compressible multiphase flows. Based solely on the conservation laws and the second law of thermodynamics, the six-equation model with the Phase-Field mechanism is first derived. In addition to satisfying Galilean invariance and consistency of reduction, the model is general to admit an arbitrary number of phases with different formulations of the Phase-Field mechanism. The isobaric closure by the pressure relaxation and the incompressible limit of the proposed model are analyzed. The derivation and analysis identify additional terms arising from the Phase-Field mechanism, which are absent from previous studies. The consistent and conservative numerical approach is adapted to the proposed six-equation model with moderate modifications, retaining the interfacial equilibrium condition, conservation, and flexibility and robustness of incorporating different formulations of the Phase-Field mechanism with bound preservation. As the new component of solving the six-equation model, both the pressure and pressure-temperature relaxations are theoretically analyzed in a general multiphase setup, with a proof of the existence and uniqueness of a thermodynamically admissible solution for these two relaxations. Various two-phase compressible flow benchmarks are performed to demonstrate the method, and good agreement with exact solutions is achieved.

MLegS is an open-source Modern Fortran code package for solving linear and nonlinear time-dependent partial differential equations on radially unbounded domains. It builds on an earlier in-house prototype, recasting it as a modular solver with a unified interface for fields, transforms, and spectral operators. Within this framework, the numerical formulation maps $0\leq r<\infty$ onto a finite interval, where associated Legendre functions provide the radial basis, while Fourier series represent the periodic azimuthal and axial directions. The mapped radial basis represents radial infinity without imposing an artificial boundary condition at finite radius while incorporating the regularity required at $r=0$ according to azimuthal order. The implementation distributes the corresponding field layouts using the Message-Passing Interface (MPI), with strong- and weak-scaling measurements extending to 512 cores across four compute nodes. Beyond parallel performance, three examples assess the solver across diffusion, reaction-diffusion, and vortex dynamics: closed-form diffusion solutions establish spectral spatial convergence and the design orders of both semi-implicit integrators; a Fisher-Kolmogorov-Petrovsky-Piskunov front matches the linearized solution and propagates at the classical speed within its logarithmic correction; and vortex-pair simulations based on toroidal-poloidal decomposition yield a measured Crow growth rate $2.7\%$ above the theoretical prediction and demonstrate the reconnection of the vortex pair.

(Suzuki-)Trotter decompositions, splitting methods, (Lie) product formulae... The most common numerical methods for the time evolution of quantum systems come with many names. And they are used practically everywhere with applications ranging from the solution of classical equations of motion and various Monte Carlo simulations to the real and imaginary time evolution on classical as well as quantum computers. Here we review the state of the art of said methods, focussing especially on the progress made over the last few years. We highlight recently discovered efficient time evolution algorithms and explain how best to use them in practice. A central part of this work is the estimation of error bounds that has improved greatly within the past decade. The relevance of time evolution methods for quantum computing is discussed with a focus on noisy hardware. Finally, a comprehensive overview of generalisations, related methods and alternatives to Trotterization is provided. This includes time-dependent Hamiltonian dynamics, processed methods, multi-product formulae, symplectic integrators, TDVP for tensor networks, quantum signal processing, Crouch-Grossman methods and more. The overall perspective in this work is that of a theoretical physicist. All mathematical proofs as well as some technical details are omitted for easier readability. Instead, this review serves as a hands-on guide and, of course, as a starting point for references that provide further details.

We study wetting on a doubly periodic rough surface in three dimensions. Although the liquid-vapor interface meets the solid at the local Young's angle, microscale roughness can cause the macroscopic apparent angle to differ substantially from this value. We formulate the directional contact angle hysteresis (CAH) interval in terms of apparent angles associated with pinned microscopic configurations. To approximate its receding and advancing endpoints, we evolve capillary mean curvature flow (CMCF) toward extremal stationary states. Computing these states is difficult because the pinning that produces hysteresis is generated at the scale of the roughness, whereas the apparent angle is only meaningful at the macroscopic scale, so a single uniform grid must resolve both. We therefore introduce a two-scale alternating (TSA) method based on a Schwarz decomposition: a Merriman-Bence-Osher (MBO) diffusion-generated scheme resolves the contact-line near region, while a linearized minimal-surface problem updates the far region. For an idealized reference iteration, we prove decay of an approximate interfacial energy. Numerical experiments on a representative doubly periodic surface show a strongly anisotropic CAH interval whose width varies by more than a factor of three with contact-line orientation and changes sharply near the diagonal directions. Because a stationary droplet must meet the solid at an apparent angle inside this interval, the computed anisotropy constrains which macroscopic wetted regions the surface can support; it is consistent with a square-like stationary droplet whose sides align with the diagonal directions.

Motivated by the Planckian thermalization rate $\Gamma \sim T$ observed in the two-body interacting SYK model, we study thermalization in the $q/2$-body case. Previous studies of such systems have established the notion of instantaneous thermalization to leading order in $1/q$. It was conjectured that the thermalization may still be Planckian but with a divergent rate $\Gamma \sim T q$, explaining the “instantaneous” part. For an analytically and numerically tractable system, we calculate the effective temperatures after a quench at time $t = 0$ and indeed find a Planckian rate, albeit with the unexpected decaying behavior $\Gamma \sim T q^{-1} $. This is contrasted with the behavior of the causal Green's function $\mathcal{G}(t_1, t_2)$, which instantly acquires a thermal form in the two-time plane block $t_1, t_2 > 0$. The resulting picture is that instant thermalization is a meaningful concept only for this block, while the off-diagonal blocks $t_1 \cdot t_2 < 0$ are inherently non-thermal at any $q$. Since the effective temperature is obtained from correlations spanning all blocks, it inherits a finite rate set by the off-diagonal. We illustrate this directly by studying the non-thermal correlations' time dependence.

Traditional theoretical treatments of ferroelectricity do not straightforwardly extend to sliding ferroelectrics, which are increasingly-studied layered materials where a switchable electrical polarization is controlled by two-dimensional relative motion of the stacked layers. Therefore, in-depth analyses of the underlying processes which dictate their polarization behavior remain challenging. In this paper, we present a comprehensive approach for identifying the symmetry-adapted microscopic parameters which are responsible for driving the emergence of this polarization. First, we outline our approach, which appeals to group theory arguments and the distortion of Wannier orbital densities to connect macroscopic symmetries to the microscopic electronic distortions which dictate the appearance of ferroelectricity. Then, we illustrate this process by using density functional theory to apply our strategy to honeycomb bilayer systems, including hexagonal boron nitride. In this way, we find that combinations of dipole-like and quadrupole-like distortions of lone pair electron orbitals control electronic reorganization, and by extension, ferroelectricity in such systems.

Most molecular transitions occur on timescales far beyond direct molecular dynamics simulations. The committor, the probability that a configuration reaches a product state before a reactant state, is a central kinetic statistic, providing a mechanism-independent reaction coordinate and a foundation for transition path theory and the calculation of rates. This review surveys modern approaches for estimating the committor and related kinetic statistics from molecular simulations, with an emphasis on self-supervised methods that learn solutions of their defining dynamical equations rather than relying on labeled shooting data. We develop a common operator viewpoint connecting generator-based partial differential equations, variational principles, Markov state models, dynamical Galerkin approximation, and neural networks. Empirical and theoretical evidence points to the efficiency of these methods. We provide theoretical and practical guidance for realizing their full potential in applications, including strategies for treating non-Markovian effects and for sampling. We conclude by identifying opportunities for further research, including connections to reinforcement learning and generative modeling.

Capillary forces are commonly regarded as an energetically closed channel in multiphase turbulence, redistributing kinetic energy across scales without net gain or loss. Here we show that this picture breaks down in bubble-laden turbulence when short-range near-contact interactions are active. A spectral analysis of the kinetic-energy budget reveals that the cumulative capillary power does not vanish at statistical stationarity, but instead retains a finite negative residual. This apparent imbalance is exactly compensated by the work of short-range repulsive forces, which is negligible at large and intermediate scales and becomes positive only at small scales. Near-contact interactions therefore open a distinct small-scale pathway in the interfacial energy transfer, rather than acting as a mere regularization of unresolved thin films. The proper scale-by-scale description is thus an extended interfacial transfer, combining capillary and near-contact work, rather than a purely capillary one.

This is the set of lecture notes for the PhD course \href{https://www.unibz.it/en/faculties/engineering/phd-computer-science/study-course-offering/2025/36967}{Physics Informed Neural Network, held at the University of Bozen/Bolzano} in the academic year 2025/2026. The goal of the course was to introduce the concept of Physics Informed Deep Neural Networks (PINN) and Neural Operators (NOs), discuss their implementation from scratch in PyTorch and using advanced ad-hoc developed open-source libraries such as NVIDia PhysicsNeMo to address real-world problems in various fields (engineering, physics, petroleum reservoir). We discuss recent topics such as Mixture-of-Models, Fourier Neural Operators, Physics-Informed Kolmogorov-Arnold Networks (PIKANs) and Fourier Neural Operators.

We establish the sharp CFL condition for the piecewise constant sparse grid discontinuous Galerkin (DG) method with forward Euler time stepping, applied to transport equations with constant coefficients on periodic domains in arbitrary dimensions. For the transport velocity $\boldsymbol c=(c_1,\ldots,c_d)$ and a uniform mesh of size $h$, we prove that the scheme is $L^2$ stable if and only if $\Delta t \leq {h}/{\max_{1\leq \ell\leq d}|c_\ell|}$, whereas the corresponding full grid upwind scheme is well-known to require $\Delta t\leq h/\sum_{\ell=1}^d |c_\ell|$. The sparse grid discretization therefore enlarges the admissible time step by a factor of ${(\sum_{\ell=1}^d |c_\ell|)}/{(\max_{1\leq \ell\leq d}|c_\ell|)}$, which lies between $1$ and $d$ and reaches $d$ for isotropic transport. The proof of sufficiency relies on projection leakage identities for the multilevel Haar decomposition, which allow the mixed directional terms in the energy estimate to be absorbed by the energy discarded by the sparse grid projection. The proof of sharpness follows from alternating modes in one dimension at the finest level. As a by-product, we obtain explicit formulas for the $L^2$ operator norm and the spectral radius of the amplification operator. For spaces over general downward closed index sets, we derive an explicit sufficient CFL condition and a geometric criterion for its sharpness. Numerical experiments in two and four dimensions confirm the theoretical results.

Multi-state HLL-type approximate Riemann solutions of ideal magnetohydrodynamics (MHD) typically assume that the medium within the Riemann fan is incompressible, and thus the slow magnetoacoustic mode cannot be included in their space-time wave configurations for the approximated states. We propose a new strategy to design multi-state HLL-type approximate solutions, allowing for the medium within the Riemann fan to be compressible. In particular, for the complete seven-wave configuration of the MHD Riemann problem, we first estimate the slow magnetoacoustic speeds and a longitudinal flow speed between the slow modes, and then follow the conservation laws and Rankine-Hugoniot jump relations across the fast, Alfvén, and slow waves, to calculate all the intermediate states within the Riemann fan. Moreover, we discuss the solutions when certain wave modes degenerate, ensuring well-posedness and smooth transitions between complete and degenerate wave configurations. Numerical simulations using a Finite Volume (FV) solver show that the proposed approximate Riemann solution is less diffusive than the classic HLLD scheme, particularly for slow mode waves. For example, in a 1D test case with a strong longitudinal magnetic field, the new scheme needs one order of magnitude fewer grid cells compared to the classic HLLD scheme to resolve all wave modes.

Numerical simulations of ocean flows typically require fine computational meshes to resolve the Munk scale, leading to high computational costs. Filtering-based large eddy simulation (LES) provides a way to relax the mesh size requirement by modeling the effects of the unresolved scales. For the implementation of this strategy, we propose a three-step algorithm called Evolve-Filter-Relax (EFR) that requires (i) the solution of a QGE problem, (ii) a nonlinear Helmholtz filter for the potential vorticity field leveraging an indicator function, and (iii) a final relaxation step. We show that the EFR algorithm can be interpreted as a splitting scheme for a perturbed QGE problem with additional dissipation and provide a practical choice for the relaxation parameter. For comparison, we also investigate a nonlinear Bardina regularization of the QGE. Numerical results on a classical benchmark show that both the EFR approach and the nonlinear Bardina regularization significantly improve the accuracy and stability of coarse mesh simulations with no LES model. Additionally, the EFR method with a deconvolution-based indicator function delivered the best balance between accuracy, stability, and computational efficiency in a test case involving a more realistic geometry (Mediterranean Sea).

A novel semi-implicit second-order finite volume scheme integrating the scalar auxiliary variable (SAV) approach is proposed for solving the pseudo-time Eikonal equation in wall-distance computation. Unconditional energy stability under zero boundary conditions is rigorously proved, eliminating the dependence of the time step on the grid scale and enabling large-time-step computation. The scheme is a priori accuracy-preserving, and its discretization matrix forms an M-matrix, thereby guaranteeing strict non-negativity of the numerical solution inherently. The framework extends readily to any non-conservative scalar equation and, being independent of the specific finite-volume reconstruction, is compatible with schemes of arbitrary order of accuracy. A vanishing artificial viscosity is introduced to smooth the solution without compromising formal accuracy, and upwinding is incorporated through directional weighting in the weighted least-squares (WLS) reconstruction. Numerical experiments confirm that the scheme achieves the designed accuracy and permits stable computations with uniformly large time steps. For complex configurations such as a three-element airfoil and the three-dimensional ONERA M6 wing, accurate results are obtained on high-aspect-ratio grids, with relative errors in the computed wall distance below 3% relative to the search-based reference, except near geometric singularities.

In this study, quantum spin pumping in an antiferromagnetic chain driven by time-dependent potential is investigated. The aim is to explore the possibility of generating and controlling spin currents in the absence of external bias and to examine the role of exchange field and periodic driving in the separation of spin-up and spin-down currents. The system is described using a tight-binding model, and spin-resolved currents are calculated employing the Keldysh non-equilibrium Green's function formalism. Two time-dependent potentials with a specific phase difference are applied to the two ends of the chain, while the chemical potentials of both electrodes are set equal. The results demonstrate that in the adiabatic regime (low frequencies), the response of the two spin channels is nearly identical. However, as the driving frequency increases and the system enters the nonadiabatic regime, absorption and emission processes of energy quanta become activated, leading to significant differences between spin-up and spin-down currents. The pumped current exhibits strong dependence on the chemical potential, allowing for the control of both magnitude and direction of the spin current through its adjustment. With increasing frequency, the spin current enhances, and parameters can be tuned such that the charge current nearly vanishes while a considerable spin current persists. This finding indicates the feasibility of achieving nearly pure spin pumping without net charge transfer in the antiferromagnetic chain. The results provide a promising perspective for designing spin-pumping devices based on antiferromagnetic systems.

Born effective charges (BEC) link atomic displacements to polarization, connecting lattice vibrations to dielectric response and infrared activity. We present ZStar, an open-source Python toolkit that automates calculations of polarization, BEC, phonons, static and frequency-dependent dielectric response, and infrared and Raman spectra. ZStar supports calculations across all dimensionalities, including bulk crystals, two-dimensional materials, one-dimensional structures, and molecules, through an integrated workflow spanning input preparation, execution, and response analysis. Berry-phase polarization and real-space dipoles describe responses along periodic and open directions, respectively. Our unified, symmetry-adapted finite-displacement framework jointly determines BEC and zone-center force constants from the same calculations, improving computational efficiency while preserving numerical accuracy. Reusing the electronic Hamiltonian in the ABACUS+PYATB route enables Raman calculations without additional self-consistent calculations. Reproducible examples and a packaged agent skill support conventional and agent-assisted use. ZStar enables efficient, automated exploration of polarization, BEC, dielectric response, and vibrational spectra across all dimensionalities.

The previously proposed tight-binding method derived from the total energy has been extended within the local density approximation (TE-TB method; J. Phys. Soc. Jpn. 87, 064802 (2018)). Unlike the earlier two-parameter formulation, the present method introduces three parameters. These parameters explicitly capture local packing effects and improve transferability. Furthermore, based on physical considerations, several boundary conditions (inductive bias) are imposed on the functionals defining the tight-binding Hamiltonian and related energy functionals. The revised formalism is tested on crystalline silicon to assess the stability of the diamond structure, a monovacancy, and the (001) surface. These benchmark tests demonstrate the high transferability and reliability of the present three-parameter TE-TB design philosophy.

We formulate Hartree–Fock as a density-matrix renormalization group (DMRG) sweep of a single Slater determinant, assuming a density–density electron–electron interaction. We compress the occupied state and long-range interaction separately, reducing each sweep step to a small local Fock problem. Exchange is retained throughout. Uniform antiferromagnetic hydrogen chains provide an almost ideal setting for this approach, while retaining the Coulomb interaction and its $1/r$ tail. We initialize and converge a chain of 100,000 electrons in 1.8 million spatial basis functions in about two hours on a 64-GB Mac mini, using less than a third of its memory. The work per sweep is nearly proportional to chain length, and the number of sweeps needed for convergence changes little from 1000 to 100,000 atoms. DMRG's compression of states and environments thus makes large HF calculations with long-range Hartree and exchange practical on an ordinary desktop computer.

Scientific observations are frequently distributed across locations, time periods, and institutions. Combining such observations into a continuous, differentiable field enables recovering governing physical parameters from its derivatives. This paper makes two contributions in this setting. First, the established additive structure of fixed-basis ridge-regression statistics is applied to tensor-product spline fields: each data holder computes a local Gram matrix and moment vector, and the merged solution is mathematically identical to centralized fitting, with no raw data shared and no iterative synchronization. This property is specific to the fixed-feature squared-error setting; the present derivation does not establish an analogous guarantee for general jointly trained multilayer networks. Second, a complete pipeline connects distributed observations to physical parameter inference through field reconstruction, derivative extraction, and linear regression. The pipeline is validated on four PDEs: diffusion, wave, heat-with-source, and the nonlinear viscous Burgers equation, recovering governing parameters to sub-percent accuracy in the linear cases and 5% for Burgers. In all cases, distributed merging introduces zero degradation relative to centralized fitting. Synthetic experiments validate parameter recovery; application to 41 years of NOAA sea-surface temperature data validates field reconstruction and aggregation equivalence on real spatiotemporal observations. Source code to reproduce all experiments is available at https://github.com/NAVEENMN/splinemerge.

Magnetic MXenes are promising candidates for future spintronics due to their intriguing properties. Nevertheless, the topological properties of magnon bands and superexchange mechanism remain relatively underexplored. In this work, we have calculated the spin wave dispersions for MXene Fe$_2$C using the linear spin wave method, with the exchange coupling parameters obtained from first-principles calculations. Owing to the staggered stacking of two Fe sub-lattices, the interlayer exchange coupling lifts the degeneracy of the ferromagnetic magnon modes. A Dirac point is identified in the magnon bands at the $K$ point. The topological properties of magnon bands, including Berry curvature, valley Chern number and edge states, are further computed by means of a two-band model. We also derive an effective Hamiltonian to explain the magnonic topology, which is protected by the $C_{3v}$ rotational symmetry. To understand the microscopic origin of the exchange couplings that govern the magnon bands, we then construct a refined model integrating perturbation theory and the tight-binding approach. The ferromagnetic superexchange coupling is mediated by the virtual hopping between the d orbitals of two distinct Fe sites via a pair of orthogonal p orbitals at the bridging C site. In detail, the intralayer exchange coupling is governed by the in-plane $p_x$ and $p_y$ orbitals, while the out-of-plane $p_z$ orbital is responsible for the interlayer exchange coupling. Our results establish a direct link between the orbital-resolved anisotropic superexchange and topological properties of the magnon bands in magnetic MXene Fe$_2$C, providing theoretical guidance for future spintronics applications.

Reduced-order modeling of transport-dominated systems remains challenging because moving fronts and shocks are poorly represented by low-dimensional linear subspaces. We develop a structure-informed data-driven reduced-order model(ROM) for scalar hyperbolic conservation laws based on the kinetic defect formulation. This formulation separates the nonlinear dynamics into known characteristic transport and a kinetic entropy defect localized on the shock manifold. We exploit this structure by first removing the known transport from the solution snapshots. We then extract and register the remaining defect-driven dynamics in a shock-attached coordinate system. Separate ROMs are used to evolve the shock geometry and the registered defect-driven source. During prediction, the predicted shock geometry is used to inverse-register the learned defect-driven source, which advances the kinetic state and recovers the physical solution. Numerical examples in one and two spatial dimensions demonstrate accurate reconstruction and prediction of nonlinear transport with shocks, including evolution beyond the training interval, while accurately capturing the mass and entropy-dissipation behavior of the reference solution.

We present an implicit time integration capability for high-order curvilinear finite element Lagrangian hydrodynamics. Starting from an existing explicit formulation, the implicit treatment builds directly on the original discretization and operator structure and does not alter the underlying spatial formulation or physics model. We demonstrate our implementation using the Laghos miniapp, which is built on the MFEM finite element library. To support gradient-based nonlinear solution methods, we compute Jacobian actions automatically using MFEM's $\partial$FEM interface together with Enzyme-based automatic differentiation, and apply the resulting Jacobian in a matrix-free or fully-assembled manner within a Newton-Krylov solver. To ensure robust and differentiable nonlinear solves in the presence of shocks, we introduce a smooth artificial viscosity treatment based on smooth approximations of non-differentiable pointwise operations. The differentiable artificial viscosity presently lacks a limiter to ensure high-order scaling away from shocks, but is sufficient for illustrating the benefits of implicit Lagrangian hydrodynamics. The behavior and performance of the implicit method are demonstrated on several standard benchmark problems. We verify high-order convergence on the smooth Taylor-Green vortex in the absence of artificial viscosity, show correct strong-shock behavior on the Sedov blast problem, and obtain significant improvements in accuracy-per-time-to-solution on the Triple Point problem where explicit stability constraints become increasingly severe for high-order discretizations.

We present a highly parallelizable, matrix-free, real-space method for computing the random phase approximation (RPA) correlation energy within Kohn-Sham density functional theory. In particular, we avoid the explicit construction and eigen-decomposition of the response function matrix and use Lanczos quadrature to evaluate the trace of a matrix function on a real-space grid. We also show it is possible to exploit the spatial smoothness of the RPA correlation energy density in real-space to reduce computational cost. Specifically, we compute the energy density on a coarse grid, then reconstruct an approximation to the full, fine grid via interpolation. We implement this formulation within the SPARC electronic structure package and demonstrate its convergence, accuracy, agreement with planewave results, and scaling. Interpolation can enable an $8\times$ reduction in the computational prefactor. Given the embarrassingly parallel nature of the proposed method, we achieve near-ideal speedups and near-cubic scaling, thus allowing us to compute the RPA correlation energy for a silicon system with 256 valence electrons at chemical accuracy in less than 30 minutes on 4,096 CPU cores.

Reaching compressible flow has usually forced lattice Boltzmann methods to abandon the compact stencil or the strict locality that make them efficient. We give up neither, solving the compressible Navier–Stokes–Fourier equations with a scheme that transports only the conserved mass, momentum and energy. The viscous stress and heat flux depend on gradients of the velocity and temperature. To capture them, existing compressible schemes go beyond a single lattice of the conserved fields. They enlarge the velocity set, carry the stress and heat flux as extra transported fields, place the energy on a separate grid, or give up exact streaming for an off-lattice advection. We instead recover the gradients from the non-equilibrium part of the distributions already present, inside the collision. No field beyond the conserved state is transported, no neighbour is read, streaming stays exact, and every computation runs in single precision. The method carries five fields where a transported-flux scheme carries fourteen, at a fraction of the memory and $4.9$ times the throughput. Verified against the exact Sod and Becker shock solutions and a supersonic Taylor–Green vortex, it tracks the direct-numerical-simulation reference on the kinetic energy and stays within the reference-solver spread on both dissipation rates.