Papers

Efficient simulation of nonlinear light propagation in complex photonic structures remains a major challenge because these systems combine intricate transverse geometries with propagation over distances spanning many diffraction lengths. Existing numerical methods often require computationally intensive uniform discretizations or struggle to accurately represent complex material boundaries, limiting the practical simulation of multiscale nonlinear photonic devices. Here we introduce a computational framework for solving the nonlinear Schrödinger equation that accelerates simulations by more than two orders of magnitude (over 100x) compared with conventional approaches while maintaining spectral-level accuracy, thereby reducing the computational time required to solve large-scale and multiscale problems from days to hours. The method is based on discrete exterior calculus, enabling geometry-conforming discretization directly on unstructured meshes without the weak formulations required by conventional finite-element methods. In contrast to Fourier-based spectral solvers, it avoids global oversampling, eliminates Gibbs-type oscillations at material interfaces, naturally incorporates absorbing boundary conditions, and preserves the topological structure of the underlying differential operators. A key feature of the framework is that higher-order propagation operators are generated algorithmically from lower-order discrete operators, providing a systematic route to extending simulations beyond the standard nonlinear Schrödinger equation. Benchmarks on fundamental solitons, asymmetric beams, and optical vortices confirm spectral-level accuracy while demonstrating computational speedups exceeding 100x.

Finite-temperature simulations of electric-field-driven dynamics need a unified description of interatomic interactions, local electronic states, and configuration-dependent electric responses. First-principles simulations remain scale-limited, whereas conventional machine-learning potentials lack electric-field effects. Recent machine-learning frameworks have incorporated electric-field response or atom-resolved electronic-state information, but rarely both within a single framework. Here, we develop an electric-field-response graph neural network (EFR-GNN) that predicts energies, forces, Born effective charge tensors, atom-resolved charges and magnetic moments, and supports long-time field-driven molecular dynamics with atom-resolved tracking of localized electronic states. In hole-doped MgO, static fields rectify thermally activated hole-polaron hopping through a forward–backward asymmetry quantified by a nearest-neighbor model. In GaAs, resonant terahertz excitation generates a coherent $\Gamma$-point transverse-optical phonon with dephasing consistent with experiment, while opposite helicities reverse its rotation. In superionic $\alpha$-AgI, it reproduces temperature-dependent Ag$^+$ mobility and collective field-driven ionic drift. Together, EFR-GNN offers an approach to finite-temperature simulations of field-driven atomic and localized-carrier dynamics.

We present AccelNet, an exact, backward-compatible method for accelerating existing trained aenet and n2p2 neural-network potentials without retraining. For angular terms with separable one-neighbor weights and a finite polynomial dependence on $\cos \theta$, the method exploits their hidden finite-rank structure to replace explicit neighbor-pair loops by one-neighbor Cartesian moments. AccelNet reads models trained with either package and reproduces their descriptors, energies, and analytic forces to floating-point roundoff. We verified this equivalence for H$_2$O and TiO$_2$ models and tested the resulting potentials in LAMMPS molecular-dynamics simulations. The implementation, model-conversion tools, and LAMMPS interfaces are released as open-source software. AccelNet also enables GPU-accelerated molecular dynamics with existing aenet and n2p2 potentials. Moment evaluation achieves speedups of up to 10.9 on a CPU and 15.8 on a GPU relative to direct evaluation within AccelNet. The implementation, model-conversion tools, and LAMMPS interfaces are released as open-source software.

Designing an effective electromagnetic inverse-scattering solver requires faithful enforcement of nonlinear full-wave physics together with an expressive prior on the unknown permittivity contrast. We propose ScoreField, a neural inverse scattering framework that integrates coupled implicit neural representations (INRs) with a pretrained score-based generative prior. ScoreField employs two INRs to parameterize the permittivity contrast and the induced current fields, and jointly optimize them under the Lippmann-Schwinger equations. In addition to the implicit regularization by the INR architecture, the score model provides a learned prior gradient on the contrast, which is propagated to the contrast INR through the chain rule. This formulation enables ScoreField to effectively handle strong multiple scattering, where nonlinear wave interactions require accurate modeling of the coupled full-wave physics. We evaluate ScoreField on simulated weak- and strong-scattering benchmarks, the canonical Austria phantom, and experimental Fresnel measurements. We note that ScoreField significantly improves reconstruction fidelity and suppresses artifacts relative to classical full-wave methods and deep learning baselines, achieving an average PSNR improvement of $1.8 \, \mathrm{dB}$ over the best competing method on real Fresnel data.

We introduce a new SVD-based tensor decomposition method for tensor networks with arbitrary graph topologies, extending classical hierarchical SVD-based techniques to networks with cycles and general connectivity. We also introduce addition and rounding procedures for traceable tensor graphs, enabling step-rounding time integration of high-dimensional PDEs directly in graph format, with rank truncation controlled to a prescribed tolerance at every time step. We demonstrate the new method on the decomposition of multivariate functions and on the numerical solution of the Fokker-Planck equation, and find that the graph-format representation attains comparable or better accuracy than the classical tensor train and hierarchical Tucker tensor formats, while using substantially fewer degrees of freedom at lower computational cost.

Polymer quantization program applied in Loop Quantum Gravity/Cosmology leads to nonseparable Hilbert spaces. Commonly, one sidesteps this problem by singling out and working with a separable superselection sector. This is however often no longer accessible in more involved models beyond isotropic ones. In an alternative approach one builds a separable Hilbert space as an integral over all available sectors. Here we test the dynamics following from the latter on the example of a flat isotropic Universe admitting negative cosmological constant and a massless scalar field. There, numerical evolution of (initially) semiclassical states shows that there is no relevant difference in their long term semiclassicality properties in comparison to those in a single sector approach. Further, the older (problem-specific) numerical methods are compared against an application of more common and more efficient standard tools (eigen library).

Pseudomode approaches allow for an exact and unapproximated description of a quantum system interacting arbitrarily strongly with a bath. In general, a system coupled to pseudomodes will not thermalize to the system's Gibbs state: This is to be expected when the system-bath coupling is non-perturbative, but conflicts with common thermodynamic intuition when the system-bath coupling is asymptotically weak. We explore under which circumstances pseudomode models satisfy detailed balance (and subsequently thermalize to the system Gibbs state) and how specific choices of parameters can force "weak" detailed balance that is restricted to a limited frequency range. A combination of Hermitian and non-Hermitian pseudomodes that yields a flat effective-temperature profile is also considered. The results and criteria established here are relevant for the construction of pseudomode models in contexts where thermodynamic consistency is required.

Airborne pollen transport is a key concern for urban air-quality assessment, allergy-risk forecasting, and smart-city planning. However, conventional dispersion models generally assume smooth spherical particles, neglecting how pollen dehydration alters particle morphology and impacts aerodynamic and thermal behavior. To address this gap, this study presents, for the first time, advanced CFD simulations evaluating the aerodynamic drag forces and convective heat transfer of realistically dehydrated (dry) pollen particles. Investigations are conducted at Reynolds numbers ($0.1 \leq Re_p \leq 15$) at the particle's scale corresponding to realistic atmospheric wind speeds ranging from 0.27 to 30 km/h. The findings reveal that dry pollen particles exhibit drag coefficients 8% to 15% higher than those predicted for hydrated pollen spherical particles. Conversely, their Nusselt numbers are 5% to 15% lower than those for hydrated pollen particles. These considerable deviations confirm that conventional spherical correlations are inadequate for simulating dry pollen Lagrangian transport and evaporation. These findings highlight the need to account for realistic dehydrated shapes when modeling airborne allergen transport in urban environments.

Metallenes have appealing properties, but stabilizing them in a monolayer phase poses challenges for their synthesis. A recent experiment showed that the van der Waals squeezing method can stabilize certain metallenes in a MoS2 sandwich. This pioneering work motivates systematic studies, but such studies are experimentally impractical, while first-principles modeling remains prohibitive. Here, armed with universal machine-learning interatomic potentials, we constructed 1620 metallene sandwich heterostructures containing 6 different sandwich layers and 45 metals. We performed phonon calculations, which revealed 1208 dynamically stable structures. We found that transition-metal dichalcogenides, particularly MoSe2, are highly effective in stabilizing metallenes. Specifically, buckled hexagonal and honeycomb crystal lattices exhibit the greatest stability. We further evaluated the thermal stability of selected heterostructures with density-functional theory molecular dynamics simulations at room temperature. By uncovering the physical and chemical factors governing the stabilization of metallenes, our results provide systematic insights to guide and accelerate synthesis for future applications.