The 2024 Nobel Prize in Physics was awarded for pioneering contributions at the intersection of artificial neural networks (ANNs) and spin-glass physics, underscoring the profound connections between these fields. The topological similarities between ANNs and Ising-type models, such as the Sherrington-Kirkpatrick model, reveal shared structures that bridge statistical physics and machine learning. In this perspective, we explore how concepts and methods from statistical physics, particularly those related to glassy and disordered systems like spin glasses, are applied to the study and development of ANNs. We discuss the key differences, common features, and deep interconnections between spin glasses and neural networks while highlighting future directions for this interdisciplinary research. Special attention is given to the synergy between spin-glass studies and neural network advancements and the challenges that remain in statistical physics for ANNs. Finally, we examine the transformative role that quantum computing could play in addressing these challenges and propelling this research frontier forward.

We develop a first-principles many-body framework to describe the dynamics of photocarriers and phonons in semiconductors following ultrafast excitation. Our approach incorporates explicit ab initio light-matter coupling and first-principles collision integrals for carrier-carrier, carrier-phonon, and phonon-phonon scattering. It also yields time-dependent quasiparticle and phonon frequency renormalizations, along with light-induced coherent atomic motion. The equations of motion are solved in a maximally localized Wannier basis, ensuring gauge-consistent scattering integrals and ultradense momentum sampling, thereby enabling direct comparison with pump-probe experiments. The method can be coupled to constrained density-functional theory to access light-induced structural phase transitions at longer times after the light pulse. We showcase the capabilities and predictive power of this framework on MoS$_2$ and h-BN monolayers. For MoS$_2$, we resolve photoinduced renormalizations of electronic and lattice properties, ultrafast carrier relaxation, hot-phonon dynamics, and displacive coherent atomic motion. Including carrier-carrier scattering is crucial to obtain realistic photocarrier equilibration times, while omitting phonon-phonon scattering leads to incorrect long-time lattice thermalization and a factor of two larger A$_{1g}$ coherent phonon damping time. For h-BN, we quantify photoinduced changes in the electronic, optical, and lattice responses in quasi-equilibrium, demonstrating a fluence-dependent enhancement of screening and melting of excitonic features.

We present a fully analytical integration of the Maxwell stress tensor and derive exact relations for interparticle forces in systems of multiple dielectric spheres immersed in a polarizable ionic solvent, within the framework of the linearized Poisson--Boltzmann theory. Building upon the screening-ranged (in ascending orders of Debye screening) expansions of the potentials developed and rigorously analyzed in the accompanying works \cite{supplem_pre,supplem_pre_math,supplem_prl}, we construct exact screening-ranged many-body expansions for electrostatic forces in explicit analytical form. These results establish a rigorous foundation for evaluating screened electrostatic interactions in complex particle systems and provide direct analytical connections to, and systematic improvements upon, various earlier approximate or limited-case formulations available in the literature, both at zero and finite ionic strength.

Light scattering by spherical-shaped particles of sizes comparable to the wavelength is foundational in many areas of science, from chemistry to atmospheric science, photonics and nanotechnology. With the new capabilities offered by machine learning, there is a great interest in end-to-end differentiable frameworks for scattering calculations. Here we introduce PyMieDiff, a fully differentiable, GPU-compatible implementation of Mie scattering for core-shell particles in PyTorch. The library provides native, autograd-compatible spherical Bessel and Hankel functions, vectorized evaluation of Mie coefficients, and APIs for computing efficiencies, angular scattering, and near-fields. All inputs - geometry, material dispersion, wavelengths, and observation angles and positions - are represented as tensors, enabling seamless integration with gradient-based optimisation or physics-informed neural networks. The toolkit can also be combined with "TorchGDM" for end-to-end differentiable multi-particle scattering simulations. PyMieDiff is available under an open source licence at this https URL.

We investigate a variational Monte Carlo framework for trapped one-dimensional mixture of spin-$\frac{1}{2}$ fermions using Kolmogorov-Arnold networks (KANs) to construct universal neural-network wavefunction ansätze. The method can, in principle, achieve arbitrary accuracy, limited only by the Monte Carlo sampling and was checked against exact results at sub-percent precision. For attractive interactions, it captures pairing effects, and in the impurity case it agrees with known results. We present a method of systematic transfer learning in the number of network parameters, allowing for efficient training for a target precision. We vastly increase the efficiency of the method by incorporating the short-distance behavior of the wavefunction into the ansätz without biasing the method.

We present an analytical many-body formalism for systems of spherical particles carrying arbitrary free charge distributions and interacting in a polarizable electrolyte solution, that we model within the linearized Poisson--Boltzmann framework. Building on the detailed spectral analysis of the associated nonstandard Neumann--Poincaré-type operators developed in our companion study~\cite{supplem_pre_math}, we construct exact explicit expansions of the electrostatic potential and energy in ascending orders of Debye screening thereby obtaining systematic "screening-ranged" series for potentials and energies. These screening-ranged expansions provide a unified and tractable description of many-body electrostatics. We demonstrate the versatility of the approach by showing how it generalizes and improves upon both classical and modern methods, enabling rigorous treatment of heterogeneously charged systems (such as Janus particles) and accurate modeling of higher-order phenomena (such as asymmetric dielectric screening, opposite-charge repulsion, like-charge attraction) as well as yielding many-body generalizations to analytical explicit results previously known only in the two-body setting.

Quantitative low-energy electron diffraction [LEED $I(V)$] is a powerful method for surface-structure determination, based on a direct comparison of experimentally observed $I(V)$ data with computations for a structure model. As the diffraction intensities $I$ are highly sensitive to subtle structural changes, local structure optimization is essential for assessing the validity of a structure model and finding the best-fit structure. The calculation of diffraction intensities is well established, but the large number of evaluations required for reliable structural optimization renders it computationally demanding. The computational effort is mitigated by the tensor-LEED approximation, which accelerates optimization by applying a perturbative treatment of small deviations from a reference structure. Nevertheless, optimization of complex structures is a tedious process. Here, the problem of surface-structure optimization is reformulated using a tree-based data structure, which helps to avoid redundant function evaluations. In the new tensor-LEED implementation presented in this work, intensities are computed on the fly, eliminating limitations of previous algorithms that are limited to precomputed values at a grid of search parameters. It also enables the use of state-of-the-art optimization algorithms. Implemented in \textsc{Python} with the JAX library, the method provides access to gradients of the $R$ factor and supports execution on graphics processing units (GPUs). Based on these developments, the computing time can be reduced by more than an order of magnitude.

The interaction of particles in an electrolytic medium can be calculated by solving the Poisson equation inside the solutes and the linearized Poisson--Boltzmann equation in the solvent, with suitable boundary conditions at the interfaces. Analytical approaches often expand the potentials in spherical harmonics, relating interior and exterior coefficients and eliminating some coefficients in favor of others, but a rigorous spectral analysis of the corresponding formulations is still lacking. Here, we introduce composite many-body Neumann--Poincaré-type operators and prove that they are compact with spectral radii strictly less than one. These results provide the foundation for systematic screening-ranged expansions, in powers of the Debye screening parameters, of electrostatic potentials, interaction energies, and forces, and establish the analytical framework for the accompanying works~\cite{supplem_prl,supplem_pre,supplem_pre_force}.

We present an exact many-body framework for electrostatic interactions among $N$ arbitrarily charged spheres in an electrolyte, modeled by the linearized Poisson--Boltzmann equation. Building on a spectral analysis of nonstandard Neumann--Poincaré-type operators introduced in a companion mathematical work~\cite{supplem_pre_math}, we construct convergent screening-ranged series for the potential, interaction energy, and forces, where each term is associated with a well-defined Debye--Hückel screening order and can be obtained evaluating an analytical expression rather than numerically solving an infinitely dimensional linear system. This formulation unifies and extends classical and recent approaches, providing a rigorous basis for electrostatic interactions among heterogeneously charged particles (including Janus colloids) and yielding many-body generalizations of analytical closed-form results previously available only for two-body systems. The framework captures and clarifies complex effects such as asymmetric dielectric screening, opposite-charge repulsion, and like-charge attraction, which remain largely analytically elusive in existing treatments. Beyond its fundamental significance, the method leads to numerically efficient schemes, offering a versatile tool for modeling colloids and soft/biological matter in electrolytic solution.

Accurate prediction of the frequency response of quantum dots under electromagnetic radiation is essential for investigating absorption spectra, excitonic effects, and nonlinear optical behavior in quantum dots and semiconductor nanoparticles. The polarization propagator provides a rigorous framework for evaluating these properties, but its construction is computationally demanding. Challenges arise from the level of electron correlation, the size of the excitonic basis, and the cost of evaluating two-electron integrals. This work addresses these difficulties by developing first- and second-order frequency-dependent polarization propagator calculations for PbS and CdS quantum dots. The propagator is formulated using the electron propagator approach and expressed as the resolvent of the Hamiltonian superoperator. Light-matter interaction is treated using the dipole approximation and represented in a particle-hole excitation operator basis. The correlated ground state is treated at the MP2 level, and all response-matrix terms up to second order in the fluctuating potential are included. A frequency-dependent inverse Krylov subspace method is derived and combined with the folded-spectrum technique to isolate excitation energies within a chosen frequency window. This strategy avoids full diagonalization of the response matrix and significantly reduces computational cost for large systems. The method is implemented in a matrix-free manner in which no explicit response matrix is assembled, and all operations rely on matrix-vector products. UV-VIS excitation spectra of PbS and CdS quantum dots were computed, demonstrating that the inverse Krylov subspace projection approach provides an efficient and accurate approximation for excitation spectra when full diagonalization is computationally prohibitive.

Thin, metallic magnetic films can support nonreciprocal spin waves due to the interfacial Dzyaloshinskii-Moriya interaction (iDMI). However, these films typically have high damping, making spin wave propagation distances short (less than one micrometer). In this work, we theoretically study a thin ferromagnetic strip with iDMI and excite spin waves by driving a central segment of the strip. Spin waves propagate with different amplitudes to the left versus to the right from the driving region (i.e. nonreciprocity occurs) due to the iDMI. Our calculation based on spin-wave-dispersion plus our micromagnetic simulations both show that changing the driving segment width, driving frequency and static applied field strength tunes the nonreciprocity. Our calculation based on spin-wave-dispersion, using a so-called "overlap function" will allow researchers to predict conditions of maximum nonreciprocity, without the need for computational solvers. Moreover, to circumvent the issue of short propagation distances, we propose a geometry where iDMI is only present in the driving region and low-damping materials comprise the remainder of the strip. Our calculations show significant spin wave amplitudes over several microns from the excitation region.

Diverse scientific and engineering research areas deal with discrete, time-stamped changes in large systems of interacting delay differential equations. Simulating such complex systems at scale on high-performance computing clusters demands efficient management of communication and memory. Inspired by the human cerebral cortex -- a sparsely connected network of $\mathcal{O}(10^{10})$ neurons, each forming $\mathcal{O}(10^{3})$--$\mathcal{O}(10^{4})$ synapses and communicating via short electrical pulses called spikes -- we study the simulation of large-scale spiking neural networks for computational neuroscience research. This work presents a novel network construction method for multi-GPU clusters and upcoming exascale supercomputers using the Message Passing Interface (MPI), where each process builds its local connectivity and prepares the data structures for efficient spike exchange across the cluster during state propagation. We demonstrate scaling performance of two cortical models using point-to-point and collective communication, respectively.

A major challenge in light-matter simulations is bridging the disparate time and length scales of electrodynamics and molecular dynamics. Current computational approaches often rely on heuristic approximations of either the electromagnetic (EM) or material component, hindering the exploration of complex light-matter systems. Herein, MaxwellLink -- a modular, open-source Python framework -- is developed for the massively parallel, self-consistent propagation of classical EM fields interacting with a large heterogeneous molecular ensemble. The package utilizes a robust TCP/UNIX socket interface to couple EM solvers with a wide range of external molecular drivers. This decoupled architecture allows users to seamlessly switch between levels of theory of either the EM solver or molecules without modifying the counterpart. Crucially, MaxwellLink supports EM solvers spanning from single-mode cavities to full-feature three-dimensional finite-difference time-domain (FDTD) engines, and molecules described by multilevel open quantum systems, force-field and first-principles molecular dynamics, and nonadiabatic real-time Ehrenfest dynamics. Benefiting from the socket-based design, the EM engine and molecular drivers scale independently across multiple high-performance computing (HPC) nodes, facilitating large-scale simulations previously inaccessible to existing numerical schemes. The versatility and accuracy of this code are demonstrated through applications including superradiance, radiative energy transfer, vibrational strong coupling in Bragg resonators, and plasmonic heating of molecular gases. By providing a unified, extensible engine, MaxwellLink potentially offers a powerful platform for exploring emerging phenomena across the research fronts of spectroscopy, quantum optics, plasmonics, and polaritonics.

We introduce FieldSeer I, a geometry-aware world model that forecasts electromagnetic field dynamics from partial observations in 2-D TE waveguides. The model assimilates a short prefix of observed fields, conditions on a scalar source action and structure/material map, and generates closed-loop rollouts in the physical domain. Training in a symmetric-log domain ensures numerical stability. Evaluated on a reproducible FDTD benchmark (200 unique simulations, structure-wise split), FieldSeer I achieves higher suffix fidelity than GRU and deterministic baselines across three practical settings: (i) software-in-the-loop filtering (64x64, P=80->Q=80), (ii) offline single-file rollouts (80x140, P=240->Q=40), and (iii) offline multi-structure rollouts (80x140, P=180->Q=100). Crucially, it enables edit-after-prefix geometry modifications without re-assimilation. Results demonstrate that geometry-conditioned world models provide a practical path toward interactive digital twins for photonic design.

We develop and analyze Riemannian optimization methods for computing ground states of rotating multicomponent Bose-Einstein condensates, defined as minimizers of the Gross-Pitaevskii energy functional. To resolve the non-uniqueness of ground states induced by phase invariance, we work on a quotient manifold endowed with a general Riemannian metric. By introducing an auxiliary phase-aligned iteration and employing fixed-point convergence theory, we establish a unified local convergence framework for Riemannian gradient descent methods and derive explicit convergence rates. Specializing this framework to two metrics tailored to the energy landscape, we study the energy-adaptive and Lagrangian-based Riemannian gradient descent methods. While monotone energy decay and global convergence are established only for the former, a quantified local convergence analysis is provided for both methods. Numerical experiments confirm the theoretical results and demonstrate that the Lagrangian-based method, which incorporates second-order information on the energy functional and mass constraints, achieves faster local convergence than the energy-adaptive scheme.

Solving partial differential equations (PDEs) for reservoir seepage is critical for optimizing oil and gas field development and predicting production performance. Traditional numerical methods suffer from mesh-dependent errors and high computational costs, while classical Physics-Informed Neural Networks (PINNs) face bottlenecks in parameter efficiency, high-dimensional expression, and strong nonlinear fitting. To address these limitations, we propose a Discrete Variable (DV)-Circuit Quantum-Classical Physics-Informed Neural Network (QCPINN) and apply it to three typical reservoir seepage models for the first time: the pressure diffusion equation for heterogeneous single-phase flow, the nonlinear Buckley-Leverett (BL) equation for two-phase waterflooding, and the convection-diffusion equation for compositional flow considering adsorption. The QCPINN integrates classical preprocessing/postprocessing networks with a DV quantum core, leveraging quantum superposition and entanglement to enhance high-dimensional feature mapping while embedding physical constraints to ensure solution consistency. We test three quantum circuit topologies (Cascade, Cross-mesh, Alternate) and demonstrate through numerical experiments that QCPINNs achieve high prediction accuracy with fewer parameters than classical PINNs. Specifically, the Alternate topology outperforms others in heterogeneous single-phase flow and two-phase BL equation simulations, while the Cascade topology excels in compositional flow with convection-dispersion-adsorption coupling. Our work verifies the feasibility of QCPINN for reservoir engineering applications, bridging the gap between quantum computing research and industrial practice in oil and gas engineering.