We present a machine learning (ML) force-field framework for simulating the non-equilibrium dynamics of charge-density-wave (CDW) order driven by the Peierls instability. Since the Peierls distortion arises from the coupling between lattice displacements and itinerant electrons, evaluating the adiabatic forces during time evolution is computationally intensive, particularly for large systems. To overcome this bottleneck, we develop a generalized Behler-Parrinello neural-network architecture -- originally formulated for ab initio molecular dynamics -- to accurately and efficiently predict forces from local structural environments. Using the locality of electronic responses, the resulting ML force field achieves linear scaling efficiency while maintaining quantitative accuracy. Large-scale dynamical simulations using this framework uncover a two-stage coarsening behavior of CDW domains: an early-time regime characterized by a power-law growth $L \sim t^{\alpha}$ with an effective exponent $\alpha \approx 0.7$, followed by a crossover to the Allen-Cahn scaling $L \sim \sqrt{t}$ at late times. The enhanced early-time coarsening is attributed to anisotropic domain-wall motion arising from electron-mediated directional interactions. This work demonstrates the promise of ML-based force fields for multiscale dynamical modeling of condensed-matter lattice models.

We extensively study the phenomenology of one dimensional Nonreciprocal Cahn Hilliard model for varying nonreciprocity $(\alpha)$ and different boundary conditions. At small $\alpha$, a perturbed uniform state evolves to a defect laden configuration that lacks global polar order. Defects are the sources and sinks of travelling waves and nonreciprocity selects defects with a unique wave number that increases monotonically with $\alpha_c$. A critical threshold $\alpha_c$ marks the onset of a transition to states with finite global polar order. For periodic boundaries, above $\alpha_c$, the system shows travelling waves that are completely ordered. In contrast, travelling waves are incompatible with Dirichlet and Neumann boundaries. Instead, for $\alpha \gtrsim \alpha_c$, we find fluctuating domains that show intermittent polar order and at large $\alpha$, the system partitions into two domains with opposite polar order.

Surrogate modeling of eccentric binary black hole waveforms has remained challenging. The complicated morphology of these waveforms due to the eccentric orbital timescale variations makes it difficult to construct accurate and efficient surrogate models, especially for waveforms long enough to cover the sensitivity band of the current ground-based gravitational wave detectors. We present a novel and scalable surrogate building technique which makes surrogate modeling of long-duration eccentric binary black hole waveforms both feasible and highly efficient. The technique aims to simplify the harmonic content of the intermediate eccentric surrogate data pieces by modeling them in terms of an angular orbital element called the mean anomaly, instead of time. We show that this novel parameterization yields an order of magnitude fewer surrogate basis functions than using the contemporary parameterization in terms of time. We show that variations in surrogate data-pieces across parameter space become much more regular when expressed in terms of the instantaneous waveform eccentricity and mean anomaly, greatly easing their parameter-space fitting. The methods presented in this work make it feasible to build long-duration eccentric surrogates for the current as well as future third-generation gravitational wave detectors.

Learning PDE dynamics with neural solvers can significantly improve wall-clock efficiency and accuracy compared with classical numerical solvers. In recent years, foundation models for PDEs have largely adopted multi-scale windowed self-attention, with the scOT backbone in \textsc{Poseidon} serving as a representative example. However, because of their locality, truly globally consistent spectral coupling can only be propagated gradually through deep stacking and window shifting. This weakens global coupling and leads to error accumulation and drift during closed-loop rollouts. To address this, we propose \textbf{DRIFT-Net}. It employs a dual-branch design comprising a spectral branch and an image branch. The spectral branch is responsible for capturing global, large-scale low-frequency information, whereas the image branch focuses on local details and nonstationary structures. Specifically, we first perform controlled, lightweight mixing within the low-frequency range. Then we fuse the spectral and image paths at each layer via bandwise weighting, which avoids the width inflation and training instability caused by naive concatenation. The fused result is transformed back into the spatial domain and added to the image branch, thereby preserving both global structure and high-frequency details across scales. Compared with strong attention-based baselines, DRIFT-Net achieves lower error and higher throughput with fewer parameters under identical training settings and budget. On Navier--Stokes benchmarks, the relative $L_{1}$ error is reduced by 7\%--54\%, the parameter count decreases by about 15\%, and the throughput remains higher than scOT. Ablation studies and theoretical analyses further demonstrate the stability and effectiveness of this design. The code is available at this https URL.

The advent of fault-tolerant quantum computing (FTQC) promises to tackle classically intractable problems. A key milestone is solving the Navier-Stokes equations (NSE), which has remained formidable for quantum algorithms due to their high input-output overhead and nonlinearity. Here, we establish a full-stack framework that charts a practical pathway to a quantum advantage for large-scale NSE simulation. Our approach integrates a spectral-based input/output algorithm, an explicit and synthesized quantum circuit, and a refined error-correction protocol. The algorithm achieves an end-to-end exponential speedup in asymptotic complexity, meeting the lower bound for general quantum linear system solvers. Through symmetry-based circuit synthesis and optimized error correction, we reduce the required logical and physical resources by two orders of magnitude. Our concrete resource analysis demonstrates that solving NSE on a $2^{80}$-grid is feasible with 8.71 million physical qubits (at an error rate of $5 \times 10^{-4}$) in 42.6 days -- outperforming a state-of-the-art supercomputer, which would require over a century. This work bridges the gap between theoretical quantum speedup and the practical deployment of high-performance scientific computing.

The lack of a unified theoretical framework for characterizing band inversions across different crystal symmetries hinders the rapid development of topological photonic band engineering. To address this issue, we have constructed a framework constrained by symmetry $k \cdot p$ that universally models bands near high-symmetry points for symmetric photonic crystals $C_6$, $C_4$, $C_3$, and $C_2$. This framework enables a coefficient-free quantitative diagnosis of band topology. We have demonstrated the power of this framework by systematically engineering band inversions. In $C_6$ crystals, we induce a reopening of the linear gap at $\Gamma$. In $C_4$ systems, mirror symmetry enforces a characteristic quadratic coupling leading to distinct spectral features. Our analysis further reveals that a lone $E$ doublet prevents inversion at the $\Gamma$ point in $C_3$ symmetry, while $C_2$ symmetry facilitates a unique inversion of $Y$ pointsints with anisotropic gap. This symmetry-first, fit-free approach establishes a direct link between experimental band maps and the extraction of fundamental topological parameters. It offers a universal tool for inversion and coupling-order identification.

We introduce LUCIE-3D, a lightweight three-dimensional climate emulator designed to capture the vertical structure of the atmosphere, respond to climate change forcings, and maintain computational efficiency with long-term stability. Building on the original LUCIE-2D framework, LUCIE-3D employs a Spherical Fourier Neural Operator (SFNO) backbone and is trained on 30 years of ERA5 reanalysis data spanning eight vertical {\sigma}-levels. The model incorporates atmospheric CO2 as a forcing variable and optionally integrates prescribed sea surface temperature (SST) to simulate coupled ocean--atmosphere dynamics. Results demonstrate that LUCIE-3D successfully reproduces climatological means, variability, and long-term climate change signals, including surface warming and stratospheric cooling under increasing CO2 concentrations. The model further captures key dynamical processes such as equatorial Kelvin waves, the Madden--Julian Oscillation, and annular modes, while showing credible behavior in the statistics of extreme events. Despite requiring longer training than its 2D predecessor, LUCIE-3D remains efficient, training in under five hours on four GPUs. Its combination of stability, physical consistency, and accessibility makes it a valuable tool for rapid experimentation, ablation studies, and the exploration of coupled climate dynamics, with potential applications extending to paleoclimate research and future Earth system emulation.

We present a benchmark designed to evaluate the predictive capabilities of universal machine learning interatomic potentials across systems of varying dimensionality. Specifically, our benchmark tests zero- (molecules, atomic clusters, etc.), one- (nanowires, nanoribbons, nanotubes, etc.), two- (atomic layers and slabs) and three-dimensional (bulk materials) compounds. The benchmark reveals that while all tested models demonstrate excellent performance for three-dimensional systems, accuracy degrades progressively for lower-dimensional structures. The best performing models for geometry optimization are orbital version 2, equiformerV2, and the equivariant Smooth Energy Network, with the equivariant Smooth Energy Network also providing the most accurate energies. Our results indicate that the best models yield, on average, errors in the atomic positions in the range of 0.01-0.02 angstrom and errors in the energy below 10~meV/atom across all dimensionalities. These results demonstrate that state-of-the-art universal machine learning interatomic potentials have reached sufficient accuracy to serve as direct replacements for density functional theory calculations, at a small fraction of the computational cost, in simulations spanning the full range from isolated atoms to bulk solids. More significantly, the best performing models already enable efficient simulations of complex systems containing subsystems of mixed dimensionality, opening new possibilities for modeling realistic materials and interfaces.

Machine learning interatomic potentials (MLIPs) enable efficient molecular dynamics (MD) simulations with ab initio accuracy and have been applied across various domains in physical science. However, their performance often relies on large-scale labeled training data. While existing pretraining strategies can improve model performance, they often suffer from a mismatch between the objectives of pretraining and downstream tasks or rely on extensive labeled datasets and increasingly complex architectures to achieve broad generalization. To address these challenges, we propose Iterative Pretraining for Interatomic Potentials (IPIP), a framework designed to iteratively improve the predictive performance of MLIP models. IPIP incorporates a forgetting mechanism to prevent iterative training from converging to suboptimal local minima. Unlike general-purpose foundation models, which frequently underperform on specialized tasks due to a trade-off between generality and system-specific accuracy, IPIP achieves higher accuracy and efficiency using lightweight architectures. Compared to general-purpose force fields, this approach achieves over 80% reduction in prediction error and up to 4x speedup in the challenging Mo-S-O system, enabling fast and accurate simulations.

Since Lorenz's seminal work on a simplified weather model, the numerical analysis of nonlinear dynamical systems has become one of the main subjects of research in physics. Despite of that, there remains a need for accessible, efficient, and easy-to-use computational tools to study such systems. In this paper, we introduce pynamicalsys, a simple yet powerful open-source Python module for the analysis of nonlinear dynamical systems. In particular, pynamicalsys implements tools for trajectory simulation, bifurcation diagrams, Lyapunov exponents and several others chaotic indicators, period orbit detection and their manifolds, as well as escape and basins analysis. It also includes many built-in models and the use of custom models is straighforward. We demonstrate the capabilities of pynamicalsys through a series of examples that reproduces well-known results in the literature while developing the mathematical analysis at the same time. We also provide the Jupyter notebook containing all the code used in this paper, including performance benchmarks. pynamicalsys is freely available via the Python Package Index (PyPI) and is indented to support both research and teaching in nonlinear dynamics.

We introduce scalable machine learning models to accurately predict two key quantum transport properties, the transmission coefficient T(E) and the local density of states (LDOS) in two-dimensional (2D) hexagonal materials with magnetic disorder. Using a tight binding Hamiltonian combined with the Non-Equilibrium Green's Function (NEGF) formalism, we generate a large dataset of over 400,000 unique configurations across graphene, germanene, silicene, and stanene nanoribbons with varying geometries, impurity concentrations, and energy levels. A central contribution of this work is the development of a geometrydriven, physically interpretable feature space that enables the models to generalize across material types and device sizes. Random Forest regression and classification models are evaluated in terms of accuracy, stability, and extrapolation ability. Regression consistently outperforms classification in capturing continuous transport behavior on in-domain data. However, extrapolation performance degrades significantly, revealing the limitations of tree-based models in unseen regimes. This study highlights both the potential and constraints of scalable ML models for quantum transport prediction and motivates future research into physics-informed or graph-based learning architectures for improved generalization in spintronic and nanoelectronic device design.

The one-dimensional Fr\"ohlich model describing the motion of a single electron interacting with optical phonons is a paradigmatic model of quantum many-body physics. We predict the existence of an arbitrarily large number of bound excited states in the strong coupling limit and calculate their excitation energies. Numerical simulations of a discretized model demonstrate the complete amelioration of the projector Monte Carlo sign problem by walker annihilation in an infinite Hilbert space. They reveal the threshold for the occurrence of the first bound excited states at a value of $\alpha \approx 1.73$ for the dimensionless coupling constant. This puts the threshold into the regime of intermediate interaction strength. We calculate the spectral weight and the number density of the dressing cloud in the discretized model.

We observe a novel 'multiple-descent' phenomenon during the training process of LSTM, in which the test loss goes through long cycles of up and down trend multiple times after the model is overtrained. By carrying out asymptotic stability analysis of the models, we found that the cycles in test loss are closely associated with the phase transition process between order and chaos, and the local optimal epochs are consistently at the critical transition point between the two phases. More importantly, the global optimal epoch occurs at the first transition from order to chaos, where the 'width' of the 'edge of chaos' is the widest, allowing the best exploration of better weight configurations for learning.

Density functional theory (DFT) is a fundamental method for simulating quantum chemical properties, but it remains expensive due to the iterative self-consistent field (SCF) process required to solve the Kohn-Sham equations. Recently, deep learning methods are gaining attention as a way to bypass this step by directly predicting the Hamiltonian. However, they rely on deterministic regression and do not consider the highly structured nature of Hamiltonians. In this work, we propose QHFlow, a high-order equivariant flow matching framework that generates Hamiltonian matrices conditioned on molecular geometry. Flow matching models continuous-time trajectories between simple priors and complex targets, learning the structured distributions over Hamiltonians instead of direct regression. To further incorporate symmetry, we use a neural architecture that predicts SE(3)-equivariant vector fields, improving accuracy and generalization across diverse geometries. To further enhance physical fidelity, we additionally introduce a fine-tuning scheme to align predicted orbital energies with the target. QHFlow achieves state-of-the-art performance, reducing Hamiltonian error by 71% on MD17 and 53% on QH9. Moreover, we further show that QHFlow accelerates the DFT process without trading off the solution quality when initializing SCF iterations with the predicted Hamiltonian, significantly reducing the number of iterations and runtime.