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arXiv2026

Convergence and efficiency proof of quantum imaginary time evolution for bounded order systems

Many current and near-future applications of quantum computing utilise parametric families of quantum circuits and variational methods that can suffer from obstacles including non-convergence to the global minimum due to local minima, critical slowing down, or exponential resource scaling. Here we show that quantum imaginary time evolution can overcome these obstacles if the underlying physical system satisfies a set of conditions. This includes many relevant applications such as ground state preparation for local theories in physics or chemistry, combinatorial optimisation problems, or quantum machine learning. In particular, we analyse the quantum imaginary time evolution showing convergence guarantees to the global minimum without critical slowing down and providing a priori estimates on the required evolution time which scale linearly in system size and inverse energy gap. Furthermore, a provided complexity analysis shows that quantum imaginary time evolution can be efficiently compiled into a parametric quantum circuit, finding the optimal parameters included, for a large class of physically relevant problems.

quant-ph↗

arXiv2026

Constrained dynamics for searching saddle points on embedded Riemannian submanifolds of Euclidean space

Finding constrained saddle points on embedded Riemannian submanifolds of Euclidean space is significant for analyzing energy landscapes arising in physics and chemistry. Existing works exploit explicit global/local regular level-set representations of manifolds, which may be unavailable or computationally inconvenient for manifolds represented through, e.g., projectors, factorizations, or rank constraints. In this paper, we develop a constrained saddle dynamic based on embedded-submanifold geometric primitives, completely avoiding the use of explicit representations. In particular, our dynamic is formulated compactly on the Grassmann bundle of the tangent bundle. By analyzing the Grassmann bundle geometry, we rigorously establish the local linear stability of the dynamic and the local linear convergence of the resulting algorithms. Remarkably, our analysis provides the first iterate convergence result for discretized algorithms to saddle points of prescribed indices in embedded-submanifold settings. Moreover, by virtue of the Grassmann bundle formulation, we remove unnecessary nondegeneracy assumptions on the eigenvalues of the Riemannian Hessian that are present in existing works. We also point out that locating saddle points can be more ill-conditioned than finding local minimizers, and requires using nonredundant parametrizations. Finally, numerical experiments on linear eigenvalue problems and electronic excited-state calculations showcase the effectiveness of the proposed algorithms and corroborate the established local theory.

math.NA↗

arXiv2026

Polarizable atomic multipoles for learning long-range electrostatics

Long-range electrostatics and polarization remain central obstacles to extending machine learning interatomic potentials (MLIPs) to ionic, polar, and interfacial systems. Here we introduce a semi-local framework for learning electrostatics from energies and forces using polarizable atomic multipoles. Local equivariant descriptors predict environment-dependent latent monopoles, dipoles, and quadrupoles, while residual non-local charge transfer and polarization are captured by non-self-consistent linear response in induced charges and dipoles. Across four diverse benchmarks and four short-range MLIP architectures, the multipole hierarchy and response terms systematically improve potential energy surface accuracy, with the largest gains in systems where long-range effects are essential. More importantly, physically meaningful electrical responses emerge without direct supervision. The learned latent multipoles yield accurate Born effective charge tensors and infrared spectra in close agreement with experiments. The induced-dipole extension introduces new capabilities: it predicts polarizabilities and thereby enables semi-quantitative Raman spectra for bulk water and hybrid MAPbI$_3$ perovskite, as well as the essential features of the surface-specific vibrational sum-frequency generation spectrum at the water-air interface. In ferroelectric HfO$_2$, the predicted electrical response also captures LO-TO splitting and polarization switching. This systematically improvable, physically transparent framework enables MLIPs trained on standard energy and force labels to predict polarization-sensitive observables.

cond-mat.mtrl-sci↗

arXiv2026

Diffusion-Based Inverse Design of Dielectric Resonator Metasurfaces for Shaping Smart Electromagnetic Environments

Future wireless systems are expected to transform the surrounding space from a passive propagation medium into a smart electromagnetic environment, where engineered surfaces control wave propagation, support wireless sensing, and create programmable electromagnetic fingerprints. A key challenge in realizing this vision is the inverse design of metasurfaces for tailored electromagnetic propagation. While forward analysis evaluates the response of a known geometry, the inverse task starts from a prescribed scattering signature and seeks a physically realizable structure that produces it. This inverse task is inherently nonlinear and often high-dimensional, while candidate solutions may be non-unique and provide no direct indication of practical realizability. Here, we introduce a conditional diffusion framework for inverse design of dielectric resonator metasurfaces from target angular scattering patterns. Trained on T-matrix simulated geometry-response pairs, the model learns a conditional distribution of geometries instead of a deterministic mapping, enabling multiple candidate designs for the ill-posed inverse problem. The best generated metasurface achieves a mean percentage error of 1.39%, outperforming CMA-ES optimization (4.1% after 10 h) while requiring only about one minute for after-training inference. The model also produces lower error distributions than deterministic neural baselines for out-of-distribution spectra, highlighting the potential of diffusion models for efficient metasurface design.

cs.LG↗

arXiv2026

Generative Diffusion Surrogates with Analytical Variance Schedule

Stochastic transport describes physical systems in which an initially structured distribution spreads under unresolved forcing, scattering, or heterogeneous media. Useful surrogates for such systems should be probabilistic, time-resolved, and able to represent non-Gaussian distributional structure. Generative diffusion models, which corrupt data with Gaussian noise and learn a reverse flow back to structured states, have these properties. Their noise schedules, however, are usually chosen heuristically: image and audio generation---the canonical use cases---provide no physical clock. In transport, by contrast, the variance, or mean-square displacement, is often known from macroscopic theory or empirical scaling even when the full distribution is not. Here we prescribe the forward noising rate as the time derivative of this variance, turning generative time into a calibrated transport clock. The variance path is enforced by construction, while the learned score field represents how non-Gaussian structure inherited from entrance data is smoothed along that path, requiring no intermediate-time physical transport data. For ballistic-to-diffusive transport in turbulent plasmas, the surrogate matches test-particle distributions, reproduces the laboratory-measured variance scale, and tracks the simulated kurtosis evolution without schedule tuning, enabling calibrated emulation and likelihood-based inference.

cs.LG↗

arXiv2026

Learning a general class of admissible multi-species collision operators from molecular dynamics

We develop a structure-preserving, data-driven collision operator for spatially homogeneous multi-species kinetic systems from molecular dynamics (MD). The operator consists of diagonal self-collision blocks and ordered off-diagonal cross-species blocks to describe intra- and inter-species momentum and energy exchange. Within a local and point-wise identifiable kernel class, we develop the necessary and sufficient condition for the admissible kernel class satisfying the conservation laws, the H-theorem, and the frame indifference. Unlike the classical Landau operator, the off-diagonal kernels are not restricted to be symmetric under permutation of the two velocity variables. This unique structural freedom captures the distinct responses of different species to unresolved correlations and many-body effects arising from micro-scale particle interactions. The equivalent parameterizable kernel formalization enables us to learn a generalized data-driven collision operator directly from MD, where the low-rank tensor representations and random sampling are used to achieve efficient kernel training and numerical simulation. Numerical experiments show that the learned operator accurately predicts transport coefficients and the non-equilibrium relaxation, while retaining discrete conservation and entropy production. In particular, it captures plasma kinetics in the moderately coupled regime, where the predictions of both the Landau and the data-driven model restricted to velocity-permutation symmetry show significant discrepancies.

physics.comp-ph↗

arXiv2026

Stochastic Optimization of Tree Tensor Networks

Tensor networks, originally developed for quantum many-body physics, are promising models for machine learning. We derive stochastic Riemannian optimizers for tree tensor networks (TTNs) on both their parameter and quotient manifolds, including adaptive and learning-rate-free schemes suitable for minibatch training. Using a hybrid CNN-TTN architecture, we evaluate the methods on Fashion-MNIST, CIFAR10, and Imagenette. The proposed optimizers achieve predictive performance comparable to unconstrained optimization while enabling numerically stable downstream compression.

math.OC↗

arXiv2026

Comparing Classical and Quantum Machine Learning for Regression in High Energy Physics Collision Data

The classification and regression of particle collision events constitute a persistent computational challenge in experimental high energy physics, where large volumes of simulated data must be processed with both speed and precision. This work carries out a systematic comparison of four classical machine learning architectures, support vector machines (SVM), artificial neural networks (ANN), convolutional neural networks (CNN), and long short-term memory (LSTM) networks against their quantum counterparts: quantum SVM (QSVM), quantum neural networks (QNN), quantum CNN (QCNN), and quantum LSTM (QLSTM). All models are trained on simulated proton-proton collision events with electron-positron and muon-antimuon final states from the CERN Open Data portal, using transverse-momentum components as input features and transverse-momentum magnitude as the regression target. Classical architectures, and in particular the CNN and LSTM, achieve marginally better quantitative performance under current hardware and dataset constraints. Quantum models, however, reach competitive accuracy with substantially fewer trainable parameters: the QCNN reproduces the performance of the deep classical CNN using only four qubits and a circuit of depth three, pointing to a genuine parameter-efficiency advantage on near-term quantum devices. A baseline analysis confirms that the regression problem is non-trivial for shallow polynomial fits, supporting the relevance of the architectural comparison. These results characterize the trade-offs between classical and quantum approaches under realistic, resource-constrained conditions and provide a benchmark for future studies on actual quantum hardware.

cs.LG↗

arXiv2026

Assessment of Numerical Lift Coefficient Data for a Circular Cylinder with Application to Bladeless Turbines

We assess computed lift coefficient data for flow past a circular cylinder to evaluate their suitability for practical applications. Specifically, we consider lift coefficient data for a circular cylinder over Reynolds numbers from 120 to 8000. The results are obtained from two-dimensional finite element simulations of the incompressible Navier-Stokes equations using pressure robust discretizations. We compare the computed lift coefficients with published experimental and numerical results, finding good agreement in some cases but significant disagreement in others. Because lift fluctuations are central to vortex-induced vibration concepts, these data therefore provide input for the analysis and preliminary design of bladeless turbines.

physics.flu-dyn↗

arXiv2026

Towards Large-Scale Heterogeneous Data Organization for Scientific Foundation Models: A Nuclear Fusion Case Study

Training effective foundation models requires massive and organized datasets, yet scientific domains such as nuclear fusion present unique challenges due to largely heterogeneous and sparse data. Here we characterize the data used in developing such a model: with over 20 sensor types spanning 5 orders of magnitude in sampling rate, mixed tensor structures (point measurements, spectrograms, images), and nonstationary physics. We analyze our input complexity and discuss trade-offs between temporal context and frequency resolution. Our analysis provides a template for representing multi-modal fluctuation data at scale, with implications for both multi-modal control systems and nuclear fusion.

physics.plasm-ph↗

arXiv2026

Separating perception from reasoning in vision-language models: a model-free render ceiling for crystal structures

Multimodal evaluations cannot say whether a vision-language model misread an image or misreasoned about it, because every existing method for separating the two places a second model in the loop. We introduce the render ceiling, a model-free reference for benchmarks built by rendering known objects: inverting the frozen cameras and re-solving cross-view correspondence recovers exactly the answer the images support. We prove the ceiling fails only through an enumerable set of projection coincidences and certify that set empty on 2,160 rendered crystal structures, so every point of a model's deficit belongs to the model. Across fourteen vision-language models, supplying exact geometry as text lifts every model yet closes under half the gap for thirteen, while a supervised vision model with no language component reads the same images at 0.8952, above every vision-language model. The instrument exposes extraction-stage fabrication that downstream accuracy would misattribute to reasoning, yields camera-placement rules for benchmark builders, and transfers to any benchmark with an invertible forward rendering.

cs.CV↗

arXiv2026

Denoising the Deep Sky: Physics-Based CCD Noise Formation for Astronomical Imaging

Astronomical imaging remains noise-limited under practical observing conditions. Standard calibration pipelines remove structured artifacts but largely leave stochastic noise unresolved. Although learning-based denoising has shown strong potential, progress is constrained by scarce paired training data and the requirement for physically interpretable models in scientific workflows. We propose a physics-based noise synthesis framework tailored to CCD noise formation in the telescope. The pipeline models photon shot noise, photo-response non-uniformity, dark-current noise, readout effects, and localized outliers arising from cosmic-ray hits and hot pixels. To obtain low-noise inputs for synthesis, we stack multiple unregistered exposures to produce high-SNR bases. Realistic noisy counterparts synthesized from these bases using our noise model enable the construction of abundant paired datasets for supervised learning. Extensive experiments on our real-world multi-band dataset curated from two ground-based telescopes demonstrate the effectiveness of our framework in both photometric and scientific accuracy.

astro-ph.IM↗

arXiv2026

Beyond sensitivity: mechanism-resolved error budgets for designing quantum sensors

Quantum sensors are specified by a headline sensitivity, yet applications also demand accuracy and reliability. The dominant limiter of one metric is often known, but no method resolves how interacting mechanisms combine into a signed, per-mechanism budget for each metric. We introduce a framework that computes a sensor's sensitivity, accuracy, and robustness from one open-system simulation and attributes each to its limiting mechanism. For a nitrogen-vacancy diamond ensemble the attribution inverts across metrics: dephasing limits sensitivity, the thermal ground-state shift limits accuracy, and optical leakage limits robustness. At identical sensitivity the recovered-field bias spans $8$ to $1500$\,nT, so tuning to sensitivity alone can miss the accuracy target by two orders of magnitude. The same modeling transfers to a cesium optically pumped magnetometer recording a human magnetocardiogram. As a digital twin, it predicts the gain from addressing each limiter, so sensors can be designed to the required metrics.

quant-ph↗

arXiv2026

Families of relative periodic orbits in the planar three-body problem via consecutive alignments

Relative periodic orbits (RPOs) are solutions of the three-body problem that are periodic in a uniformly rotating reference frame and, in general, quasi-periodic in inertial coordinates. We present a numerical procedure for computing and continuing one-parameter families of RPOs of the planar Newtonian three-body problem. The method exploits consecutive syzygies, understood here as configurations in which the three bodies are aligned and their velocities satisfy the corresponding symmetry conditions. Matching the positions and momenta at two consecutive alignments reduces the computation of RPOs to a low-dimensional nonlinear problem. Its solutions are then numerically continued, and linear stability is determined from the nontrivial eigenvalues of the rotated monodromy matrix after removing the neutral directions associated with conserved quantities and continuous symmetries. The procedure is applied to several mass distributions and initial configurations, producing families of Poincaré, Hill, and binary-type solutions. These families exhibit transitions from nearly circular to highly eccentric motion, changes of stability near resonances and turning points, and absolute periodic solutions when the rotation angle is a rational multiple of 2π. In the Hill families, the continuation connects satellite configurations with circumstellar motion as the smallest body loses its gravitational binding to the intermediate body. Circumbinary and circumstellar configurations are also obtained in the binary regime. The results illustrate the dynamical diversity of RPOs and provide coherent three-body motions that can be used as prescribed trajectories in restricted four-body models.

math.DS↗

arXiv2026

Structure-Preserving Physics-Informed Neural Network for the Korteweg--de Vries (KdV) Equation

Physics-Informed Neural Networks (PINNs) offer a flexible framework for solving nonlinear partial differential equations (PDEs), yet conventional implementations often fail to preserve key physical invariants during long-term integration. This paper introduces a \emph{structure-preserving PINN} framework for the nonlinear Korteweg--de Vries (KdV) equation, a prototypical model for nonlinear and dispersive wave propagation. The proposed method embeds the conservation of mass and Hamiltonian energy directly into the loss function, ensuring physically consistent and energy-stable evolution throughout training and prediction. Unlike standard \texttt{tanh}-based PINNs~\cite{raissi2019pinn,wang2022modifiedpinn}, our approach employs sinusoidal activation functions that enhance spectral expressiveness and accurately capture the oscillatory and dispersive nature of KdV solitons. Through representative case studies -- including single-soliton propagation (shape-preserving translation), two-soliton interaction (elastic collision with phase shift), and cosine-pulse initialization (nonlinear dispersive breakup) -- the model successfully reproduces hallmark behaviors of KdV dynamics while maintaining conserved invariants. Ablation studies demonstrate that combining invariant-constrained optimization with sinusoidal feature mappings accelerates convergence, improves long-term stability, and mitigates drift without multi-stage pretraining. These results highlight that computationally efficient, invariant-aware regularization coupled with sinusoidal representations yields robust, energy-consistent PINNs for Hamiltonian partial differential equations such as the KdV equation.

cs.LG↗

arXiv2019

Small worlds and clustering in spatial networks

Networks with underlying metric spaces attract increasing research attention in network science, statistical physics, applied mathematics, computer science, sociology, and other fields. This attention is further amplified by the current surge of activity in graph embedding. In the vast realm of spatial network models, only a few reproduce even the most basic properties of real-world networks. Here, we focus on three such properties--sparsity, small worldness, and clustering--and identify the general subclass of spatial homogeneous and heterogeneous network models that are sparse small worlds and that have nonzero clustering in the thermodynamic limit. We rely on the maximum entropy approach where network links correspond to noninteracting fermions whose energy dependence on spatial distances determines network small worldness and clustering.

physics.soc-ph↗

arXiv2026

Entropy-Stable and Physical-Constraint-Preserving DGSEM for Symmetry-Reduced General-Relativistic Hydrodynamics on Stationary Spacetimes

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.

math.NA↗

arXiv2026

Physics-informed Learning for Orbital Uncertainty Propagation with Error Bounds

The Fokker-Planck partial differential equation (FP-PDE) governs uncertainty evolution in stochastic dynamical systems. In orbital dynamics, solving the FP-PDE is challenging because of nonlinear motion, high-dimensional states, and large space-time domains. We develop a physics-informed neural network (PINN) approach that approximates the FP-PDE solution as a single space-time probability density, while also quantifying its worst-case approximation error. This approach is, in principle, independent of the choice of state coordinates and neural network architecture. Specifically, to enforce probability density function (PDF) properties into the neural network, we design a Physics-informed Gaussian mixture model (PINN-GMM). Then a companion error PINN learns the dynamics of the approximation error and yields time-dependent bounds that define an ambiguity set of PDFs. This ambiguity set enables rigorous computation of upper and lower bounds on event probabilities through tractable linear programs. Numerical studies on illustrative 1D examples and several 4D--6D orbital test cases demonstrate accurate uncertainty propagation, correct and informative error bounds, and improved reliability over common uncertainty-propagation baseline methods (Gaussian approximation, unscented transform, and Gaussian mixture model). Constructing the PINN-GMM requires offline training, making it costlier than the baseline approximations; once trained, however, a single forward pass returns the density at any time in sub-millisecond time $(0.16~\mathrm{ms}$ in our implementation).

physics.comp-ph↗