Instantons play a crucial role in understanding non-perturbative dynamics in quantum field theories, including those with spontaneously broken gauge symmetries. In the broken phase, finite-size instanton-like configurations are no longer exact stationary points of the Euclidean action, in contrast to the symmetric phase. Non-perturbative effects in this setting are therefore typically studied within the constrained instanton framework. However, a previous study pointed out a possible difficulty in constructing consistent constrained instanton solutions based on conventional gauge-invariant constraints. In this work, we revisit the asymptotic structure of constrained instantons and re-examine the claimed difficulty. By carefully tracking the behavior of the solutions near the spatial origin and at infinity, we show that the required boundary conditions can be satisfied without encountering the inconsistency. We explicitly construct consistent constrained instantons in both massive $ϕ^4$ theory and Yang--Mills theory with spontaneous symmetry breaking, and we support our analytic matching procedure with numerical solutions. Our results establish that conventional gauge-invariant constraints can be consistently employed in semiclassical computations when asymptotic expansions are treated properly.

We prove a bilinear Kakeya inequality in the first Heisenberg group and a sharp bilinear Kakeya estimate for Euclidean curved tubes in $\R^2$. By adapting an argument of Fässler, Pinamonti and Wald involving Heisenberg projections, we show that the latter implies the former. We prove the estimate for curved tubes using a combination of techniques developed by Pramanik, Yang and Zahl, Wolff and Schlag. We introduce a novel broadness hypothesis inspired by works of Zahl, which rules out bush-type configurations that break transversal structure. We argue that such a hypothesis is needed for proving the bilinear estimates we present. We also introduce necessary additional linear terms to the estimate to counteract Szemerédi--Trotter-type clustering phenomena.

Given a root system $R$, two roots are said to be \emph{strongly orthogonal} if neither their sum nor difference is a root. Gashi defined a family of graphs with vertices labelled by sums of $k$-element strongly orthogonal subsets of roots, and edges connect vertices whose difference is also a vertex. Gashi and the current authors established Erdős--Ko--Rado type results for graphs developed from Type $A$ root systems. In this paper, we study graphs developed from the exceptional root systems $G_2$, $F_4$, $E_6$, $E_7$, and $E_8$. We compute graph-theoretic invariants including regularity, connectivity, and clique numbers, and analyze clique structures with respect to sunflower properties. The automorphism group contains the Weyl group; we use these symmetries to obtain complete counts of maximum cliques and maximum sunflowers. Unlike type $A$, where all maximal cliques are sunflowers for large rank, sunflower cliques comprise at most 11\% of maximum cliques in the simply-laced exceptional types $E_6$, $E_7$, and $E_8$.

Fluid stretching in porous media governs the mixing of reactants, contaminants, and nutrients, yet how the solid microstructure controls the stretching statistics remains poorly understood. We investigate how porous-medium heterogeneity controls stretching using (i) particle-tracking velocimetry experiments in 3D-printed millifluidic cells, (ii) numerical simulations of solute-plume deformation in the measured flow fields, and (iii) analytical calculations of fluid stretching. The cells contain arrays of cylindrical rods with systematically-varying disorder levels, from ordered to random. Velocity and shear-rate measurements reveal that fluid deformation is strongly localized near solid boundaries for all disorder levels, suggesting that near-wall flow is the main driver of stretching. The mean stretching grows linearly in time for ordered media and quadratically for disordered media, while the stretching distributions are approximately log-normal. We analytically describe the stretching produced by flow around an isolated cylinder and embed this description in a random-walk model that reproduces the observed stretching statistics in random media. These results provide the first quantitative connection between porous-medium structure and fluid-stretching statistics, revealing the extent to which disordered media accelerate mixing relative to ordered media and enabling progress beyond the common mean-field description of stretching in two-dimensional media as a simple shear flow.

Visualizing large 3D scientific datasets requires balancing performance and fidelity, but traditional tools often demand excessive technical expertise. We introduce UnrealVis, an Unreal Engine optimization laboratory for configuring and evaluating rendering techniques during interactive exploration. Following a review of 55 papers, we established a taxonomy of 22 optimization techniques across six families, implementing them through engine subsystems such as Nanite, Level of Detail(LOD) schemes, and culling. The system features an intuitive workflow with live telemetry and A/B comparisons for local and global performance analysis. Validated through case studies of ribosomal structures and volumetric flow fields, along with an expert evaluation, UnrealVis facilitates the selection of optimization combinations that meet performance goals while preserving structural fidelity. UnrealVis is available at https://github.com/XAIber-lab/UnrealVis

This article constructs two families of nodal solutions to the Yamabe equation, each concentrating along two planar circles. One family is conformally equivalent to the one previously obtained by Medina--Musso. The second family is a twisted variant of the first; it is new and is derived from ansatzes that are not Kelvin invariant, in contrast to a standard assumption in earlier works. In addition, in dimension 3, these solutions attain maximal rank. By means of a continuous family of conformal transformations, we then analyze the interaction of the two circles, which display a crossing phenomenon reminiscent, in some sense, of leap-frogging behavior in vortex dynamics.

In this study, we have explored an application of deep learning architecture of the U-Net model, originally designed for biomedical image segmentation, in a regression analysis aimed at predicting fluid flows through textured microchannels. The data for this analysis is generated using the lattice Boltzmann method through extensive simulations, capturing the intricate behaviors of fluid dynamics in a microscale environment. The raw simulation data was meticulously preprocessed to prepare it for training the U-Net model, ensuring that the input features and labels were appropriately formatted and normalized to optimize the learning process of the model. The U-Net model, with its inherent capability of capturing spatial hierarchies and producing better predictions, proved effective in this novel application. We have evaluated the performance of the model using metrics including MSE, RMSE, MAE, and $R^2$ scores. These metrics were crucial in assessing the accuracy and reliability of the model predictions. The results demonstrate that the U-Net model can predict fluid flows with high accuracy and less error, indicating its potential for broader applications in fluid dynamics and other fields requiring precise regression modeling. A parametric analysis of the U-Net with attention mechanism showed that the velocity field prediction is contingent upon the solid-fluid interaction parameter and surface wettability. The U-Net equipped with an attention mechanism predicts the velocity magnitude and components for textured microchannels with an average error of 5.18%, which upon optimization may subsequently lower to 2.1%. The U-Net model including an attention mechanism (U-Net AM) regularly surpasses the conventional U-Net model in all measures, evidencing enhanced accuracy and generalization.

We show that the geometric classification of smooth projective curves admitting infinitely many points of degree $d\leq 5$ extends from number fields to function fields of characteristic 0. Over number fields, this classification was established by Faltings for $d=1$, Harris--Silverman for $d=2$, Abramovich--Harris for $d=3,4$ and Kadets--Vogt for $d=4,5$. Our approach uses a specialization argument to reduce the problem over function fields to the number field case.

We compute the automorphism group of the dual complex $\mathsf{T}_{d, n}$ of the boundary divisor in the Kontsevich moduli space $\overline{\mathcal{M}}_{0, n}(\mathbb{P}^r, d)$. When $d \geq 2$, we find that $\mathrm{Aut}(\mathsf{T}_{d, n}) \cong \mathbb{S}_{n}$, while $\mathrm{Aut}(\mathsf{T}_{1, n}) \cong \mathbb{S}_{n + 1}$ for all $n \geq 4$. The complex $\mathsf{T}_{1, n}$ is also the dual complex of the boundary divisor in the Fulton--MacPherson compactification of the configuration space of $n$ points on $X$, if $X$ is any smooth, proper, and connected algebraic variety over $\mathbb{C}$. Following work of Massarenti, this implies that $\mathsf{T}_{1, n}$ admits automorphisms which in general do not extend to $X[n]$.

This paper studies exact semidefinite programming relaxations (SDPRs) for separable quadratically constrained quadratic programs (QCQPs). We consider the construction of a larger separable QCQP from multiple QCQPs with exact SDPRs. We show that exactness is preserved when such QCQPs are combined through a separable horizontal connection, where the coupling is induced through the right-hand-side parameters of the constraints. The proposed framework provides a simple sufficient condition for exactness of the resulting SDPR. We then identify notable classes of QCQPs for which this condition holds, including convex QCQPs, QCQPs defined by sign-pattern and graph-structural conditions, and separable homogeneous QCQPs with a limited number of constraints. Two examples illustrate the constructive nature of the proposed framework, showing how heterogeneous QCQPs can be combined to yield new instances with exact SDP relaxations.

We initiate a probabilistic study of forward stability for products of Schubert polynomials through the record statistic (left-to-right maxima) of permutations. Building on the explicit record formula for forward stability obtained by Hardt and Wallach, we study random pairs of permutations drawn from three natural families: uniform permutations, Grassmannian permutations, and Boolean permutations. For each family, we determine record probabilities and use them to analyze the asymptotic behavior of forward stability. For uniform and Grassmannian permutations, we obtain asymptotics for the mean together with limiting distribution results. For Boolean permutations, we prove linear-order growth of the mean, and our analysis also produces an explicit time-inhomogeneous Markov chain that yields an exact linear-time uniform sampler. Beyond these cases, we prove that the record-set statistic is equidistributed on the avoidance classes of $132$ and $231$, and consequently the corresponding forward stability distributions coincide. We conclude with conjectures for numerous further permutation classes and a conjectural recursive criterion for when two avoidance classes have the same record-set distribution.

Geometric quantum computation offers a potential route to fault-tolerant quantum information processing by exploiting the global nature of geometric phases. However, achieving controlled high-order suppression of multiple error sources remains a long-standing limitation, particularly in realistic large-scale circuits with complex noise environments. This limitation is largely due to the absence of a general framework that directly characterizes error accumulation and enables systematic improvement. Here we establish such a framework for universal doubly geometric gates by embedding target operations into a hierarchy of level-n identity constructions. This approach enables direct quantification of error accumulation while removing structural constraints inherent in previous schemes. We analytically show that the defining conditions lead to simultaneous fourth-order suppression of control errors, with a systematic extension to sixth-order suppression via higher-level constructions. Our results establish doubly geometric control as a general and scalable route toward high-order robust quantum gates, with potential implications for fault-tolerant quantum information processing.

Electron vortices are the quintessential signature of a viscous electron fluid. For decades, their detection relied on indirect transport measurements with persistently debated interpretations. Recently, scanning magnetometry enabled direct visualization, yet these techniques demand considerable sophistication. Here we introduce a conceptually different and inherently simpler paradigm based on nanomechanics. By integrating a circular cavity into a suspended resonator, we create a vortex whose circulating current generates a magnetic moment. In an in-plane magnetic field, this moment experiences a torque, driving vibrations that directly reveal the vortex's presence and nature. We detect ballistic and hydrodynamic vortices and trace their temperature-driven crossover. Our work establishes nanomechanics as a platform for electron hydrodynamics, showing that viscosity - subtle in transport - is one of the dominant factors shaping nanoelectromechanical response.

We obtain (conditional and unconditional) results on large values of $L$-functions $L(s,χ)$ in the critical strip $1/2 \leq \Re s \leq 1$ when the character $χ$ runs through a thin subgroup of all characters modulo an integer $q$. Some of these bounds are based on new zero-density estimates on average over a subgroup of characters. These bounds follow from a mean value estimate for character sums, which is based on the work of D. R. Heath-Brown (1979). As yet another application of this mean value estimate, we obtain an unconditional version of a conditional (on the Generalised Riemann Hypothesis) result of Z. Rudnick and A. Zaharescu (2000) about gaps between primitive roots.

Two-dimensional noncollinear magnetic states, such as spin-spiral magnets, offer an excellent platform for investigating fundamental phenomena, with potential for advancing stray-field-free spintronics. However, detection and characterization of noncollinear magnetic states in two-dimensional systems remain challenging, motivating the development of alternative probing methods. Here, we present a methodology for extracting the spin-spiral $\mathbf{q}$ vector from lateral electronic transport measurements. Our approach leverages the magnetic field and bias dependence of the conductance to train a supervised machine learning algorithm, which enables us to extract the $\mathbf{q}$ vectors of arbitrary spin-spiral magnets. We demonstrate that this methodology is robust to the presence of impurities in the system and noise in the conductance data. Our findings show that the conductance pattern reveals a complex dependence on the $\mathbf{q}$ vector of the spin spiral, providing a new strategy to learn magnetic structures directly from transport experiments.

In the inverse problem in particle physics, given an unexpected observation, one aims to identify a unique choice from amongst several competing hypotheses. We explore a novel approach of applying self-organizing maps to the inverse problem in a search for vector-like leptons in a trilepton final state. We define an approach combining the inherent clustering of these maps and elements of supervised learning. We compare the performance of this approach with a multiclassfying neural network. We find that the method using self-organizing maps competes well (despite not using any standard model processes in the training), and provides additional tools that would help characterize any observed excesses in searches.

This technical report contains the formal definitions and metatheory for the act specification and verification language. It documents the syntax, the operational pointer semantics, the type system and the main metatheoretic results (type-safety).

Reachability analysis evaluates system safety, by identifying the set of states a system may evolve within over a finite time horizon. In contrast to model-based reachability analysis, data-driven reachability analysis estimates reachable sets and derives probabilistic guarantees directly from data. Several popular techniques for validating reachable sets -- conformal prediction, scenario optimization, and the holdout method -- admit similar Probably Approximately Correct (PAC) guarantees. We establish a formal connection between these PAC bounds and present an empirical case study on reachable sets to illustrate the computational and sample trade-offs associated with these methods. We argue that despite the formal relationship between these techniques, subtle differences arise in both the interpretation of guarantees and the parameterization. As a result, these methods are not generally interchangeable. We conclude with practical advice on the usage of these methods.

The electrochromic response of Ni-deficient NiO is governed by vacancy-mediated electronic processes that can be strongly influenced by dopant chemistry and lattice deformation. Using density functional theory, we systematically investigated Cu-, Sn-, and V-doped Ni-deficient NiO(001) surfaces and examined alkali-ion insertion at surface Ni vacancies. Li insertion proceeds as nearly complete ionic electron donation (~+0.9 e), but the fate of the injected electron depends on dopant identity. V-doping preserves framework-dominated charge compensation and leads to conventional bleaching through filling of vacancy-associated hole states. In contrast, Sn actively traps the injected charge, generating dopant-assisted optical transitions and reversing the electrochromic response, while Cu produces an intermediate spectral redistribution without significant dopant reduction. Substitution of Li by Na or K in the V-doped system does not alter the switching mechanism, confirming that vacancy-state filling governs the optical behavior. Biaxial tensile strain enhances the energetics of Li insertion but reduces optical contrast by altering the defect electronic structure. These results establish dopant activity, vacancy stabilization, and lattice strain as key parameters controlling electrochromism in NiO-based materials.

Although resetting has widespread applicability, applying it to the dynamics in the presence of spatial quenched disorder, which is essential in many physical problems, is challenging. In this study, we consider a well-known one-dimensional model of particle hopping on a lattice with quenched disorder in the form of site-dependent hopping probabilities, drawn from a power-law distribution, and apply the resetting formalism. As a physical example, we recast the growth dynamics of microtubules with sudden catastrophic disassembly events as a resetting dynamics. We consider two distinct regimes for growth dynamics: a strongly biased case and a less biased case. Motivated by experimental results, we take a Gamma distribution for the resetting time. Our results show that occasional disassembly events are crucial for the experimentally observed distribution of reset (or catastrophe) lengths. We also analyze steady-state distributions under different resetting protocols-resetting to the initial position versus a random site. We also investigate the distribution of first-passage times to a fixed distance following reset. Finally, by considering other resetting probability distributions, we identify a regime where the mean displacement grows as slowly as $\log^2 t$. We also elucidate the role of disorder in the system properties under the resetting dynamics. Our study paves the way to treat the dynamics of complex physical systems using resetting.

Sample compression schemes were defined by Littlestone and Warmuth (1986) as an abstraction of the structure underlying many learning algorithms. In a sample compression scheme, we are given a large sample of vertices of a fixed hypergraph with labels indicating the containment in some hyperedge. The task is to compress the sample in such a way that we can retrieve the labels of the original sample. The size of a sample compression scheme is the amount of information that is kept in the compression. Every hypergraph with a sample compression scheme of bounded size must have bounded VC-dimension. Conversely, Moran and Yehudayoff (J. ACM, 2016) showed that every hypergraph of bounded VC-dimension admits a sample compression scheme of bounded size. We study a specific class of hypergraphs emerging from balls in graphs. The schemes that we construct (contrary to the ones constructed by Moran and Yehudayoff) are \textit{proper}, meaning that we retrieve not only the labeling of the original sample but also a hyperedge (ball) consistent with the original labeling. First, we prove that for every graph $G$ of treewidth at most $t$, the hypergraph of balls in $G$ has a proper sample compression scheme of size $\mathcal{O}(t\log t)$; this is tight up to the logarithmic factor and improves the quadratic (improper) bound that follows from the result of Moran and Yehudayoff. Second, we prove an analogous result for graphs of cliquewidth at most $t$.

Multimodal large language models (MLLMs) enable powerful cross-modal reasoning capabilities but impose substantial computational and latency burdens, posing critical challenges for deployment on resource-constrained edge devices. In this paper, we propose MSAO, an adaptive modality sparsity-aware offloading framework with edge-cloud collaboration for efficient MLLM Inference. First, a lightweight heterogeneous modality-aware via fine-grained sparsity module performs spatial-temporal-modal joint analysis to compute the Modality Activation Sparsity (MAS) metric, which quantifies the necessity of each modality with minimal computational overhead. Second, an adaptive speculative edge-cloud collaborative offloading mechanism dynamically schedules workloads between edge and cloud based on the derived MAS scores and real-time system states, leveraging confidence-guided speculative execution to hide communication latency. Extensive experiments on VQAv2 and MMBench benchmarks demonstrate that MSAO achieves a 30% reduction in end-to-end latency and 30%-65% decrease in resource overhead, while delivering a throughput improvement of 1.5x to 2.3x compared to traditional approaches, all without compromising competitive accuracy.

We study the non-equilibrium dynamics, thermalisation and attractor behaviour of charm quarks in a longitudinally expanding Quark-Gluon Plasma within the Relativistic Boltzmann Transport approach in 1+1D Bjorken expansion. Considering both a strong AdS/CFT coupling scenario with constant $2πT D_s=1$ and a temperature-dependent diffusion coefficient $D_s^\text{lQCD}(T)$ from the recent unquenched lattice QCD data, we analyse the evolution of effective temperature, momentum moments and distribution functions for different initial conditions, including FONLL and EPOS4HQ spectra. We find that charm quarks exhibit dynamical attractors; however, the temperature dependence of $D_s^\text{lQCD}(T)$ leads to significantly longer relaxation times compared to the strong coupling limit. While dynamical attractors occur within $\sim 1-1.5 \rm \,fm$ for $2πT D_s=1$, they are delayed to $\sim 5 \rm \,fm$ for $D_s^\text{lQCD}(T)$, becoming comparable to the lifetime of the Quark-Gluon Plasma phase in ultra-relativistic collisions. This indicates that charm quarks may not fully thermalise, especially in small systems such as peripheral or light-ion collisions. We further show that, for $D_s^\text{lQCD}(T)$, the deviation from equilibrium becomes as large as $δf_{HQ}/f_{eq} \sim p_T^β\sim \mathcal{O}(1)$ already at $p_T\simeq 3\rm\, GeV$, rising with $β\sim 4.5$, thus questioning the applicability of viscous hydrodynamics to charm dynamics.

The Proximal Point Method (PPM) (Rockafellar, 1976) is a fundamental tool for nonsmooth convex optimization. However, its convergence is not linear under general convexity in the absence of strong convexity or other structural assumptions. To address this limitation, we study a trust-region stabilized proximal point scheme in which each proximal update is computed over a localized feasible region. We show that this simple stabilization enforces non-vanishing steps and yields a linear decrease in objective values outside any prescribed neighborhood, without assuming smoothness or strong convexity. Our analysis identifies a displacement condition as the key driver of linear descent and provides two complementary parameter regimes to guarantee it: fixing the trust-region radius and choosing the regularization properly, or fixing the regularization and selecting radii via a uniform displacement lower bound. We further give explicit characterization of the linear regime conditions respectively, and prove that the trust-region is redundant under strong convexity, Finally, we establish an exact equivalence with the Broximal Point Method (BPM) (Gruntkowska et al., 2025) in the active constraint regime.

This study investigates the existence and stability of limit cycles resulting from self-excited oscillations in linear multi-degree-of-freedom systems subjected to discontinuous, state-dependent forcing. Using the method of averaging and slow-flow phase-plane analysis, analytical expressions are derived for the amplitudes and stability boundaries of limit cycles in a two-degree-of-freedom system. The analysis demonstrates that stable limit cycles may exist in all natural modes, with the steady-state response governed by initial conditions in regimes of multistability. A central contribution of this work is the identification and analytical characterization of the stability-axis-flipping (SAF) bifurcation, which serves as the governing mechanism for the exchange of stability between modes. The framework is then systematically extended to systems with higher degrees of freedom, confirming that the SAF bifurcation remains a universal feature, even under varying feedback configurations. The steady-state dynamics, summarized through stability maps and validated by numerical simulations, delineate the existence and stability regions of modal limit cycles as functions of key system parameters. These results provide efficient criteria for guiding optimization studies to mitigate or generate limit cycles at targeted frequencies in flexible mechanical structures.

We study the problem of statistically certifying viable initial sets (VISs) -- sets of initial conditions whose trajectories satisfy a given control specification. While VISs can be obtained from model-based methods, these methods typically rely on simplified models. We propose a simulation-based framework to certify VISs by estimating the probability of specification violations under a high-fidelity or black-box model. Since detecting these violations may be challenging due to their scarcity, we propose a sample-efficient framework that leverages importance sampling to target high-risk regions. We derive an empirical Bernstein inequality for weighted random variables, enabling finite-sample guarantees for importance sampling estimators. We demonstrate the effectiveness of the proposed approach on two systems and show improved convergence of the resulting bounds on an Adaptive Cruise Control benchmark.

Advancements in extended reality (XR) are driving the development of the metaverse, which demands efficient real-time transformation of 2D scenes into 3D objects, a computation-intensive process that necessitates task offloading because of complex perception, visual, and audio processing. This challenge is further compounded by asymmetric uplink (UL) and downlink (DL) data characteristics, where 2D data are transmitted in the UL and 3D content is rendered in the DL. To address this issue, we propose a digital twin (DT)-based in-network computing (INC)-assisted multi-access edge computing (MEC) framework that enables real-time synchronization and collaborative computing via URLLC. In this framework, a network operator manages wireless and computational resources for XR user devices (XUDs), while XUDs autonomously offload tasks to maximize their utilities. We model the interactions between XUDs and the operator as a Stackelberg Markov game, where the optimal offloading strategy constitutes an exact potential game with a Nash Equilibrium (NE), and the operator's problem is formulated as an asynchronous Markov decision process (MDP). We further propose a decentralized solution in which XUDs determine offloading decisions based on the operator's joint UL-DL optimization of offloading mode (INC-E or MEC only) and DL power allocation. A Nash-asynchronous hybrid multi-agent reinforcement learning (AMRL) algorithm is developed to predict the UL user-associated and DL transmission power, thereby achieving NE. Simulation results demonstrate that the proposed approach considerably improves system utility, uplink rate, and energy efficiency by reducing latency and optimizing resource utilization in metaverse environments.

To support the high data rates for latency-critical applications, future wireless systems will employ fully digital beamforming multiple-input multiple-output (MIMO) architectures at millimeter wave (mmWave) frequencies. Moreover, mmWave MIMO deployments will coexist with conventional sub-6 GHz MIMO systems, creating opportunities to exploit out-of-band sub-6 GHz information to enhance channel estimation at mmWave frequencies. In this work, we analyze the pilot-aided channel estimation performance of mmWave MIMO systems under various pilot configurations in both static and dynamic environments. We evaluate the system performance in terms of spectral efficiency (SE) for line-of-sight and non-line-of-sight propagation conditions. Simulation results show that incorporating out-of-band sub-6 GHz information yields notable SE gains in both static and dynamic scenarios.

A search for the rare decays $B_{(s)}^0\to J/ψγ$ is performed with proton-proton collision data collected by the LHCb experiment, corresponding to integrated luminosities of $3~\rm{fb}^{-1}$ at centre-of-mass energies of 7 and 8 TeV, and $6~\rm{fb}^{-1}$ at 13 TeV. Assuming no contribution from $B^0\to J/ψγ$ decay, an upper limit is set on the branching fraction $\mathcal{B}(B_{s}^0\to J/ψγ)<2.9\times10^{-6}$ at the 90% confidence level. If instead no contribution from $B_{s}^0\to J/ψγ$ decay is assumed, the limit is $\mathcal{B}(B^0\to J/ψγ)<2.5\times10^{-6}$ at the 90% confidence level. These results supersede the previous LHCb results, with the limit for $B_{s}^0\to J/ψγ$ improved by a factor of 2.5.

The integration of renewable energy sources and distributed generation in the power system calls for fast and reliable predictions of grid dynamics to achieve efficient control and ensure stability. In this work, we present a novel nonparametric data-driven prediction algorithm based on kriging interpolation, which exploits the problem's numerical structure to achieve the required computational efficiency for fast real-time forecasting. Our results enable accurate frequency prediction directly from measurements, achieving sub-second computation times. We validate our findings on a simulated distribution grid case study.