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Topologically protected edge state transport in quantum materials is dissipationless and features quantized Hall conductance, and shows great potential in highly fault-tolerant computing technologies. However, it remains elusive about how to develop topological edge state-based computing devices. Recently, exploration and understanding of interfacial ferroelectricity in various van der Waals heterostructure material systems have received widespread attention among the community of materials science and condensed matter physics3-11. Such ferroelectric polarization emergent at the vdW interface can coexist with other quantum states and thus provides an unprecedented opportunity to electrically switch the topological edge states of interest, which is of crucial significance to the fault-tolerant electronic device applications based on the topological edge states. Here, we report the selective and quasi-continuous ferroelectric switching of topological Chern insulator devices and demonstrate its promising application in noise-immune neuromorphic computing. We fabricate this ferroelectric Chern insulator device by encapsulating magic-angle twisted bilayer graphene with doubly-aligned h-BN layers, and observe the coexistence of the interfacial ferroelectricity and the topological Chern insulating states. This ferroelectricity exhibits an anisotropic dependence on the in-plane magnetic field. By using a VBG pulse with delicately controlled amplitude, we realize the nonvolatile switching between any pair of Chern insulating states and achieve 1280 distinguishable nonvolatile resistance levels on a single device. Furthermore, we demonstrate deterministic switching between two arbitrary levels among the record-high number of nonvolatile resistance levels.

With the rapid advancements of large-scale text-to-image diffusion models, various practical applications have emerged, bringing significant convenience to society. However, model developers may misuse the unauthorized data to train diffusion models. These data are at risk of being memorized by the models, thus potentially violating citizens' privacy rights. Therefore, in order to judge whether a specific image is utilized as a member of a model's training set, Membership Inference Attack (MIA) is proposed to serve as a tool for privacy protection. Current MIA methods predominantly utilize pixel-wise comparisons as distinguishing clues, considering the pixel-level memorization characteristic of diffusion models. However, it is practically impossible for text-to-image models to memorize all the pixel-level information in massive training sets. Therefore, we move to the more advanced structure-level memorization. Observations on the diffusion process show that the structures of members are better preserved compared to those of nonmembers, indicating that diffusion models possess the capability to remember the structures of member images from training sets. Drawing on these insights, we propose a simple yet effective MIA method tailored for text-to-image diffusion models. Extensive experimental results validate the efficacy of our approach. Compared to current pixel-level baselines, our approach not only achieves state-of-the-art performance but also demonstrates remarkable robustness against various distortions.

The asymmetry in hard X-ray (HXR) emission at the footpoints (FPs) of flare loops is a ubiquitous feature closely associated with nonthermal electron transport. We analyze the asymmetric HXR radiation at two flare ribbons which is thermal-dominated during a long-duration C4.4 flare that occurred on March 20, 2023, combining multi-view and multi-waveband observations from the ASO-S, SolO, and SDO spacecraft. We find that the H I Ly$\alpha$ emission captures similar features to the He II $\lambda$304 in both light curve and spatio-temporal evolution of a pair of conjugate flare ribbons. The spectra and imaging analysis of the HXR emission, detected by STIX in 4-18 keV, reveal that the two-ribbon flare radiation is thermal dominated by over 95%, and the radiation source mainly concentrates on the northern ribbon, leading to an asymmetric distribution. To understand the underlying reasons for the HXR radiation asymmetry, we extrapolate the magnetic field within the active region using the NLFFF model. For 78% of the magnetic field lines starting from the northern flare ribbon, their lengths from the loop-tops (LTs) to the northern FPs are shorter than those to the southern FPs. For 62% of the field lines, their magnetic field strengths at the southern FPs exceed those at the northern FPs. In addition, considering the larger density, $\approx1.0\times10^{10}$ cm$^{-3}$, of the low-lying flare loops (< 32 Mm), we find the shorter path from the LT to the northern FP enables more electrons to reach the northern FP more easily after collisions with the surrounding plasma. Therefore, in this thermal-dominated C-class flare, the asymmetric location of the flare LT relative to its two FPs plays a dominant role in the HXR radiation asymmetry, while such asymmetry is also slightly influenced by the magnetic mirror effect resulting in larger HXR radiation at the FPs with weaker magnetic strength., Comment: 21 pages, 7 figures, accepted by Solar Physics. Comments welcome

Sympathetic eruptions of solar prominences have been studied for decades, however, it is usually difficult to identify their causal links. Here we present two failed prominence eruptions on 26 October 2022 and explore their connections. Using stereoscopic observations, the south prominence (PRO-S) erupts with untwisting motions, flare ribbons occur underneath, and new connections are formed during the eruption. The north prominence (PRO-N) rises up along with PRO-S, and its upper part disappears due to catastrophic mass draining along an elongated structure after PRO-S failed eruption. We suggest that the eruption of PRO-S initiates due to a kink instability, further rises up, and fails to erupt due to reconnection with surrounding fields. The elongated structure connecting PRO-N overlies PRO-S, which causes the rising up of PRO-N along with PRO-S and mass drainage after PRO-S eruption. This study suggests that a prominence may end its life through mass drainage forced by an eruption underneath., Comment: 15 pages, 7 figures, has been accepted by Solar Physics

Over the years, great efforts have been devoted in introducing a sizable and tunable band gap in graphene for its potential application in next-generation electronic devices. The primary challenge in modulating this gap has been the absence of a direct method for observing changes of the band gap in momentum space. In this study, we employ advanced spatial- and angle-resolved photoemission spectroscopy technique to directly visualize the gap formation in bilayer graphene, modulated by both displacement fields and moir\'e potentials. The application of displacement field via in-situ electrostatic gating introduces a sizable and tunable electronic bandgap, proportional to the field strength up to 100 meV. Meanwhile, the moir\'e potential, induced by aligning the underlying hexagonal boron nitride substrate, extends the bandgap by ~ 20 meV. Theoretical calculations, effectively capture the experimental observations. Our investigation provides a quantitative understanding of how these two mechanisms collaboratively modulate the band gap in bilayer graphene, offering valuable guidance for the design of graphene-based electronic devices., Comment: 16 pages,4 figures

Fast radio bursts (FRBs) are cosmological radio transients with millisecond durations and extremely high brightness temperatures. One FRB repeater, FRB 180916.J0158+65 (FRB 180916B), was confirmed to appear 16.35-day periodic activities with 5-day activity window. Another FRB repeater, FRB 121102, and two soft gamma-ray repeaters (SGRs), SGR 1935+2154 and SGR 1806-20, also show possible periodic activities. These periodicities might originate from the precession process of young magnetars due to the anisotropic pressure from the inner magnetic fields as proposed in the literature. In this work, we analyze a self-consistent model for the rotation evolution of magnetars and obtain the evolutions of magnetar precession and obliquity. We find that if the FRB repeaters and the SGRs with (possible) periodic activities originate from the magnetar precession, their ages would be constrained to be hundreds to tens of thousands of years, which is consistent with the typical ages of magnetars. Assuming that the FRB emission is beaming in the magnetosphere as proposed in the literature, we calculate the evolution of the observable probability and the duty cycle of the active window period. We find that for a given magnetar the observable probability increases with the magnetar age in the early stage and decreases with the magnetar age in the later stage, meanwhile, there are one or two active windows in one precession period if the emission is not perfectly axisymmetric with respect to the deformation axis of a magnetar, which could be tested by the future observation for repeating FRB sources., Comment: 10 pages, 9 figures. Accepted for publication in MNRAS. Comments welcome!

Solar white-light flares are characterized by an enhancement in the optical continuum, which are usually large flares (say X- and M-class flares). Here we report a small C2.3 white-light flare (SOL2022-12-20T04:10) observed by the \emph{Advanced Space-based Solar Observatory} and the \emph{Chinese H$\alpha$ Solar Explorer}. This flare exhibits an increase of $\approx$6.4\% in the photospheric Fe \textsc{i} line at 6569.2\,\AA\ and {$\approx$3.2\%} in the nearby continuum. The continuum at 3600\,\AA\ also shows an enhancement of $\approx$4.7\%. The white-light brightening kernels are mainly located at the flare ribbons and co-spatial with nonthermal hard X-ray sources, which implies that the enhanced white-light emissions are related to nonthermal electron-beam heating. At the brightening kernels, the Fe \textsc{i} line displays an absorption profile that has a good Gaussian shape, with a redshift up to $\approx$1.7 km s$^{-1}$, while the H$\alpha$ line shows an emission profile though having a central reversal. The H$\alpha$ line profile also shows a red or blue asymmetry caused by plasma flows with a velocity of several to tens of km s$^{-1}$. It is interesting to find that the H$\alpha$ asymmetry is opposite at the conjugate footpoints. It is also found that the CHASE continuum increase seems to be related to the change of photospheric magnetic field. Our study provides comprehensive characteristics of a small white-light flare that help understand the energy release process of white-light flares., Comment: 23 pages, 6 figures, accepted by Solar Physics

Diffusion models pose risks of privacy breaches and copyright disputes, primarily stemming from the potential utilization of unauthorized data during the training phase. The Training Membership Inference (TMI) task aims to determine whether a specific sample has been used in the training process of a target model, representing a critical tool for privacy violation verification. However, the increased stochasticity inherent in diffusion renders traditional shadow-model-based or metric-based methods ineffective when applied to diffusion models. Moreover, existing methods only yield binary classification labels which lack necessary comprehensibility in practical applications. In this paper, we explore a novel perspective for the TMI task by leveraging the intrinsic generative priors within the diffusion model. Compared with unseen samples, training samples exhibit stronger generative priors within the diffusion model, enabling the successful reconstruction of substantially degraded training images. Consequently, we propose the Degrade Restore Compare (DRC) framework. In this framework, an image undergoes sequential degradation and restoration, and its membership is determined by comparing it with the restored counterpart. Experimental results verify that our approach not only significantly outperforms existing methods in terms of accuracy but also provides comprehensible decision criteria, offering evidence for potential privacy violations., Comment: 18 pages, 6 figures, 7 tables

Strong interactions between particles can lead to emergent collective excitations. These phenomena have been extensively established in electronic systems, but are also expected to occur for gases of neutral particles like spin waves, also known as magnons, in a ferromagnet. In a hydrodynamic regime where magnons are strongly interacting, they can form a slow collective density mode -- in analogy to sound waves in water -- with characteristic low-frequency signatures. While such a mode has been predicted in theory, its signatures have yet to be observed experimentally. In this work, we isolate atomically-thin sheets of ferromagnetic CrCl$_3$ where magnon interactions are strong, and develop a technique to measure its collective magnon dynamics via the quantum coherence of nearby Nitrogen-Vacancy (NV) centers in diamond. We find that the thermal magnetic fluctuations generated by CrCl$_3$ exhibit an anomalous temperature-dependence, whereby fluctuations increase upon decreasing temperature. Our analysis reveals that this anomalous trend is a consequence of the damping rate of a low-energy magnon sound mode which sharpens as magnon interactions increase with increasing temperature, providing a first glimpse of the magnon hydrodynamic regime.

The white-light continuum emissions in solar flares (i.e., white-light flares) are usually observed on the solar disk but, in a few cases, off the limb. Here we present on-disk as well as off-limb continuum emissions at 3600 {\AA} (in the Balmer continuum) in an X2.1 flare (SOL2023-03-03T17:52) and an X1.5 flare (SOL2023-08-07T20:46), respectively, observed by the White-light Solar Telescope (WST) on the Advanced Space-based Solar Observatory (ASO-S). These continuum emissions are seen at the ribbons for the X2.1 flare and on loops during the X1.5 event, in which the latter also appears in the decay phase. These emissions also show up in the pseudo-continuum images at Fe I {\lambda}6173 from the Helioseismic and Magnetic Imager (HMI) on the Solar Dynamics Observatory (SDO). In addition, the ribbon sources in the X2.1 flare exhibit significant enhancements in the Fe I line at 6569.2 {\AA} and the nearby continuum observed by the Chinese H{\alpha} Solar Explorer (CHASE). It is found that the on-disk continuum emissions in the X2.1 flare are related to a nonthermal electron-beam heating either directly or indirectly, while the off-limb emissions in the X1.5 flare are associated with thermal plasma cooling or due to Thomson scattering. These comprehensive continuum observations can provide good constraints on flare energy deposition models, which helps well understand the physical mechanism of white-light flares., Comment: 13 pages, 1 table, 4 figures, accepted for publication in ApJL

By accurately measuring composition and energy spectrum of cosmic ray, the origin problem of so called "keen" region (energy > 1 PeV) can be solved. However, up to the present, the results of the spectrum in the knee region obtained by several previous experiments have shown obvious differences, so they cannot give effective evidence for judging the theoretical models on the origin of the knee. Recently, the Large High Altitude Air Shower Observatory (LHAASO) has reported several major breakthroughs and important results in astro-particle physics field. Relying on its advantages of wide-sky survey, high altitude location and large area detector arrays, the research content of LHAASO experiment mainly includes ultra high-energy gamma-ray astronomy, measurement of cosmic ray spectra in the knee region, searching for dark matter and new phenomena of particle physics at higher energy. The electron and Thermal Neutron detector (EN-Detector) is a new scintillator detector which applies thermal neutron detection technology to measure cosmic ray extensive air shower (EAS). This technology is an extension of LHAASO. The EN-Detector Array (ENDA) can highly efficiently measure thermal neutrons generated by secondary hadrons so called "skeleton" of EAS. In this paper, we perform the optimization of ENDA configuration, and obtain expectations on the ENDA results, including thermal neutron distribution, trigger efficiency and capability of cosmic ray composition separation. The obtained real data results are consistent with those by the Monte Carlo simulation.

The decay of sunspot plays a key role in magnetic flux transportation in solar active regions (ARs). To better understand the physical mechanism of the entire decay process of a sunspot, an {\alpha}-configuration sunspot in AR NOAA 12411 was studied. Based on the continuum intensity images and vector magnetic field data with stray light correction from Solar Dynamics Observatory/Helioseismic and Magnetic Imager, the area, vector magnetic field and magnetic flux in the umbra and penumbra are calculated with time, respectively. Our main results are as follows: (1) The decay curves of the sunspot area in its umbra, penumbra, and whole sunspot take the appearance of Gaussian profiles. The area decay rates of the umbra, penumbra and whole sunspot are -1.56 MSH/day, -12.61 MSH/day and -14.04 MSH/day, respectively; (2) With the decay of the sunspot, the total magnetic field strength and the vertical component of the penumbra increase, and the magnetic field of the penumbra becomes more vertical. Meanwhile, the total magnetic field strength and vertical magnetic field strength for the umbra decrease, and the inclination angle changes slightly with an average value of about 20{\deg}; (3) The magnetic flux decay curves of the sunspot in its umbra, penumbra, and whole sunspot exhibit quadratic patterns, their magnetic flux decay rates of the umbra, penumbra and whole sunspot are -9.84 * 10^19 Mx/day, -1.59 * 10^20 Mx/day and -2.60 * 10^20 Mx/day , respectively. The observation suggests that the penumbra may be transformed into the umbra, resulting in the increase of the average vertical magnetic field strength and the reduction of the inclination angle in the penumbra during the decay of the sunspot.

Quantum geometry of electronic wavefunctions results in fascinating topological phenomena. A prominent example is the intrinsic anomalous Hall effect (AHE) in which a Hall voltage arises in the absence of an applied magnetic field. The AHE requires a coexistence of Berry curvature and spontaneous time-reversal symmetry breaking. These conditions can be realized in two-dimensional moir\'e systems with broken $xy$-inversion symmetry ($C_{2z}$) that host flat electronic bands. Here, we explore helical trilayer graphene (HTG), three graphene layers twisted sequentially by the same angle forming two misoriented moir\'e patterns. Although HTG is globally $C_{2z}$-symmetric, surprisingly we observe clear signatures of topological bands. At a magic angle $\theta_\mathrm{m}\approx 1.8^\circ$, we uncover a robust phase diagram of correlated and magnetic states using magnetotransport measurements. Lattice relaxation leads to large periodic domains in which $C_{2z}$ is broken on the moir\'e scale. Each domain harbors flat topological bands with valley-contrasting Chern numbers $\pm(1,-2)$. We find correlated states at integer electron fillings per moir\'e unit cell $\nu=1,2,3$ and fractional fillings $2/3,7/2$ with the AHE arising at $\nu=1,3$ and $2/3,7/2$. At $\nu=1$, a time-reversal symmetric phase appears beyond a critical electric displacement field, indicating a topological phase transition. Finally, hysteresis upon sweeping $\nu$ points to first-order phase transitions across a spatial mosaic of Chern domains separated by a network of topological gapless edge states. We establish HTG as an important platform that realizes ideal conditions for exploring strongly interacting topological phases and, due to its emergent moir\'e-scale symmetries, demonstrates a novel way to engineer topology.

Recently, some fast radio bursts (FRBs) have been reported to exhibit complex and diverse variations in Faraday rotation measurements (RM) and polarization, suggesting that dynamically evolving magnetization environments may surround them. In this paper, we investigate the Faraday conversion (FC) effect in a binary system involving an FRB source and analyze the polarization evolution of FRBs. For an strongly magnetized high-mass companion binary (HMCB), when an FRB with $\sim100\%$ linear polarization passes through the radial magnetic field of the companion star, the circular polarization (CP) component will be induced and oscillate symmetrically around the point with the CP degree equal to zero, the rate and amplitude of the oscillation decrease as the frequency increases. The very strong plasma column density in the HMCBs can cause CP to oscillate with frequency at a very drastic rate, which may lead to depolarization. Near the superior conjunction of the binary orbit, the DM varies significantly due to the dense plasma near the companion, and the significant FC also occurs in this region. As the pulsar moves away from the superior conjunction, the CP gradually tends towards zero and then returns to its value before incidence. We also investigate the effect of the rotation of the companion star. We find that a sufficiently significant RM reversal can be produced at large magnetic inclinations and the RM variation is very diverse. Finally, we apply this model to explain some polarization observations of PSR B1744-24A and FRB 20201124A., Comment: 24 pages, 14 figures, accepted for publication in ApJ

We report on the spectral features of the Si IV 1402.77 \AA, C II 1334.53 \AA, and Mg II h or k lines, formed in the layers from the transition region to the chromosphere, in three two-ribbon flares (with X-, M-, and C-class) observed with IRIS. All the three lines show significant redshifts within the main flare ribbons, which mainly originate from the chromospheric condensation during the flares. The average redshift velocities of the Si IV line within the main ribbons are 56.6, 25.6, and 10.5 km s$^{-1}$ for the X-, M-, and C-class flares, respectively, which show a decreasing tendency with the flare class. The C II and Mg II lines show a similar tendency but with smaller velocities compared to the Si IV line. Additionally, the Mg II h or k line shows a blue-wing enhancement in the three flares in particular at the flare ribbon fronts, which is supposed to be caused by an upflow in the upper chromosphere due to the heating of the atmosphere. Moreover, the Mg II h or k line exhibits a central reversal at the flare ribbons, but turns to pure emission shortly after 1--4 minutes. Correspondingly, the C II line also shows a central reversal but in a smaller region. However, for the Si IV line, the central reversal is only found in the X-class flare, but not in the other two flares. As usual, the central reversal of these lines can be caused by the opacity effect. This implies that in addition to the optically thick lines (C II and Mg II lines), the Si IV line can become optically thick in a strong flare, which is likely related to the nonthermal electron beam heating., Comment: 26 pages, 13 figures, accepted for publication in ApJS

The linear conjugate gradient method is an efficient iterative method for the convex quadratic minimization problems $ \mathop {\min }\limits_{x \in { \mathbb R^n}} f(x) =\dfrac{1}{2}x^TAx+b^Tx $, where $ A \in R^{n \times n} $ is symmetric and positive definite and $ b \in R^n $. It is generally agreed that the gradients $ g_k $ are not conjugate with respective to $ A $ in the linear conjugate gradient method (see page 111 in Numerical optimization (2nd, Springer, 2006) by Nocedal and Wright). In the paper we prove the conjugacy of the gradients $ g_k $ generated by the linear conjugate gradient method, namely, $$g_k^TAg_i=0, \; i=0,1,\cdots, k-2.$$ In addition,a new way is exploited to derive the linear conjugate gradient method based on the conjugacy of the search directions and the orthogonality of the gradients, rather than the conjugacy of the search directions and the exact stepsize.

The heating mechanisms of solar white-light flares remain unclear. We present an X1.0 white-light flare on 2022 October 2 (SOL2022-10-02T20:25) observed by the Chinese \ha\ Solar Explorer (CHASE) that provides two-dimensional spectra in the visible light for the full solar disk with a seeing-free condition. The flare shows a prominent enhancement of $\sim$40\% in the photospheric \fe\ line at 6569.2 \AA, and the nearby continuum also exhibits a maximum enhancement of $\sim$40\%. For the continuum near the \fe\ line at 6173 \AA\ from the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO), it is enhanced up to $\sim$20\%. At the white-light kernels, the \fe\ line at 6569.2 \AA\ has a symmetric Gaussian profile that is still in absorption and the H$\alpha$ line at 6562.8 \AA\ displays a very broad emission profile with a central reversal plus a red or blue asymmetry. The white-light kernels are co-spatial with the microwave footpoint sources observed by the Expanded Owens Valley Solar Array (EOVSA) and the time profile of the white-light emission matches that of the hard X-ray emission above 30 keV from the Gamma-ray Burst Monitor (GBM) on Fermi. These facts indicate that the white-light emission is qualitatively related to a nonthermal electron beam. We also perform a radiative hydrodynamic simulation with the electron beam parameters constrained by the hard X-ray observations from Fermi/GBM. The result reveals that the white-light enhancement cannot be well explained by a pure electron-beam heating together with its induced radiative backwarming but may need additional heating sources such as \alfven\ waves., Comment: 15 pages, 5 figures, and 1 table

The BNL and FNAL measurements of the anomalous magnetic moment of the muon disagree with the Standard Model (SM) prediction by more than $4\sigma$. The hadronic vacuum polarization (HVP) contributions are the dominant source of uncertainty in the SM prediction. There are, however, tensions between different estimates of the HVP contributions, including data-driven estimates based on measurements of the $R$-ratio. To investigate that tension, we modeled the unknown $R$-ratio as a function of CM energy with a treed Gaussian process (TGP). This is a principled and general method grounded in data-science that allows complete uncertainty quantification and automatically balances over- and under-fitting to noisy data. Our tool yields exploratory results are similar to previous ones and we find no indication that the $R$-ratio was previously mismodeled. Whilst we advance some aspects of modeling the $R$-ratio and develop new tools for doing so, a competitive estimate of the HVP contributions requires domain-specific expertise and a carefully curated database of measurements., Comment: 23 pages, 5 figures

In this paper, we carry out a detailed analysis of the M1.6 class eruptive flare occurring in NOAA active region 13078 on 2022 August 19. The flare is associated with a fast coronal mass ejection (CME) propagating in the southwest direction with an apparent speed of $\sim$926 km s$^{-1}$. Meanwhile, a shock wave is driven by the CME at the flank. The eruption of CME generates an extreme-ultraviolet (EUV) wave expanding outward from the flare site with an apparent speed of $\geq$200 km s$^{-1}$. As the EUV wave propagates eastward, it encounters and interacts with the low-lying adjacent coronal loops (ACLs), which are composed of two loops. The compression of EUV wave results in contraction, expansion, and transverse vertical oscillations of ACLs. The commencements of contraction are sequential from western to eastern footpoints and the contraction lasts for $\sim$15 minutes. The speeds of contraction lie in the range of 13$-$40 km s$^{-1}$ in 171 {\AA} and 8$-$54 km s$^{-1}$ in 193 {\AA}. A long, gradual expansion follows the contraction at lower speeds. Concurrent vertical oscillations are superposed on contraction and expansion of ACLs. The oscillations last for 2$-$9 cycles and the amplitudes are $\leq$4 Mm. The periods are between 3 to 12 minutes with an average value of 6.7 minutes. The results show rich dynamics of coronal loops., Comment: 10 pages, 10 figures, accepted for publication in ApJ

We propose helical trilayer graphene (HTG), a helical structure featuring identical rotation angles $\theta\approx 1.5^\circ$ between three consecutive layers of graphene, as a unique and experimentally accessible platform for realizing exotic correlated topological states of matter. While nominally forming a supermoir\'e (or moir\'e-of-moir\'e) structure, we show that HTG locally relaxes into large regions of a periodic single-moir\'e structure in which $C_{2z}$ is broken, giving rise to flat topological bands carrying valley-Chern numbers $C=\pm(1,-2)$. These bands feature near-ideal quantum geometry and are isolated from remote bands by a large gap $E_{\mathrm{gap}}\sim 100$ meV, making HTG a promising platform for experimental realization of correlated topological states such as integer and fractional quantum anomalous Hall states in $C=1$ and $2$ bands.

Objective: Gaussian Processes (GP)-based filters, which have been effectively used for various applications including electrocardiogram (ECG) filtering can be computationally demanding and the choice of their hyperparameters is typically ad hoc. Methods: We develop a data-driven GP filter to address both issues, using the notion of the ECG phase domain -- a time-warped representation of the ECG beats onto a fixed number of samples and aligned R-peaks, which is assumed to follow a Gaussian distribution. Under this assumption, the computation of the sample mean and covariance matrix is simplified, enabling an efficient implementation of the GP filter in a data-driven manner, with no ad hoc hyperparameters. The proposed filter is evaluated and compared with a state-of-the-art wavelet-based filter, on the PhysioNet QT Database. The performance is evaluated by measuring the signal-to-noise ratio (SNR) improvement of the filter at SNR levels ranging from -5 to 30dB, in 5dB steps, using additive noise. For a clinical evaluation, the error between the estimated QT-intervals of the original and filtered signals is measured and compared with the benchmark filter. Results: It is shown that the proposed GP filter outperforms the benchmark filter for all the tested noise levels. It also outperforms the state-of-the-art filter in terms of QT-interval estimation error bias and variance. Conclusion: The proposed GP filter is a versatile technique for preprocessing the ECG in clinical and research applications, is applicable to ECG of arbitrary lengths and sampling frequencies, and provides confidence intervals for its performance.