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Learning dynamics from dissipative chaotic systems is notoriously difficult due to their inherent instability, as formalized by their positive Lyapunov exponents, which exponentially amplify errors in the learned dynamics. However, many of these systems exhibit ergodicity and an attractor: a compact and highly complex manifold, to which trajectories converge in finite-time, that supports an invariant measure, i.e., a probability distribution that is invariant under the action of the dynamics, which dictates the long-term statistical behavior of the system. In this work, we leverage this structure to propose a new framework that targets learning the invariant measure as well as the dynamics, in contrast with typical methods that only target the misfit between trajectories, which often leads to divergence as the trajectories' length increases. We use our framework to propose a tractable and sample efficient objective that can be used with any existing learning objectives. Our Dynamics Stable Learning by Invariant Measure (DySLIM) objective enables model training that achieves better point-wise tracking and long-term statistical accuracy relative to other learning objectives. By targeting the distribution with a scalable regularization term, we hope that this approach can be extended to more complex systems exhibiting slowly-variant distributions, such as weather and climate models., Comment: ICML 2024; Code to reproduce our experiments is available at https://github.com/google-research/swirl-dynamics/tree/main/swirl_dynamics/projects/ergodic

High temperature superconductivity was recently found in the bilayer nickelate $\rm{La}_3 \rm{Ni}_2 \rm{O}_7$ (La327), followed by the discovery of superconductivity in the trilayer $\rm{La}_4 \rm{Ni}_3 \rm{O}_{10}$ (La4310), under high pressure. Through studying the electronic correlation of La4310 with DFT+DMFT, and further comparing it with that of La327, we find that the $e_g$ orbitals of the outer-layer Ni cations in La4310 have a similar (but slightly weaker) electronic correlation to those in La327, in which the electrons behave as a non-Fermi liquid with Hund correlation and linear-in-temperature scattering rate. Our results suggest that the experimentally observed ``strange metal'' behavior may be explained by the Hund spin correlation featuring high spin states and spin-orbital separation. In contrast, the electrons in the inner-layer Ni cations in La4310 behave as a Fermi liquid. The weaker electronic correlation in La4310 is attributed to more hole-doping, which may explain its lower superconducting transition temperature., Comment: 6 pages, 4 figures

Spin-orbit coupling is a key to realize many novel physical effects in condensed matter physics, but the mechanism to achieve strong spin-orbit coupling effect in light element antiferromagnetic compounds has not been explored. In this work, based on symmetry analysis and the first-principles electronic structure calculations, we demonstrate that strong spin-orbit coupling effect can be realized in light element altermagnetic materials, and propose a mechanism for realizing the corresponding effective spin-orbit coupling. This mechanism reveals the cooperative effect of crystal symmetry, electron occupation, electronegativity, electron correlation, and intrinsic spin-orbit coupling. Our work not only promotes the understanding of light element compounds with strong spin-orbit coupling effect, but also provides an alternative for realizing light element compounds with an effective strong spin-orbit coupling., Comment: 5 pages, 4 figures

Self--interactions of dark matter particles impact the distribution of dark matter in halos. The exact nature of the self--interactions can lead to either expansion or collapse of the core within the halo lifetime, leaving distinctive signatures in the dark matter distributions not only at the halo center but throughout the virial region. Optical galaxy surveys, which precisely measure the weak lensing of background galaxies by massive foreground clusters, allow us to directly measure the matter distribution within clusters and probe subtle effects of self--interacting dark matter (SIDM) throughout the halo's full radial range. We compare the weak--lensing measurements reported by Shin et al. 2021, which use lens clusters identified by the Atacama Cosmology Telescope Survey and source galaxies from the Dark Energy Survey, with predictions from SIDM models having either elastic or dissipative self--interactions. To model the weak--lensing observables, we use cosmological N-body simulations for elastic self--interactions and semi-analytical fluid simulations for dissipative self--interactions. We find that current weak--lensing measurements already constrain the isotropic and elastic SIDM to a cross-section per mass of $\sigma/m<1~{\rm cm^2/g}$ at a $95\%$ confidence level. The same measurements also impose novel constraints on the energy loss per unit mass for dissipative SIDM. Upcoming surveys are anticipated to enhance the signal-to-noise of weak--lensing observables significantly making them effective tools for investigating the nature of dark matter, including self--interactions, through weak lensing.

The Galactic Center Excess (GCE) remains an enduring mystery, with leading explanations being annihilating dark matter or an unresolved population of millisecond pulsars. Analyzing the morphology of the GCE provides critical clues to identify its exact origin. We investigate the robustness of the inferred GCE morphology against the effects of masking, an important step in the analysis where the gamma-ray emission from point sources and the galactic disk are excluded. Using different masks constructed from Fermi point source catalogs and a wavelet method, we find that the GCE morphology, particularly its ellipticity and cuspiness, is relatively independent of the choice of mask for energies above 2-3 GeV. The GCE morphology systematically favors an approximately spherical shape, as expected for dark matter annihilation. Compared to various stellar bulge profiles, a spherical dark matter annihilation profile better fits the data across different masks and galactic diffuse emission backgrounds, except for the stellar bulge profile from Coleman et al. (2020), which provides a similar fit to the data. Modeling the GCE with two components, one from dark matter annihilation and one tracing the Coleman Bulge, we find this two-component model outperforms any single component or combinations of dark matter annihilation and other stellar bulge profiles. Uncertainty remains about the exact fraction contributed by each component across different background models and masks. However, when the Coleman Bulge dominates, its corresponding spectrum lacks characteristics typically associated with millisecond pulsars, suggesting that it mostly models the emission from other sources instead of the GCE that is still present and spherically symmetric., Comment: v2 as accepted by PRD, masks available at https://github.com/ymzhong/gce_mask

Altermagnetism is a new magnetic phase with k-dependent spin polarization and may exist in an insulating state with a high N\'eel temperature. This provides a new opportunity to obtain both spin and electric polarization in one material. Here, based on symmetry analysis and the first-principles electronic structures calculations, we predict that LiFe2F6 is a d-wave altermagnetic and charge-ordering-mediated ferroelectric material. Moreover, the LiFe2F6 transforms into a ferrimagnetic and ferroelectric phase with strong magnetoelectric coupling under biaxial compressive strain. Interestingly, the spins of the valence band and the conduction band are opposite in ferrimagnetic LiFe2F6, which facilitates a simultaneous spin-triplet excitonic insulator phase. More importantly, the spin-triplet excitons with spin 1 and -1 can be switched by electric fields in ferrimagnetic LiFe2F6 due to strong magnetoelectric coupling. Due to the abundance of novel physical properties, LiFe2F6 will certainly attract a wide range of theoretical and experimental interest., Comment: 6 pages, 4 figures

Recently, it was found that the vector field can be naturally localized on the thick brane in chameleon gravity. In this work, we extend this study to encompass de Sitter brane scenario. We focus on the localization of q-form fields. The scalar and vector fields can be localized on the de Sitter brane, while the KR field cannot be localized. The condition for localization of the scalar and vector fields is obtained. Furthermore, we investigate the localization characteristics in two examples with given conformal factor $b(\phi)$. In the first case, the effective potentials and KK modes of the matter fields are obtained asymmetric even though the de Sitter brane has $Z_2$ symmetry. In the second case, volcano-like effective potentials are generated in the de Sitter brane model., Comment: 14 pages, 8 figures

By means of density functional theory plus dynamical mean-field theory (DFT+DMFT), we investigate the correlated electronic structures of La$_3$Ni$_2$O$_7$ under high pressure. Our calculations show that La$_3$Ni$_2$O$_7$ is a multi-orbital Hund metal. Both the 3$d_{z^2}$ and 3$d_{x^2 - y^2}$ orbitals of Ni are close to be half filled and contribute the bands across the Fermi level. Band renormalization and orbital selective electronic correlation are observed. Through imaginary-time correlation functions, the discovery of high-spin configuration, spin-frozen phase, and spin-orbital separation shows that the system is in a frozen moment phase at high temperatures above 290 K and is a Fermi liquid at low temperatures, which is further comfirmed by the calculated spin, orbital, and charge susceptibilities under high temperatures. Our study uncovers Hundness in La$_3$Ni$_2$O$_7$ under high pressure., Comment: 6 pages, 5 figures, 2 tables

Altermagnetism, a new magnetic phase, has been theoretically proposed and experimentally verified to be distinct from ferromagnetism and antiferromagnetism. Although altermagnets have been found to possess many exotic physical properties, the limited availability of known altermagnetic materials hinders the study of such properties. Hence, discovering more types of altermagnetic materials with different properties is crucial for a comprehensive understanding of altermagnetism and thus facilitating new applications in the next generation information technologies, e.g., storage devices and high-sensitivity sensors. Since each altermagnetic material has a unique crystal structure, we propose an automated discovery approach empowered by an AI search engine that employs a pre-trained graph neural network to learn the intrinsic features of the material crystal structure, followed by fine-tuning a classifier with limited positive samples to predict the altermagnetism probability of a given material candidate. Finally, we successfully discovered 50 new altermagnetic materials that cover metals, semiconductors, and insulators confirmed by the first-principles electronic structure calculations. The wide range of electronic structural characteristics reveals that various novel physical properties manifest in these newly discovered altermagnetic materials, e.g., anomalous Hall effect, anomalous Kerr effect, and topological property. Noteworthy, we discovered 4 $i$-wave altermagnetic materials for the first time. Overall, the AI search engine performs much better than human experts and suggests a set of new altermagnetic materials with unique properties, outlining its potential for accelerated discovery of the materials with targeted properties., Comment: 46 pages; 23 figures; 4 tables

Exploring various topological states (TS) and topological phase transitions (TPT) has attracted great attention in condensed matter physics. However, so far, there is rarely a typical material system that can be used as a platform to study the TS and TPT as the system transforms from one-dimensional (1D) nanoribbons to two-dimensional (2D) sheet then to three-dimensional (3D) bulk. Here, we first propose that some typical TS in 1D, 2D, and 3D systems can be realized in a tight-binding (TB) model. Following the TB model and further based on first-principles electronic structure calculations, we demonstrate that the structurally stable (4,0) carbon nanotube derivatives are an ideal platform to explore the semiconductor/nodal-point semimetal states in 1D nanoribbons [1D-(4,0)-C16H4 and 1D-(4,0)-C32H4], nodal-ring semimetal state in 2D sheet [2D-(4,0)-C16], and nodal-cage semimetal state in 3D bulk [3D-(4,0)-C16]. Furthermore, we calculate the characteristic band structures and the edge/surface states of 2D-(4,0)-C16 and 3D-(4,0)-C16 to confirm their nontrivial topological properties. Our work not only provides new excellent 2D and 3D members for the topological carbon material family, but also serves as an ideal template for the study of TS and TPT with the change of system dimension., Comment: 17 pages, 7 figures

Alzheimer's disease is a progressive neurological disorder characterized by cognitive impairment and memory loss. With the increasing aging population, the incidence of AD is continuously rising, making early diagnosis and intervention an urgent need. In recent years, a considerable number of teams have applied computer-aided diagnostic techniques to early classification research of AD. Most studies have utilized imaging modalities such as magnetic resonance imaging (MRI), positron emission tomography (PET), and electroencephalogram (EEG). However, there have also been studies that attempted to use other modalities as input features for the models, such as sound, posture, biomarkers, cognitive assessment scores, and their fusion. Experimental results have shown that the combination of multiple modalities often leads to better performance compared to a single modality. Therefore, this paper will focus on different modalities and their fusion, thoroughly elucidate the mechanisms of various modalities, explore which methods should be combined to better harness their utility, analyze and summarize the literature in the field of early classification of AD in recent years, in order to explore more possibilities of modality combinations.

Guitar tablature is a form of music notation widely used among guitarists. It captures not only the musical content of a piece, but also its implementation and ornamentation on the instrument. Guitar Tablature Transcription (GTT) is an important task with broad applications in music education, composition, and entertainment. Existing GTT datasets are quite limited in size and scope, rendering models trained on them prone to overfitting and incapable of generalizing to out-of-domain data. In order to address this issue, we present a methodology for synthesizing large-scale GTT audio using commercial acoustic and electric guitar plugins. We procure SynthTab, a dataset derived from DadaGP, which is a vast and diverse collection of richly annotated symbolic tablature. The proposed synthesis pipeline produces audio which faithfully adheres to the original fingerings and a subset of techniques specified in the tablature, and covers multiple guitars and styles for each track. Experiments show that pre-training a baseline GTT model on SynthTab can improve transcription performance when fine-tuning and testing on an individual dataset. More importantly, cross-dataset experiments show that pre-training significantly mitigates issues with overfitting., Comment: Accepted to ICASSP 2024

Continual learning aims to empower artificial intelligence (AI) with strong adaptability to the real world. For this purpose, a desirable solution should properly balance memory stability with learning plasticity, and acquire sufficient compatibility to capture the observed distributions. Existing advances mainly focus on preserving memory stability to overcome catastrophic forgetting, but remain difficult to flexibly accommodate incremental changes as biological intelligence (BI) does. By modeling a robust Drosophila learning system that actively regulates forgetting with multiple learning modules, here we propose a generic approach that appropriately attenuates old memories in parameter distributions to improve learning plasticity, and accordingly coordinates a multi-learner architecture to ensure solution compatibility. Through extensive theoretical and empirical validation, our approach not only clearly enhances the performance of continual learning, especially over synaptic regularization methods in task-incremental settings, but also potentially advances the understanding of neurological adaptive mechanisms, serving as a novel paradigm to progress AI and BI together.

Quantum interference between identical single particles reveals the intrinsic quantum statistic nature of particles, which could not be interpreted through classical physics. Here, we demonstrate quantum interference between non-identical bosons using a generalized beam splitter based on a quantum memory. The Hong-Ou-Mandel type interference between single photons and single magnons with high visibility is demonstrated, and the crossover from the bosonic to fermionic quantum statistics is observed by tuning the beam splitter to be non-Hermitian. Moreover, multi-particle interference that simulates the behavior of three fermions by three input photons is realized. Our work extends the understanding of the quantum interference effects and demonstrates a versatile experimental platform for studying and engineering quantum statistics of particles., Comment: 6 pages, 4 figures

Possible high-$T_c$ superconductivity (SC) has been found experimentally in the bilayer material La$_3$Ni$_2$O$_7$ under high pressure recently, in which the Ni-$3d_{3z^2-r^2}$ and $3d_{x^2-y^2}$ orbitals are expected to play a key role in the electronic structure and the SC. Here we study the two-orbital electron correlations and the nature of the SC using the bilayer two-orbital Hubbard model downfolded from the band structure of La3Ni2O7 in the framework of the dynamical mean-field theory. We find that each of the two orbitals forms $s_\pm$-wave SC pairing. Because of the nonlocal inter-orbital hoppings, the two-orbital SCs are concomitant and they transition to Mott insulating states simultaneously when tuning the system to half filling. The Hund's coupling induced local inter-orbital spin coupling enhances the electron correlations pronouncedly and is crucial to the SC., Comment: 5 pages, 5 figures

Neural-network quantum states (NQSs), variationally optimized by combining traditional methods and deep learning techniques, is a new way to find quantum many-body ground states and gradually becomes a competitor of traditional variational methods. However, there are still some difficulties in the optimization of NQSs, such as local minima, slow convergence, and sign structure optimization. Here, we split a quantum many-body variational wave function into a multiplication of a real-valued amplitude neural network and a sign structure, and focus on the optimization of the amplitude network while keeping the sign structure fixed. The amplitude network is a convolutional neural network (CNN) with residual blocks, namely a ResNet. Our method is tested on three typical quantum many-body systems. The obtained ground state energies are lower than or comparable to those from traditional variational Monte Carlo (VMC) methods and density matrix renormalization group (DMRG). Surprisingly, for the frustrated Heisenberg $J_1$-$J_2$ model, our results are better than those of the complex-valued CNN in the literature, implying that the sign structure of the complex-valued NQS is difficult to be optimized. We will study the optimization of the sign structure of NQSs in the future., Comment: 9 pages, 3 figures, 4 tables, published version

By taking advantage of the braneworld sum rules, we explore the feasibility of constructing a flat 3-brane scenario consisting solely of positive tension branes in a 5D extension of the Lorentz-violating massive gravity. It is found that the theory supports three distinct brane configurations, one of which is exactly what we expected, consisting solely of two positive tension branes. The cosmological problem of Randall-Sundrum-1 model and the gauge hierarchy problem can be solved in this model simultaneously. Furthermore, the analysis of linear perturbations reveals that the tensor, vector and scalar modes are all massive and share the same mass spectrum, except that the ground state of vector mode is absent. Moreover, the tensor and vector modes are robust, but the scalar mode is ghost-like. Interestingly, even though the Kaluza-Klein gravitons have an extremely small mass splitting scale, an estimation of the effective gravitational potential and production of these gravitons on the brane indicates that the phenomenology of the present model is equivalent to that of the 6D ADD model., Comment: 7 pages and 1 figure, published version

The NASA/DART (Double Asteroid Redirection Test) spacecraft successfully crashed on Dimorphos, the secondary component of the binary (65803) Didymos system. Following the impact, a large dust cloud was released, and a long-lasting dust tail was developed. We have extensively monitored the dust tail from the ground and from the Hubble Space Telescope (HST). We provide a characterization of the ejecta dust properties, i.e., particle size distribution and ejection speeds, ejection geometric parameters, and mass, by combining both observational data sets, and by using Monte Carlo models of the observed dust tail. The differential size distribution function that best fits the imaging data was a broken power-law, having a power index of --2.5 for particles of r$\le$ 3 mm, and of --3.7 for larger particles. The particles range in sizes from 1 $\mu$m up to 5 cm. The ejecta is characterized by two components, depending on velocity and ejection direction. The northern component of the double tail, observed since October 8th 2022, might be associated to a secondary ejection event from impacting debris on Didymos, although it is also possible that this feature results from the binary system dynamics alone. The lower limit to the total dust mass ejected is estimated at $\sim$6$\times$10$^6$ kg, half of this mass being ejected to interplanetary space., Comment: Accepted by Planetary Science Journal, July 7th, 2023

Segmentation of the infected areas of the lung is essential for quantifying the severity of lung disease like pulmonary infections. Existing medical image segmentation methods are almost uni-modal methods based on image. However, these image-only methods tend to produce inaccurate results unless trained with large amounts of annotated data. To overcome this challenge, we propose a language-driven segmentation method that uses text prompt to improve to the segmentation result. Experiments on the QaTa-COV19 dataset indicate that our method improves the Dice score by 6.09% at least compared to the uni-modal methods. Besides, our extended study reveals the flexibility of multi-modal methods in terms of the information granularity of text and demonstrates that multi-modal methods have a significant advantage over image-only methods in terms of the size of training data required., Comment: Provisional Acceptance by MICCAI 2023

We report the radio observations of the eclipsing black widow pulsar J1720-0534, a 3.26 ms pulsar in orbit with a low mass companion of mass 0.029 to 0.034 M$_{\odot}$. We obtain the phase-connected timing ephemeris and polarization profile of this millisecond pulsar (MSP) using the Five-hundred-meter Aperture Spherical Radio Telescope (FAST), the Green Bank Telescope (GBT), and the Parkes Telescope. For the first time from such a system, an oscillatory polarisation angle change was observed from a particular eclipse egress with partial depolarization, indicating 10-milliGauss-level reciprocating magnetic fields oscillating in a length scale of 5000 km (assuming an orbital inclination angle of 90 degrees) outside the companion's magnetosphere. The dispersion measure variation observed during the ingresses and egresses shows the rapid raising of the electron density in the shock boundary between the companion's magnetosphere and the surrounding pulsar wind. We suggest that the observed oscillatory magnetic fields originate from the pulsar wind outside the companion's magnetosphere., Comment: 15 pages, 8 figures, 1 table, accepted by RAA

Very recently, a report on possible room-temperature superconductivity in N-doped lutetium hydrides near 1 GPa pressure has drawn lots of attentions. To date, the superconductivity is not confirmed under relatively low pressure in subsequent studies. Based on the density functional theory first-principles calculations, we extensively investigate the influence of charge doping on the stability and superconductivity of LuH$_3$ at ambient pressure. Although electron doping can not stabilize LuH$_3$, we find that the room-pressure stability of LuH$_3$ can be achieved by doping holes with concentrations in between 0.15-0.30 holes/cell. Moreover, our calculations reveal a positive dependence of superconducting transition temperature on the number of doped holes, with the highest value close to 54 K. These findings suggest that realizing superconductivity in hole-doped LuH$_3$ at ambient pressure is not impossible, although the transition temperature is still far away from the room temperature., Comment: 6 pages, 6 figures

The infinite-layer cuprate $A$CuO$_2$ ($A=$ Ca, Sr, Ba) has the simplest crystal structure among numerous cuprate superconductors and can serve a prototypical system to explore the unconventional superconductivity. Based on the first-principles electronic structure calculations, we have studied the electronic and magnetic properties of the infinite-layer cuprate SrCuO$_{2}$ from a phonon perspective. We find that interesting fluctuations of charges, electrical dipoles, and local magnetic moments can be induced by the zero-point vibrations of phonon modes in SrCuO$_{2}$ upon the hole doping. Among all optical phonon modes of SrCuO$_{2}$ in the antiferromagnetic N\'{e}el state, only the $A_{1}$$_g$ mode that involves the full-breathing O vibrations along the Cu-O bonds can cause significant fluctuations of local magnetic moments on O atoms and dramatic charge redistributions between Cu and O atoms. Notably, due to the zero-point vibration of the $A_{1g}$ mode, both the charge fluctuations on Cu and the electrical dipoles on O show a dome-like evolution with increasing hole doping, quite similar to the experimentally observed behavior of the superconducting $T_c$; in comparison, the fluctuations of local magnetic moments on O display a monotonic enhancement along with the hole doping. Further analyses indicate that around the optimal doping, there exist a large softening in the frequency of the $A_{1g}$ phonon mode and a van Hove singularity in the electronic structure close to the Fermi level, suggesting potential electron-phonon coupling. Our work reveals the important role of the full-breathing O phonon mode playing in the infinite-layer SrCuO$_{2}$, which may provide new insights in understanding the cuprate superconductivity., Comment: 7 pages, 4 figures, 1 table

The presence of a central baryonic potential can have a significant impact on the gravothermal evolution of self-interacting dark matter (SIDM) haloes. We extend a semi-analytical fluid model to incorporate the influence of a static baryonic potential and calibrate it using controlled N-body simulations. We construct benchmark scenarios with varying baryon concentrations and different SIDM models, including constant and velocity-dependent self-interacting cross sections. The presence of the baryonic potential induces changes in SIDM halo properties, including central density, core size, and velocity dispersion, and it accelerates the halo's evolution in both expansion and collapse phases. Furthermore, we observe a quasi-universality in the gravothermal evolution of SIDM haloes with the baryonic potential, resembling a previously known feature in the absence of the baryons. By appropriately rescaling the physical quantities that characterize the SIDM haloes, the evolution of all our benchmark cases exhibits remarkable similarity. Our findings offer a framework for testing SIDM predictions using observations of galactic systems where baryons play a significant dynamical role., Comment: 9 pages + references + appendices, 10 figures, 3 tables; v3: as published in MNRAS

We investigate the electronic and phonon properties of hydrogen sulfide (SH$_3$) under ultrahigh pressure to elucidate the origin of its high-T$_c$ superconductivity. Contrary to the prevailing belief that the metalized S-H $\sigma$ bond is responsible, our analysis, based on the anisotropic Migdal-Eliashberg equation and the crystal orbital Hamilton population (COHP) calculation, reveals that the H-H $\sigma$-antibonding states play a dominant role in the large electron-phonon coupling that leads to the superconducting pairing in SH$_3$. Furthermore, by partially restricting the vibration of S atoms, we demonstrate that the S-H bonds provide subsidiary contributions to the pairing interaction. These findings shed light on the importance of the previously overlooked H-H $\sigma^*$ bonds in driving high-T$_c$ superconductivity in SH$_3$ and offer insights into the relationship between metallic H-H covalent antibonding and high-T$_c$ superconductivity in other hydrogen-rich materials under high pressure., Comment: 11 pages, 9 figures, 59 references

We introduce a data-driven learning framework that assimilates two powerful ideas: ideal large eddy simulation (LES) from turbulence closure modeling and neural stochastic differential equations (SDE) for stochastic modeling. The ideal LES models the LES flow by treating each full-order trajectory as a random realization of the underlying dynamics, as such, the effect of small-scales is marginalized to obtain the deterministic evolution of the LES state. However, ideal LES is analytically intractable. In our work, we use a latent neural SDE to model the evolution of the stochastic process and an encoder-decoder pair for transforming between the latent space and the desired ideal flow field. This stands in sharp contrast to other types of neural parameterization of closure models where each trajectory is treated as a deterministic realization of the dynamics. We show the effectiveness of our approach (niLES - neural ideal LES) on a challenging chaotic dynamical system: Kolmogorov flow at a Reynolds number of 20,000. Compared to competing methods, our method can handle non-uniform geometries using unstructured meshes seamlessly. In particular, niLES leads to trajectories with more accurate statistics and enhances stability, particularly for long-horizon rollouts., Comment: 18 pages