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We report a novel approach based on the non-equilibrium self-consistent generalized Langevin equation (NESCGLE) theory that allows for the first principles prediction of the zero-shear viscosity in glass- and- gel-forming materials. This new modulus of the NESCGLE theory facilitates the theoretical description and interpretation of experimental data concerning out-of-equilibrium rheological properties of viscous liquids during their amorphous solidification. The predictive capability of our approach is illustrated here by means of a quantitative comparison between theoretical and experimental results for the zero shear viscosity in suspensions of oligomer-tethered nanoparticles in a polymeric host, finding an almost perfect correspondence between experiments and theory. This comparison also highlights the crucial relevance of including a kinetic perspective, such as that provided by the NESCGLE theory, in the description of dynamic and viscoelastic properties of amorphous states of matter.

We propose Diffusion Model Predictive Control (D-MPC), a novel MPC approach that learns a multi-step action proposal and a multi-step dynamics model, both using diffusion models, and combines them for use in online MPC. On the popular D4RL benchmark, we show performance that is significantly better than existing model-based offline planning methods using MPC and competitive with state-of-the-art (SOTA) model-based and model-free reinforcement learning methods. We additionally illustrate D-MPC's ability to optimize novel reward functions at run time and adapt to novel dynamics, and highlight its advantages compared to existing diffusion-based planning baselines., Comment: Preprint

In this work, we present a comprehensive method for determining the dispersion relation in one-dimensional waveguides, applicable to a wide range of structures, regardless of their specific characteristics. This general framework employs a unified mathematical model, referred to as *generalized beams*, where varying types of waveguides and scatterers are incorporated by adjusting certain parameters. The generalized beam consists of a host waveguide, which is a homogeneous elastic structure with physical properties represented in matrix form. The model also accounts for an arbitrary set of scatterers within the unit cell, including resonators (discrete and continuous), small material inclusions, or variations in cross-sectional area. Based on general assumptions, we develop a matrix-based algorithm utilizing the plane wave expansion method to derive the solution. Additionally, we propose an iterative procedure that provides analytical expressions for the first- and second-order terms, particularly useful in the context of weak scattering. The convergence conditions of the method are rigorously defined. The approach's effectiveness is demonstrated through several numerical examples, highlighting its versatility in different waveguide configurations and scattering scenarios.

This work reports the conditions under which weak scattering assumptions can be applied in a beam loaded by multiple resonators supporting both longitudinal and flexural waves. The work derives the equations of motion of a one-dimensional elastic waveguide with several point resonators by utilizing the Green's matrix approach. The derivations include any resonator morphology, either with a discrete or continuous distribution of resonances. The method employed is based on applying multiple scattering theory. The response can be expressed as an infinite series whose convergence is closely linked to the scattering intensity provided by the resonators. The convergence conditions are reduced to studying the spectral radius of the scattering matrix. Furthermore, the the leading order of the multiple scattering expansion is associated with the Born approximation. The work also provides approximate expressions for the spectral radius, offering a physical interpretation to the concept of weak scattering in beams. Several numerical examples are presented to validate the proposed methodology.

Learning from previously collected data via behavioral cloning or offline reinforcement learning (RL) is a powerful recipe for scaling generalist agents by avoiding the need for expensive online learning. Despite strong generalization in some respects, agents are often remarkably brittle to minor visual variations in control-irrelevant factors such as the background or camera viewpoint. In this paper, we present theDeepMind Control Visual Benchmark (DMC-VB), a dataset collected in the DeepMind Control Suite to evaluate the robustness of offline RL agents for solving continuous control tasks from visual input in the presence of visual distractors. In contrast to prior works, our dataset (a) combines locomotion and navigation tasks of varying difficulties, (b) includes static and dynamic visual variations, (c) considers data generated by policies with different skill levels, (d) systematically returns pairs of state and pixel observation, (e) is an order of magnitude larger, and (f) includes tasks with hidden goals. Accompanying our dataset, we propose three benchmarks to evaluate representation learning methods for pretraining, and carry out experiments on several recently proposed methods. First, we find that pretrained representations do not help policy learning on DMC-VB, and we highlight a large representation gap between policies learned on pixel observations and on states. Second, we demonstrate when expert data is limited, policy learning can benefit from representations pretrained on (a) suboptimal data, and (b) tasks with stochastic hidden goals. Our dataset and benchmark code to train and evaluate agents are available at: https://github.com/google-deepmind/dmc_vision_benchmark., Comment: NeurIPS 2024 Datasets and Benchmarks Track. Dataset available at: https://github.com/google-deepmind/dmc_vision_benchmark

We prove that under some extra hypothesis, given an \'etale endomorphism of a normal irreducible Noetherian and simply connected scheme, if the endomorphism is surjective then it is injective. The additional assumption concerns the possibility of constructing an \'etale cover out of a surjective \'etale morphism. We show that in some cases the surjectivity hypothesis can be removed if the intended \'etale cover is Galois., Comment: Theorem 2 of the previous version is incorrect

We explore full-shape analysis with simulation-based priors, which is the simplest approach to galaxy clustering data analysis that combines effective field theory (EFT) on large scales and numerical simulations on small scales. The core ingredient of our approach is the prior density of EFT parameters which we extract from a suite of 10500 galaxy simulations based on the halo occupation distribution (HOD) model. We measure the EFT parameters with the field-level forward model, which enables us to cancel cosmic variance. On the theory side, we develop a new efficient approach to calculate field-level transfer functions using time-sliced perturbation theory and the logarithmic fast Fourier transform. We study cosmology dependence of EFT parameters of dark matter halos and HOD galaxies and find that it can be ignored for the purpose of prior generation. We use neural density estimation to model the measured distribution of EFT parameters. Our distribution model is then used as a prior in a reanalysis of the BOSS full-shape galaxy power spectrum data. Assuming the $\Lambda$CDM model, we find significant ($\approx 30\%$ and $\approx 60\%$) improvements for the matter density fraction and the mass fluctuation amplitude, which are constrained to $\Omega_m= 0.315 \pm 0.010$ and $\sigma_8 = 0.671 \pm 0.027$. The value of the Hubble constant does not change, $H_0= 68.7\pm 1.1$ km/s/Mpc. This reaffirms earlier reports of the structure growth tension from the BOSS data. Finally, we use the measured EFT parameters to constrain galaxy formation physics., Comment: 40 pages, 14 figs

The connection between galaxies and their host dark matter (DM) halos is critical to our understanding of cosmology, galaxy formation, and DM physics. To maximize the return of upcoming cosmological surveys, we need an accurate way to model this complex relationship. Many techniques have been developed to model this connection, from Halo Occupation Distribution (HOD) to empirical and semi-analytic models to hydrodynamic. Hydrodynamic simulations can incorporate more detailed astrophysical processes but are computationally expensive; HODs, on the other hand, are computationally cheap but have limited accuracy. In this work, we present NeHOD, a generative framework based on variational diffusion model and Transformer, for painting galaxies/subhalos on top of DM with an accuracy of hydrodynamic simulations but at a computational cost similar to HOD. By modeling galaxies/subhalos as point clouds, instead of binning or voxelization, we can resolve small spatial scales down to the resolution of the simulations. For each halo, NeHOD predicts the positions, velocities, masses, and concentrations of its central and satellite galaxies. We train NeHOD on the TNG-Warm DM suite of the DREAMS project, which consists of 1024 high-resolution zoom-in hydrodynamic simulations of Milky Way-mass halos with varying warm DM mass and astrophysical parameters. We show that our model captures the complex relationships between subhalo properties as a function of the simulation parameters, including the mass functions, stellar-halo mass relations, concentration-mass relations, and spatial clustering. Our method can be used for a large variety of downstream applications, from galaxy clustering to strong lensing studies., Comment: Submitted to ApJ; 30 + 6 pages; 11 + 4 figures; Comments welcomed

A major aim of current and upcoming cosmological surveys is testing deviations from the standard $\Lambda$CDM model, but the full scientific value of these surveys will only be realised through efficient simulation methods that keep up with the increasing volume and precision of observational data. $N$-body simulations of modified gravity (MG) theories are computationally expensive since highly non-linear equations need to be solved to model the non-linear matter evolution; this represents a significant bottleneck in the path to reach the data volume and resolution attained by equivalent $\Lambda$CDM simulations. We develop a field-level, neural-network-based emulator that generates density and velocity divergence fields under the $f(R)$ gravity MG model from the corresponding $\Lambda$CDM simulated fields. Using attention mechanisms and a complementary frequency-based loss function, our model is able to learn this intricate mapping. We further use the idea of latent space extrapolation to generalise our emulator to $f(R)$ models with differing field strengths. The predictions of our emulator agree with the $f(R)$ simulations to within 5% for matter density and to within 10% for velocity divergence power spectra up to $k \sim 2\,h$ $\mathrm{Mpc}^{-1}$. But for a few select cases, higher-order statistics are reproduced with $\lesssim$10% agreement with the $f(R)$ simulations. Latent extrapolation allows our emulator to generalise to different $f(R)$ model variants without explicitly training on those variants. Given a $\Lambda$CDM simulation, the GPU-based emulator is able to reproduce the equivalent $f(R)$ realisation $\sim$600 times faster than full $N$-body simulations. This lays the foundations for a valuable tool for realistic yet rapid mock field generation and robust cosmological analyses., Comment: 20 pages, 10 figures. To be submitted to MNRAS

Simultaneous Localization and Mapping (SLAM) is an essential component of autonomous robotic applications and self-driving vehicles, enabling them to understand and operate in their environment. Many SLAM systems have been proposed in the last decade, but they are often complex to adapt to different settings or sensor setups. In this work, we present LiDAR Graph-SLAM (LG-SLAM), a versatile range-inertial SLAM framework that can be adapted to different types of sensors and environments, from underground mines to offices with minimal parameter tuning. Our system integrates range, inertial and GNSS measurements into a graph-based optimization framework. We also use a refined submap management approach and a robust loop closure method that effectively accounts for uncertainty in the identification and validation of putative loop closures, ensuring global consistency and robustness. Enabled by a parallelized architecture and GPU integration, our system achieves pose estimation at LiDAR frame rate, along with online loop closing and graph optimization. We validate our system in diverse environments using public datasets and real-world data, consistently achieving an average error below 20 cm and outperforming other state-of-the-art algorithms., Comment: 8 pages, 8 figures, 3 tables

We propose an approach to simulating trajectories of multiple interacting agents (road users) based on transformers and probabilistic graphical models (PGMs), and apply it to the Waymo SimAgents challenge. The transformer baseline is based on the MTR model, which predicts multiple future trajectories conditioned on the past trajectories and static road layout features. We then improve upon these generated trajectories using a PGM, which contains factors which encode prior knowledge, such as a preference for smooth trajectories, and avoidance of collisions with static obstacles and other moving agents. We perform (approximate) MAP inference in this PGM using the Gauss-Newton method. Finally we sample $K=32$ trajectories for each of the $N \sim 100$ agents for the next $T=8 \Delta$ time steps, where $\Delta=10$ is the sampling rate per second. Following the Model Predictive Control (MPC) paradigm, we only return the first element of our forecasted trajectories at each step, and then we replan, so that the simulation can constantly adapt to its changing environment. We therefore call our approach "Model Predictive Simulation" or MPS. We show that MPS improves upon the MTR baseline, especially in safety critical metrics such as collision rate. Furthermore, our approach is compatible with any underlying forecasting model, and does not require extra training, so we believe it is a valuable contribution to the community., Comment: Special Mention at the Waymo Sim Agents Challenge 2024

Multiple types of inference are available for probabilistic graphical models, e.g., marginal, maximum-a-posteriori, and even marginal maximum-a-posteriori. Which one do researchers mean when they talk about "planning as inference"? There is no consistency in the literature, different types are used, and their ability to do planning is further entangled with specific approximations or additional constraints. In this work we use the variational framework to show that all commonly used types of inference correspond to different weightings of the entropy terms in the variational problem, and that planning corresponds _exactly_ to a _different_ set of weights. This means that all the tricks of variational inference are readily applicable to planning. We develop an analogue of loopy belief propagation that allows us to perform approximate planning in factored state Markov decisions processes without incurring intractability due to the exponentially large state space. The variational perspective shows that the previous types of inference for planning are only adequate in environments with low stochasticity, and allows us to characterize each type by its own merits, disentangling the type of inference from the additional approximations that its practical use requires. We validate these results empirically on synthetic MDPs and tasks posed in the International Planning Competition., Comment: Corrected fontsize in Fig. 1. No other changes

Recent studies using four-point correlations suggest a parity violation in the galaxy distribution, though the significance of these detections is sensitive to the choice of simulation used to model the noise properties of the galaxy distribution. In a recent paper, we introduce an unsupervised learning approach which offers an alternative method that avoids the dependence on mock catalogs, by learning parity violation directly from observational data. However, the Convolutional Neural Network (CNN) model utilized by our previous unsupervised approach struggles to extend to more realistic scenarios where data is limited. We propose a novel method, the Neural Field Scattering Transform (NFST), which enhances the Wavelet Scattering Transform (WST) technique by adding trainable filters, parameterized as a neural field. We first tune the NFST model to detect parity violation in a simplified dataset, then compare its performance against WST and CNN benchmarks across varied training set sizes. We find the NFST can detect parity violation with $4\times$ less data than the CNN and $32\times$ less than the WST. Furthermore, in cases with limited data the NFST can detect parity violation with up to $6\sigma$ confidence, where the WST and CNN fail to make any detection. We identify that the added flexibility of the NFST, and particularly the ability to learn asymmetric filters, as well as the specific symmetries built into the NFST architecture, contribute to its improved performance over the benchmark models. We further demonstrate that the NFST is readily interpretable, which is valuable for physical applications such as the detection of parity violation.

In magnetized plasmas, a radial gradient of parallel velocity, where parallel refers to the direction of magnetic field, can destabilise an electrostatic mode called as Parallel Velocity Gradient (PVG). The theory of PVG has been mainly developed assuming a single species of ions. Here, the role of impurities is investigated based on a linear, local analysis, in a homogeneous, constant magnetic field. To further simplify the analysis, the plasma is assumed to contain only two ion species - main ions and one impurity species - while our methodology can be straightforwardly extended to more species. In the cold-ion limit, retaining polarization drift for both main ions and impurity ions, and assuming Boltzmann electrons, the system is described by 4 fluid equations closed by quasi-neutrality. The linearized equations can be reduced to 2 coupled equations: one for the electric potential, and one for the effective parallel velocity fluctuations, which is a linear combination of main ion and impurity parallel velocity fluctuations. This reduced system can be understood as a generalisation of the Hasegawa-Mima model. With finite radial gradient of impurity parallel flow, the linear dispersion relation then describes a new instability: the impurity-modified PVG (i-PVG). Instability condition is described in terms of either the main ion flow shear, or equivalently, an effective flow shear, which combines main ion and impurity flow shears. Impurities can have a stabilising or destabilising role, depending on the parameters, and in particular the direction of main flow shear against impurity flow shear. Assuming a reasonable value of perpendicular wavenumber, the maximum growth rate is estimated, depending on impurity mass, charge, and concentration., Comment: 18 pages, 12 figures. Modifications in v2: language errors corrected, model's limits highlighted and discussed (pages 5 and 17)

Tattoos have been used effectively as soft biometrics to assist law enforcement in the identification of offenders and victims, as they contain discriminative information, and are a useful indicator to locate members of a criminal gang or organisation. Due to various privacy issues in the acquisition of images containing tattoos, only a limited number of databases exists. This lack of databases has delayed the development of new methods to effectively retrieve a potential suspect's tattoo images from a candidate gallery. To mitigate this issue, in our work, we use an unsupervised generative approach to create a balanced database consisting of 28,550 semi-synthetic images with tattooed subjects from 571 tattoo categories. Further, we introduce a novel Tattoo Template Reconstruction Network (TattTRN), which learns to map the input tattoo sample to its respective tattoo template to enhance the distinguishing attributes of the final feature embedding. Experimental results with real data, i.e., WebTattoo and BIVTatt databases, demonstrate the soundness of the presented approach: an accuracy of up to 99% is achieved for checking at most the first 20 entries of the candidate list., Comment: Accepted at CVPR Workshop 2024

The way heuristic optimizers are designed has evolved over the decades, as computing power has increased. Such has been the case for the Linear Ordering Problem (LOP), a field in which trajectory-based strategies led the way during the 1990s, but which have now been surpassed by memetic schemes.This paper focuses on understanding how the design of LOP optimizers will change in the future, as computing power continues to increase, yielding two main contributions.On the one hand, a metaheuristic was designed that is capable of effectively exploiting a large amount of computational resources, specifically, computing power equivalent to what a recent core can output during runs lasting over four months.Our analyses show that as the power of the computational resources increases, it will be necessary to boost the capacities of the intensification methods applied in the memetic algorithms to keep the population from stagnating.And on the other, the best-known results for today's most challenging set of instances (xLOLIB2) were significantly outperformed. New bounds were established in this benchmark, which provides a new frame of reference for future research.

Diffusion generative models have excelled at diverse image generation and reconstruction tasks across fields. A less explored avenue is their application to discriminative tasks involving regression or classification problems. The cornerstone of modern cosmology is the ability to generate predictions for observed astrophysical fields from theory and constrain physical models from observations using these predictions. This work uses a single diffusion generative model to address these interlinked objectives -- as a surrogate model or emulator for cold dark matter density fields conditional on input cosmological parameters, and as a parameter inference model that solves the inverse problem of constraining the cosmological parameters of an input field. The model is able to emulate fields with summary statistics consistent with those of the simulated target distribution. We then leverage the approximate likelihood of the diffusion generative model to derive tight constraints on cosmology by using the Hamiltonian Monte Carlo method to sample the posterior on cosmological parameters for a given test image. Finally, we demonstrate that this parameter inference approach is more robust to the addition of noise than baseline parameter inference networks., Comment: 14 pages, 10 figures

Localization in already mapped environments is a critical component in many robotics and automotive applications, where previously acquired information can be exploited along with sensor fusion to provide robust and accurate localization estimates. In this work, we offer a new perspective on map-based localization by reusing prior topological and metric information. Thus, we reformulate this long-studied problem to go beyond the mere use of metric maps. Our framework seamlessly integrates LiDAR, inertial and GNSS measurements, and cloud-to-map registrations in a sliding window graph fashion, which allows to accommodate the uncertainty of each observation. The modularity of our framework allows it to work with different sensor configurations (e.g., LiDAR resolutions, GNSS denial) and environmental conditions (e.g., mapless regions, large environments). We have conducted several validation experiments, including the deployment in a real-world automotive application, demonstrating the accuracy, efficiency, and versatility of our system in online localization., Comment: 8 pages

We propose a new model to approximate the wave response of waveguides containing an arbitrary number of small inclusions. The theory is developed to consider any one-dimensional waveguide (longitudinal, flexural, shear, torsional waves or a combination of them by mechanical coupling), containing small inclusions with different material and/or sectional properties. The exact problem is modelled through the formalism of generalised functions, with the Heaviside function accounting for the discontinuous jump in different sectional properties of the inclusions. For asymptotically small inclusions, the exact solution is shown to be equivalent to the Green's function. We hypothesize that these expressions are also valid when the size of the inclusions are small in comparison to the wavelength, allowing us to approximate small inhomogeneities as regular perturbations to the empty-waveguide (the homogeneous waveguide in the absence of scatterers) as point source terms. By approximating solutions through the Green's function, the multiple scattering problem is considerably simplified, allowing us to develop a general methodology in which the solution is expressed for any model for any elastic waveguide. The advantage of our approach is that, by expressing the constitutive equations in first order form as a matrix, the solutions can be expressed in matrix form; therefore, it is trivial to consider models with more degrees of freedom and to arrive at solutions to multiple scattering problems independent of the elastic model used. The theory is validated with two numerical examples, where we perform an error analysis to demonstrate the validity of the approximate solutions, and we propose a parameter quantifying the expected errors in the approximation dependent upon the parameters of the waveguide.

The last few years have seen the emergence of a wide array of novel techniques for analyzing high-precision data from upcoming galaxy surveys, which aim to extend the statistical analysis of galaxy clustering data beyond the linear regime and the canonical two-point (2pt) statistics. We test and benchmark some of these new techniques in a community data challenge "Beyond-2pt", initiated during the Aspen 2022 Summer Program "Large-Scale Structure Cosmology beyond 2-Point Statistics," whose first round of results we present here. The challenge dataset consists of high-precision mock galaxy catalogs for clustering in real space, redshift space, and on a light cone. Participants in the challenge have developed end-to-end pipelines to analyze mock catalogs and extract unknown ("masked") cosmological parameters of the underlying $\Lambda$CDM models with their methods. The methods represented are density-split clustering, nearest neighbor statistics, BACCO power spectrum emulator, void statistics, LEFTfield field-level inference using effective field theory (EFT), and joint power spectrum and bispectrum analyses using both EFT and simulation-based inference. In this work, we review the results of the challenge, focusing on problems solved, lessons learned, and future research needed to perfect the emerging beyond-2pt approaches. The unbiased parameter recovery demonstrated in this challenge by multiple statistics and the associated modeling and inference frameworks supports the credibility of cosmology constraints from these methods. The challenge data set is publicly available and we welcome future submissions from methods that are not yet represented., Comment: New submissions welcome! Challenge data available at https://github.com/ANSalcedo/Beyond2ptMock

We investigate the age of information (AoI) in a scenario where energy-harvesting devices send status updates to a gateway following the slotted ALOHA protocol and receive no feedback. We let the devices adjust the transmission probabilities based on their current battery level. Using a Markovian analysis, we derive analytically the average AoI. We further provide an approximate analysis for accurate and easy-to-compute approximations of both the average AoI and the age-violation probability (AVP), i.e., the probability that the AoI exceeds a given threshold. We also analyze the average throughput. Via numerical results, we investigate two baseline strategies: transmit a new update whenever possible to exploit every opportunity to reduce the AoI, and transmit only when sufficient energy is available to increase the chance of successful decoding. The two strategies are beneficial for low and high update-generation rates, respectively. We show that an optimized policy that balances the two strategies outperforms them significantly in terms of both AoI metrics and throughput. Finally, we show the benefit of decoding multiple packets in a slot using successive interference cancellation and adapting the transmission probability based on both the current battery level and the time elapsed since the last transmission., Comment: Submitted to IEEE Transaction of Communications. A short version [arXiv:[2310.00348] was presented at GLOBECOM 2023. Simulation code: https://github.com/khachoang1412/AoI_slottedALOHA_energyHarvesting. arXiv admin note: text overlap with arXiv:2310.00348

Despite its amazing quantitative successes and contributions to revolutionary technologies, physics currently faces many unsolved mysteries ranging from the meaning of quantum mechanics to the nature of the dark energy that will determine the future of the Universe. It is clearly prohibitive for the general reader, and even the best informed physicists, to follow the vast number of technical papers published in the thousands of specialized journals. For this reason, we have asked the leading experts across many of the most important areas of physics to summarise their global assessment of some of the most important issues. In lieu of an extremely long abstract summarising the contents, we invite the reader to look at the section headings and their authors, and then to indulge in a feast of stimulating topics spanning the current frontiers of fundamental physics from The Future of Physics by William D Phillips and What characterises topological effects in physics? by Gerard t Hooft through the contributions of the widest imaginable range of world leaders in their respective areas. This paper is presented as a preface to exciting developments by senior and young scientists in the years that lie ahead, and a complement to the less authoritative popular accounts by journalists., Comment: 54 pages, 13 figures

Galaxies are biased tracers of the underlying cosmic web, which is dominated by dark matter components that cannot be directly observed. Galaxy formation simulations can be used to study the relationship between dark matter density fields and galaxy distributions. However, this relationship can be sensitive to assumptions in cosmology and astrophysical processes embedded in the galaxy formation models, that remain uncertain in many aspects. In this work, we develop a diffusion generative model to reconstruct dark matter fields from galaxies. The diffusion model is trained on the CAMELS simulation suite that contains thousands of state-of-the-art galaxy formation simulations with varying cosmological parameters and sub-grid astrophysics. We demonstrate that the diffusion model can predict the unbiased posterior distribution of the underlying dark matter fields from the given stellar mass fields, while being able to marginalize over uncertainties in cosmological and astrophysical models. Interestingly, the model generalizes to simulation volumes approximately 500 times larger than those it was trained on, and across different galaxy formation models. Code for reproducing these results can be found at https://github.com/victoriaono/variational-diffusion-cdm

Motivated by a valuation theorem, recently obtained by Rangachev, we study the \'etale extensions $A\subset B$ of polynomial rings over an algebraically closed field of characteristic zero, such that the integral closure $\overline{A}$ is a primary $\overline{A}$-submodule of $B$. We prove that in this case $\overline{A}$ has infinite cyclic divisor class group, where the generator is a prime divisor equal to the complement of $\textrm{Spec}(B)$ in $\textrm{Spec}(\overline{A})$. Moreover, this prime divisor coincides with the ramification divisor of the finite extension $A\subset \overline{A}$. In this situation we carry out Wright's geometric approach for two-dimensional non-integral \'etale extensions. It follows from the work of Miyanishi that $\textrm{Spec}(\overline{A})$ is a smooth affine surface. We show that $\textrm{Spec}(\overline{A})$ is an $\mathbb{A}^{1}$-bundle over $\mathbb{P}^{1}$, more precisely a Danilov-Gizatullin surface of index three. Based on Wright's analysis of which of these affine surfaces can factorize an \'etale morphism of the complex affine plane and his description of its affine coordinate rings, we prove that under the strong assumption that $\overline{A}$ is always a primary $\overline{A}$-submodule of $B$, any two-dimensional complex \'etale extension is integral., Comment: 7 pages. The Lemma 2.3 in the previous version was wrong. We have conditioned the results accordingly