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Dec 17

Solving Navier-Stokes Equations Using Data-free Physics-Informed Neural Networks With Hard Boundary Conditions

In recent years, Physics-Informed Neural Networks (PINNs) have emerged as a powerful and robust framework for solving nonlinear differential equations across a wide range of scientific and engineering disciplines, including biology, geophysics, astrophysics and fluid dynamics. In the PINN framework, the governing partial differential equations, along with initial and boundary conditions, are encoded directly into the loss function, enabling the network to learn solutions that are consistent with the underlying physics. In this work, we employ the PINN framework to solve the dimensionless Navier-Stokes equations for three two-dimensional incompressible, steady, laminar flow problems without using any labeled data. The boundary and initial conditions are enforced in a hard manner, ensuring they are satisfied exactly rather than penalized during training. We validate the PINN predicted velocity profiles, drag coefficients and pressure profiles against the conventional computational fluid dynamics (CFD) simulations for moderate to high values of Reynolds number (Re). It is observed that the PINN predictions show good agreement with the CFD results at lower Re. We also extend our analysis to a transient condition and find that our method is equally capable of simulating complex time-dependent flow dynamics. To quantitatively assess the accuracy, we compute the L_2 normalized error, which lies in the range O(10^{-4}) - O(10^{-1}) for our chosen case studies.

  • 4 authors
·
Nov 18

Robust Neural Rendering in the Wild with Asymmetric Dual 3D Gaussian Splatting

3D reconstruction from in-the-wild images remains a challenging task due to inconsistent lighting conditions and transient distractors. Existing methods typically rely on heuristic strategies to handle the low-quality training data, which often struggle to produce stable and consistent reconstructions, frequently resulting in visual artifacts. In this work, we propose Asymmetric Dual 3DGS, a novel framework that leverages the stochastic nature of these artifacts: they tend to vary across different training runs due to minor randomness. Specifically, our method trains two 3D Gaussian Splatting (3DGS) models in parallel, enforcing a consistency constraint that encourages convergence on reliable scene geometry while suppressing inconsistent artifacts. To prevent the two models from collapsing into similar failure modes due to confirmation bias, we introduce a divergent masking strategy that applies two complementary masks: a multi-cue adaptive mask and a self-supervised soft mask, which leads to an asymmetric training process of the two models, reducing shared error modes. In addition, to improve the efficiency of model training, we introduce a lightweight variant called Dynamic EMA Proxy, which replaces one of the two models with a dynamically updated Exponential Moving Average (EMA) proxy, and employs an alternating masking strategy to preserve divergence. Extensive experiments on challenging real-world datasets demonstrate that our method consistently outperforms existing approaches while achieving high efficiency. Codes and trained models will be released.

  • 5 authors
·
Jun 3 2

Understanding Transformers through the Lens of Pavlovian Conditioning

Transformer architectures have revolutionized artificial intelligence (AI) through their attention mechanisms, yet the computational principles underlying their success remain opaque. We present a novel theoretical framework that reinterprets the core computation of attention as Pavlovian conditioning. Our model finds a direct mathematical analogue in linear attention, which simplifies the analysis of the underlying associative process. We demonstrate that attention's queries, keys, and values can be mapped to the three elements of classical conditioning: test stimuli that probe associations, conditional stimuli (CS) that serve as retrieval cues, and unconditional stimuli (US) that contain response information. Through this lens, we suggest that each attention operation constructs a transient associative memory via a Hebbian rule, where CS-US pairs form dynamic associations that test stimuli can later retrieve. Our framework yields several theoretical insights grounded in this linearized model: (1) a capacity theorem showing that attention heads can store O(d_k) associations before interference degrades retrieval; (2) an error propagation analysis revealing fundamental architectural trade-offs of balancing model depth, width, and head redundancy to maintain reliability; and (3) an understanding of how biologically plausible learning rules could enhance transformer architectures. By establishing this deep connection, we suggest that the success of modern AI may stem not from architectural novelty alone, but from implementing computational principles that biology optimized over millions of years of evolution.

  • 1 authors
·
Aug 5

Analyzing black-hole ringdowns II: data conditioning

Time series data from observations of black hole ringdown gravitational waves are often analyzed in the time domain by using damped sinusoid models with acyclic boundary conditions. Data conditioning operations, including downsampling, filtering, and the choice of data segment duration, reduce the computational cost of such analyses and can improve numerical stability. Here we analyze simulated damped sinsuoid signals to illustrate how data conditioning operations, if not carefully applied, can undesirably alter the analysis' posterior distributions. We discuss how currently implemented downsampling and filtering methods, if applied too aggressively, can introduce systematic errors and skew tests of general relativity. These issues arise because current downsampling and filtering methods do not operate identically on the data and model. Alternative downsampling and filtering methods which identically operate on the data and model may be achievable, but we argue that the current operations can still be implemented safely. We also show that our preferred anti-alias filtering technique, which has an instantaneous frequency-domain response at its roll-off frequency, preserves the structure of posterior distributions better than other commonly used filters with transient frequency-domain responses. Lastly, we highlight that exceptionally long data segments may need to be analyzed in cases where thin lines in the noise power spectral density overlap with central signal frequencies. Our findings may be broadly applicable to any analysis of truncated time domain data with acyclic boundary conditions.

  • 3 authors
·
Oct 3, 2024

CloudFormer: An Attention-based Performance Prediction for Public Clouds with Unknown Workload

Cloud platforms are increasingly relied upon to host diverse, resource-intensive workloads due to their scalability, flexibility, and cost-efficiency. In multi-tenant cloud environments, virtual machines are consolidated on shared physical servers to improve resource utilization. While virtualization guarantees resource partitioning for CPU, memory, and storage, it cannot ensure performance isolation. Competition for shared resources such as last-level cache, memory bandwidth, and network interfaces often leads to severe performance degradation. Existing management techniques, including VM scheduling and resource provisioning, require accurate performance prediction to mitigate interference. However, this remains challenging in public clouds due to the black-box nature of VMs and the highly dynamic nature of workloads. To address these limitations, we propose CloudFormer, a dual-branch Transformer-based model designed to predict VM performance degradation in black-box environments. CloudFormer jointly models temporal dynamics and system-level interactions, leveraging 206 system metrics at one-second resolution across both static and dynamic scenarios. This design enables the model to capture transient interference effects and adapt to varying workload conditions without scenario-specific tuning. Complementing the methodology, we provide a fine-grained dataset that significantly expands the temporal resolution and metric diversity compared to existing benchmarks. Experimental results demonstrate that CloudFormer consistently outperforms state-of-the-art baselines across multiple evaluation metrics, achieving robust generalization across diverse and previously unseen workloads. Notably, CloudFormer attains a mean absolute error (MAE) of just 7.8%, representing a substantial improvement in predictive accuracy and outperforming existing methods at least by 28%.

  • 4 authors
·
Sep 3

SparseGS-W: Sparse-View 3D Gaussian Splatting in the Wild with Generative Priors

Synthesizing novel views of large-scale scenes from unconstrained in-the-wild images is an important but challenging task in computer vision. Existing methods, which optimize per-image appearance and transient occlusion through implicit neural networks from dense training views (approximately 1000 images), struggle to perform effectively under sparse input conditions, resulting in noticeable artifacts. To this end, we propose SparseGS-W, a novel framework based on 3D Gaussian Splatting that enables the reconstruction of complex outdoor scenes and handles occlusions and appearance changes with as few as five training images. We leverage geometric priors and constrained diffusion priors to compensate for the lack of multi-view information from extremely sparse input. Specifically, we propose a plug-and-play Constrained Novel-View Enhancement module to iteratively improve the quality of rendered novel views during the Gaussian optimization process. Furthermore, we propose an Occlusion Handling module, which flexibly removes occlusions utilizing the inherent high-quality inpainting capability of constrained diffusion priors. Both modules are capable of extracting appearance features from any user-provided reference image, enabling flexible modeling of illumination-consistent scenes. Extensive experiments on the PhotoTourism and Tanks and Temples datasets demonstrate that SparseGS-W achieves state-of-the-art performance not only in full-reference metrics, but also in commonly used non-reference metrics such as FID, ClipIQA, and MUSIQ.

  • 5 authors
·
Mar 25

StyledStreets: Multi-style Street Simulator with Spatial and Temporal Consistency

Urban scene reconstruction requires modeling both static infrastructure and dynamic elements while supporting diverse environmental conditions. We present StyledStreets, a multi-style street simulator that achieves instruction-driven scene editing with guaranteed spatial and temporal consistency. Building on a state-of-the-art Gaussian Splatting framework for street scenarios enhanced by our proposed pose optimization and multi-view training, our method enables photorealistic style transfers across seasons, weather conditions, and camera setups through three key innovations: First, a hybrid embedding scheme disentangles persistent scene geometry from transient style attributes, allowing realistic environmental edits while preserving structural integrity. Second, uncertainty-aware rendering mitigates supervision noise from diffusion priors, enabling robust training across extreme style variations. Third, a unified parametric model prevents geometric drift through regularized updates, maintaining multi-view consistency across seven vehicle-mounted cameras. Our framework preserves the original scene's motion patterns and geometric relationships. Qualitative results demonstrate plausible transitions between diverse conditions (snow, sandstorm, night), while quantitative evaluations show state-of-the-art geometric accuracy under style transfers. The approach establishes new capabilities for urban simulation, with applications in autonomous vehicle testing and augmented reality systems requiring reliable environmental consistency. Codes will be publicly available upon publication.

  • 7 authors
·
Mar 26

Flashlights: An Off-Caustic Lensed Star at Redshift z = 1.26 in Abell 370

We report the discovery of a transient seen in a strongly lensed arc at redshift z_{rm s}=1.2567 in Hubble Space Telescope imaging of the Abell 370 galaxy cluster. The transient is detected at 29.51pm0.14 AB mag in a WFC3/UVIS F200LP difference image made using observations from two different epochs, obtained in the framework of the Flashlights program, and is also visible in the F350LP band (m_{rm F350LP} approx 30.53pm0.76 AB mag). The transient is observed on the negative-parity side of the critical curve at a distance of sim 0.6" from it, greater than previous examples of lensed stars. The large distance from the critical curve yields a significantly smaller macromagnification, but our simulations show that bright, O/B-type supergiants can reach sufficiently high magnifications to be seen at the observed position and magnitude. In addition, the observed transient image is a trailing image with an observer-frame time delay of sim+0.8 days from its expected counterpart, so that any transient lasting for longer than that should have also been seen on the minima side and is thus excluded. This, together with the blue colour we measure for the transient (m_{rm F200LP} - m_{rm F350LP} approx [-0.3,-1.6] AB), rules out most other transient candidates such as (kilo)novae, for example, and makes a lensed star the prime candidate. Assuming the transient is indeed a lensed star as suggested, many more such events should be detected in the near future in cluster surveys with the Hubble Space Telescope and James Webb Space Telescope.

  • 13 authors
·
Nov 2, 2022

Understanding the Neutron Star Population with the SKA

Since their discovery in the late 1960's the population of known neutron stars (NSs) has grown to ~2500. The last five decades of observations have yielded many surprises and demonstrated that the observational properties of NSs are remarkably diverse. The surveys that will be performed with SKA (the Square Kilometre Array) will produce a further tenfold increase in the number of Galactic NSs known. Moreover, the SKA's broad spectral coverage, sub-arraying and multi-beaming capabilities will allow us to characterise these sources with unprecedented efficiency, in turn enabling a giant leap in the understanding of their properties. Here we review the NS population and outline our strategies for studying each of the growing number of diverse classes that are populating the "NS zoo". Some of the main scientific questions that will be addressed by the much larger statistical samples and vastly improved timing efficiency provided by SKA include: (i) the spin period and spin-down rate distributions (and thus magnetic fields) at birth, and the associated information about the SNe wherein they are formed; (ii) the radio pulsar-magnetar connection; (iii) the link between normal radio pulsars, intermittent pulsars and rotating radio transients; (iv) the slowest possible spin period for a radio pulsar (revealing the conditions at the pulsar death-line); (v) proper motions of pulsars (revealing SN kick physics); (vi) the mass distribution of NSs (vii) the fastest possible spin period for a recycled pulsar (constraining magnetosphere-accretion disc interactions, gravitational wave radiation and the equation-of-state); (viii) the origin of high eccentricity millisecond pulsars (MSPs); (ix) the formation channels for recently identified triple systems; and finally (x) how isolated MSPs are formed. We expect that the SKA will break new ground unveiling exotic systems that will challenge... [abridged]

  • 12 authors
·
Dec 30, 2014

Real-Time Prediction of Gas Flow Dynamics in Diesel Engines using a Deep Neural Operator Framework

We develop a data-driven deep neural operator framework to approximate multiple output states for a diesel engine and generate real-time predictions with reasonable accuracy. As emission norms become more stringent, the need for fast and accurate models that enable analysis of system behavior have become an essential requirement for system development. The fast transient processes involved in the operation of a combustion engine make it difficult to develop accurate physics-based models for such systems. As an alternative to physics based models, we develop an operator-based regression model (DeepONet) to learn the relevant output states for a mean-value gas flow engine model using the engine operating conditions as input variables. We have adopted a mean-value model as a benchmark for comparison, simulated using Simulink. The developed approach necessitates using the initial conditions of the output states to predict the accurate sequence over the temporal domain. To this end, a sequence-to-sequence approach is embedded into the proposed framework. The accuracy of the model is evaluated by comparing the prediction output to ground truth generated from Simulink model. The maximum mathcal L_2 relative error observed was approximately 6.5%. The sensitivity of the DeepONet model is evaluated under simulated noise conditions and the model shows relatively low sensitivity to noise. The uncertainty in model prediction is further assessed by using a mean ensemble approach. The worst-case error at the (mu + 2sigma) boundary was found to be 12%. The proposed framework provides the ability to predict output states in real-time and enables data-driven learning of complex input-output operator mapping. As a result, this model can be applied during initial development stages, where accurate models may not be available.

  • 4 authors
·
Apr 2, 2023