Daily Papers

The widespread use of neural surrogates in automotive aerodynamics, enabled by datasets such as DrivAerML and DrivAerNet++, has primarily focused on bluff-body flows with large wakes. Extending these methods to aerospace, particularly in the transonic regime, remains challenging due to the high level of non-linearity of compressible flows and 3D effects such as wingtip vortices. Existing aerospace datasets predominantly focus on 2D airfoils, neglecting these critical 3D phenomena. To address this gap, we present a new dataset of CFD simulations for 3D wings in the transonic regime. The dataset comprises volumetric and surface-level fields for around 30,000 samples with unique geometry and inflow conditions. This allows computation of lift and drag coefficients, providing a foundation for data-driven aerodynamic optimization of the drag-lift Pareto front. We evaluate several state-of-the-art neural surrogates on our dataset, including Transolver and AB-UPT, focusing on their out-of-distribution (OOD) generalization over geometry and inflow variations. AB-UPT demonstrates strong performance for transonic flowfields and reproduces physically consistent drag-lift Pareto fronts even for unseen wing configurations. Our results demonstrate that AB-UPT can approximate drag-lift Pareto fronts for unseen geometries, highlighting its potential as an efficient and effective tool for rapid aerodynamic design exploration. To facilitate future research, we open-source our dataset at https://huggingface.co/datasets/EmmiAI/Emmi-Wing.

This paper presents a methodology to learn surrogate models of steady state fluid dynamics simulations on meshed domains, based on Implicit Neural Representations (INRs). The proposed models can be applied directly to unstructured domains for different flow conditions, handle non-parametric 3D geometric variations, and generalize to unseen shapes at test time. The coordinate-based formulation naturally leads to robustness with respect to discretization, allowing an excellent trade-off between computational cost (memory footprint and training time) and accuracy. The method is demonstrated on two industrially relevant applications: a RANS dataset of the two-dimensional compressible flow over a transonic airfoil and a dataset of the surface pressure distribution over 3D wings, including shape, inflow condition, and control surface deflection variations. On the considered test cases, our approach achieves a more than three times lower test error and significantly improves generalization error on unseen geometries compared to state-of-the-art Graph Neural Network architectures. Remarkably, the method can perform inference five order of magnitude faster than the high fidelity solver on the RANS transonic airfoil dataset. Code is available at https://gitlab.isae-supaero.fr/gi.catalani/aero-nepf

We prove a new existence theorem for proper solutions of Huisken and Ilmanen's weak inverse mean curvature flow, assuming certain non-degeneracy conditions on the isoperimetric profile. In particular, no curvature assumption is imposed in our existence theorem.

We consider a Schr\"odinger-Poisson system involving a general nonlinearity at critical growth and we prove the existence of positive solutions. The Ambrosetti-Rabinowitz condition is not required. We also study the asymptotics of solutions with respect to a parameter.

Unconditional flow-matching trains diffusion models to transport samples from a source distribution to a target distribution by enforcing that the flows between sample pairs are unique. However, in conditional settings (e.g., class-conditioned models), this uniqueness is no longer guaranteed--flows from different conditions may overlap, leading to more ambiguous generations. We introduce Contrastive Flow Matching, an extension to the flow matching objective that explicitly enforces uniqueness across all conditional flows, enhancing condition separation. Our approach adds a contrastive objective that maximizes dissimilarities between predicted flows from arbitrary sample pairs. We validate Contrastive Flow Matching by conducting extensive experiments across varying model architectures on both class-conditioned (ImageNet-1k) and text-to-image (CC3M) benchmarks. Notably, we find that training models with Contrastive Flow Matching (1) improves training speed by a factor of up to 9x, (2) requires up to 5x fewer de-noising steps and (3) lowers FID by up to 8.9 compared to training the same models with flow matching. We release our code at: https://github.com/gstoica27/DeltaFM.git.

The Earth's atmosphere is an aerosol, it contains suspended particles. When air flows over an obstacle such as an aircraft wing or tree branch, these particles may not follow the same paths as the air flowing around the obstacle. Instead the particles in the air may deviate from the path of the air and so collide with the surface of the obstacle. It is known that particle inertia can drive this deposition, and that there is a critical value of this inertia, below which no point particles deposit. Particle inertia is measured by the Stokes number, St. We show that near the critical value of the Stokes number, St_c, the amount of deposition has the unusual scaling law of exp(-1/(St-St_c)^{1/2}). The scaling is controlled by the stagnation point of the flow. This scaling is determined by the time for the particle to reach the surface of the cylinder varying as 1/(St-St_c)^{1/2}, together with the distance away from the stagnation point (perpendicular to the flow direction) increasing exponentially with time. The scaling law applies to inviscid flow, a model for flow at high Reynolds numbers. The unusual scaling means that the amount of particles deposited increases only very slowly above the critical Stokes number. This has consequences for applications ranging from rime formation and fog harvesting to pollination.

We present Piecewise Rectified Flow (PeRFlow), a flow-based method for accelerating diffusion models. PeRFlow divides the sampling process of generative flows into several time windows and straightens the trajectories in each interval via the reflow operation, thereby approaching piecewise linear flows. PeRFlow achieves superior performance in a few-step generation. Moreover, through dedicated parameterizations, the obtained PeRFlow models show advantageous transfer ability, serving as universal plug-and-play accelerators that are compatible with various workflows based on the pre-trained diffusion models. The implementations of training and inference are fully open-sourced. https://github.com/magic-research/piecewise-rectified-flow

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.

It is well known that the reversibility of Stokes flow makes it difficult for small microorganisms to swim. Inertial effects break this reversibility, allowing new mechanisms of propulsion and feeding. Therefore it is important to understand the effects of unsteady and fluid inertia on the dynamics of microorganisms in flow. In this work, we show how to translate known inertial effects for non-motile organisms to motile ones, from passive to active particles. The method relies on a principle used earlier by Legendre and Magnaudet (1997) to deduce inertial corrections to the lift force on a bubble from the inertial drag on a solid sphere, using the fact that small inertial effects are determined by the far field of the disturbance flow. The method allows for example to compute the inertial effect of unsteady fluid accelerations on motile organisms, and the inertial forces such organisms experience in steady shear flow. We explain why the method fails to describe the effect of convective fluid inertia.

Conditional generative modeling aims to learn a conditional data distribution from samples containing data-condition pairs. For this, diffusion and flow-based methods have attained compelling results. These methods use a learned (flow) model to transport an initial standard Gaussian noise that ignores the condition to the conditional data distribution. The model is hence required to learn both mass transport and conditional injection. To ease the demand on the model, we propose Condition-Aware Reparameterization for Flow Matching (CAR-Flow) -- a lightweight, learned shift that conditions the source, the target, or both distributions. By relocating these distributions, CAR-Flow shortens the probability path the model must learn, leading to faster training in practice. On low-dimensional synthetic data, we visualize and quantify the effects of CAR. On higher-dimensional natural image data (ImageNet-256), equipping SiT-XL/2 with CAR-Flow reduces FID from 2.07 to 1.68, while introducing less than 0.6% additional parameters.

We present Inferflow, an efficient and highly configurable inference engine for large language models (LLMs). With Inferflow, users can serve most of the common transformer models by simply modifying some lines in corresponding configuration files, without writing a single line of source code. Compared with most existing inference engines, Inferflow has some key features. First, by implementing a modular framework of atomic build-blocks and technologies, Inferflow is compositionally generalizable to new models. Second, 3.5-bit quantization is introduced in Inferflow as a tradeoff between 3-bit and 4-bit quantization. Third, hybrid model partitioning for multi-GPU inference is introduced in Inferflow to better balance inference speed and throughput than the existing partition-by-layer and partition-by-tensor strategies.

We study a discrete model for generalized exchange-driven growth in which the particle exchanged between two clusters is not limited to be of size one. This set of models include as special cases the usual exchange-driven growth system and the coagulation-fragmentation system with binary fragmentation. Under reasonable general condition on the rate coefficients we establish the existence of admissible solutions, meaning solutions that are obtained as appropriate limit of solutions to a finite-dimensional truncation of the infinite-dimensional ODE. For these solutions we prove that, in the class of models we call isolated both the total number of particles and the total mass are conserved, whereas in those models we can non-isolated only the mass is conserved. Additionally, under more restrictive growth conditions for the rate equations we obtain uniqueness of solutions to the initial value problems.

We introduce Lagrangian Flow Networks (LFlows) for modeling fluid densities and velocities continuously in space and time. By construction, the proposed LFlows satisfy the continuity equation, a PDE describing mass conservation in its differentiable form. Our model is based on the insight that solutions to the continuity equation can be expressed as time-dependent density transformations via differentiable and invertible maps. This follows from classical theory of the existence and uniqueness of Lagrangian flows for smooth vector fields. Hence, we model fluid densities by transforming a base density with parameterized diffeomorphisms conditioned on time. The key benefit compared to methods relying on numerical ODE solvers or PINNs is that the analytic expression of the velocity is always consistent with changes in density. Furthermore, we require neither expensive numerical solvers, nor additional penalties to enforce the PDE. LFlows show higher predictive accuracy in density modeling tasks compared to competing models in 2D and 3D, while being computationally efficient. As a real-world application, we model bird migration based on sparse weather radar measurements.

In an experiment on a turbulent jet, we detect interfacial turbulent layers in a frame that moves, on average, along with the \tnti. This significantly prolongs the observation time of scalar and velocity structures and enables the measurement of two types of Lagrangian coherent structures. One structure, the finite-time Lyapunov field (FTLE), quantifies advective transport barriers of fluid parcels while the other structure highlights barriers of diffusive momentum transport. These two complementary structures depend on large-scale and small-scale motion and are therefore associated with the growth of the turbulent region through engulfment or nibbling, respectively. We detect the \tnti\ from cluster analysis, where we divide the measured scalar field into four clusters. Not only the \tnti\ can be found this way, but also the next, internal, turbulent-turbulent interface. Conditional averages show that these interfaces are correlated with barriers of advective and diffusive transport when the Lagrangian integration time is smaller than the integral time scale. Diffusive structures decorrelate faster since they have a smaller timescale. Conditional averages of these structures at internal turbulent-turbulent interfaces show the same pattern with a more pronounced jump at the interface indicative of a shear layer. This is quite an unexpected outcome, as the internal interface is now defined not by the presence or absence of vorticity, but by conditional vorticity corresponding to two uniform concentration zones. The long-time diffusive momentum flux along Lagrangian paths represents the growth of the turbulent flow into the irrotational domain, a direct demonstration of nibbling. The diffusive flux parallel to the \tnti\ appears to be concentrated in a diffusive superlayer whose width is comparable with the Taylor microscale, which is relatively invariant in time.

Flow matching has recently emerged as a powerful alternative to diffusion models, providing a continuous-time formulation for generative modeling and representation learning. Yet, we show that this framework suffers from a fundamental instability in the low-noise regime. As noise levels approach zero, arbitrarily small perturbations in the input can induce large variations in the velocity target, causing the condition number of the learning problem to diverge. This ill-conditioning not only slows optimization but also forces the encoder to reallocate its limited Jacobian capacity toward noise directions, thereby degrading semantic representations. We provide the first theoretical analysis of this phenomenon, which we term the low-noise pathology, establishing its intrinsic link to the structure of the flow matching objective. Building on these insights, we propose Local Contrastive Flow (LCF), a hybrid training protocol that replaces direct velocity regression with contrastive feature alignment at small noise levels, while retaining standard flow matching at moderate and high noise. Empirically, LCF not only improves convergence speed but also stabilizes representation quality. Our findings highlight the critical importance of addressing low-noise pathologies to unlock the full potential of flow matching for both generation and representation learning.

We present new JWST-NIRSpec IFS data for the luminous infrared galaxy NGC7469: a nearby (70.6Mpc) active galaxy with a Sy 1.5 nucleus that drives a highly ionized gas outflow and a prominent nuclear star-forming ring. Using the superb sensitivity and high spatial resolution of the JWST instrument NIRSpec-IFS, we investigate the role of the Seyfert nucleus in the excitation and dynamics of the circumnuclear gas. Our analysis focuses on the [Fe ii], H2, and hydrogen recombination lines that trace the radiation/shocked-excited molecular and ionized ISM around the AGN. We investigate the gas excitation through H2/Br{\gamma} and [Fe ii]/Paeta emission line ratios and find that photoionization by the AGN dominates within the central 300 pc of the galaxy and together with a small region show ing signatures of shock-heated gas; these shock-heated regions are likely associated with a compact radio jet. In addition, the velocity field and velocity dispersion maps reveal complex gas kinematics. Rotation is the dominant feature, but we also identify non-circular motions consistent with gas inflows as traced by the velocity residuals and the spiral pattern in the Pa{\alpha} velocity dispersion map. The inflow is consistent with the mass outflow rate and two orders of magnitude higher than the AGN accretion rate. The compact nuclear radio jet has enough power to drive the highly ionized outflow. This scenario suggests that the inflow and outflow are in a self-regulating feeding-feedback process, with a contribution from the radio jet helping to drive the outflow.

Minibatch optimal transport coupling straightens paths in unconditional flow matching. This leads to computationally less demanding inference as fewer integration steps and less complex numerical solvers can be employed when numerically solving an ordinary differential equation at test time. However, in the conditional setting, minibatch optimal transport falls short. This is because the default optimal transport mapping disregards conditions, resulting in a conditionally skewed prior distribution during training. In contrast, at test time, we have no access to the skewed prior, and instead sample from the full, unbiased prior distribution. This gap between training and testing leads to a subpar performance. To bridge this gap, we propose conditional optimal transport C^2OT that adds a conditional weighting term in the cost matrix when computing the optimal transport assignment. Experiments demonstrate that this simple fix works with both discrete and continuous conditions in 8gaussians-to-moons, CIFAR-10, ImageNet-32x32, and ImageNet-256x256. Our method performs better overall compared to the existing baselines across different function evaluation budgets. Code is available at https://hkchengrex.github.io/C2OT

We present a formulation of flow matching as variational inference, which we refer to as variational flow matching (VFM). Based on this formulation we develop CatFlow, a flow matching method for categorical data. CatFlow is easy to implement, computationally efficient, and achieves strong results on graph generation tasks. In VFM, the objective is to approximate the posterior probability path, which is a distribution over possible end points of a trajectory. We show that VFM admits both the CatFlow objective and the original flow matching objective as special cases. We also relate VFM to score-based models, in which the dynamics are stochastic rather than deterministic, and derive a bound on the model likelihood based on a reweighted VFM objective. We evaluate CatFlow on one abstract graph generation task and two molecular generation tasks. In all cases, CatFlow exceeds or matches performance of the current state-of-the-art models.

Text-to-image diffusion models offer powerful image editing capabilities. To edit real images, many methods rely on the inversion of the image into Gaussian noise. A common approach to invert an image is to gradually add noise to the image, where the noise is determined by reversing the sampling equation. This process has an inherent tradeoff between reconstruction and editability, limiting the editing of challenging images such as highly-detailed ones. Recognizing the reliance of text-to-image models inversion on a text condition, this work explores the importance of the condition choice. We show that a condition that precisely aligns with the input image significantly improves the inversion quality. Based on our findings, we introduce Tight Inversion, an inversion method that utilizes the most possible precise condition -- the input image itself. This tight condition narrows the distribution of the model's output and enhances both reconstruction and editability. We demonstrate the effectiveness of our approach when combined with existing inversion methods through extensive experiments, evaluating the reconstruction accuracy as well as the integration with various editing methods.

Moist convection is a physical process where the latent heat released by condensation acts as a buoyancy source that can enhance or even trigger an overturning convective instability. Since the saturation temperature often decreases with height, condensation releases latent heat preferentially in regions of upflow. Due to this inhomogeneous heat source, moist convection may be more sensitive to changes in flow morphology, such as those induced by rotation, than dry Rayleigh-B\'enard convection. In order to study the effects of rotation on flows driven by latent heat release, we present a suite of numerical simulations that solve the Rainy-B\'enard equations (Vallis et al. 2019). We identify three morphological regimes: a cellular regime and a plume regime broadly analogous to those found in rotating Rayleigh B\'enard convection, and a novel funnel regime that lacks a clear analog within the regimes exhibited by dry convection. We measure energy fluxes through the system and report rotational scalings of the Reynolds and moist Nusselt numbers. We find that moist static energy transport, as measured by a moist Nusselt number, is significantly enhanced in the funnel regime without a corresponding enhancement in Reynolds number, indicating that this funnel regime produces structures with more favorable correlations between the temperature and vertical velocity.

Conditional flow matching (CFM) has emerged as a powerful framework for training continuous normalizing flows due to its computational efficiency and effectiveness. However, standard CFM often produces paths that deviate significantly from straight-line interpolations between prior and target distributions, making generation slower and less accurate due to the need for fine discretization at inference. Recent methods enhance CFM performance by inducing shorter and straighter trajectories but typically rely on computationally expensive mini-batch optimal transport (OT). Drawing insights from entropic optimal transport (EOT), we propose Weighted Conditional Flow Matching (W-CFM), a novel approach that modifies the classical CFM loss by weighting each training pair (x, y) with a Gibbs kernel. We show that this weighting recovers the entropic OT coupling up to some bias in the marginals, and we provide the conditions under which the marginals remain nearly unchanged. Moreover, we establish an equivalence between W-CFM and the minibatch OT method in the large-batch limit, showing how our method overcomes computational and performance bottlenecks linked to batch size. Empirically, we test our method on unconditional generation on various synthetic and real datasets, confirming that W-CFM achieves comparable or superior sample quality, fidelity, and diversity to other alternative baselines while maintaining the computational efficiency of vanilla CFM.

In this paper, we revisit the joint low-Mach and low-Frode number limit for the compressible Navier-Stokes equations with degenerate, density-dependent viscosity. Employing the relative entropy framework based on the concept of κ-entropy, we rigorously justify the convergence of weak solutions toward the generalized anelastic system in a three-dimensional periodic domain for well-prepared initial data. For general ill-prepared initial data, we establish a similar convergence result in the whole space, relying essentially on dispersive estimates for acoustic waves. Compared with the work of Fanelli and Zatorska [Commun. Math. Phys., 400 (2023), pp. 1463-1506], our analysis is conducted for the standard isentropic pressure law, thereby eliminating the need for the cold pressure term that played a crucial role in the previous approach. To the best of our knowledge, this is the first rigorous singular limit result for the compressible Navier-Stokes equations with degenerate viscosity that requires no additional regularization of the system.

Editing real images using a pre-trained text-to-image (T2I) diffusion/flow model often involves inverting the image into its corresponding noise map. However, inversion by itself is typically insufficient for obtaining satisfactory results, and therefore many methods additionally intervene in the sampling process. Such methods achieve improved results but are not seamlessly transferable between model architectures. Here, we introduce FlowEdit, a text-based editing method for pre-trained T2I flow models, which is inversion-free, optimization-free and model agnostic. Our method constructs an ODE that directly maps between the source and target distributions (corresponding to the source and target text prompts) and achieves a lower transport cost than the inversion approach. This leads to state-of-the-art results, as we illustrate with Stable Diffusion 3 and FLUX. Code and examples are available on the project's webpage.

In the literature, flows produced by synthetic jets (SJ) have been studied extensively through experiments and numeric simulations. The essential physics of such a complex system has been simplified successfully to Lumped-element models in a wide range of conditions. LE models effectively predict the pressure in the cavity and the velocity in the neck of SJ. But, this does not comprise the complete dynamics of SJ. As soon as the flow starts separating from the neck of the SJ device, vortices and jets form at some distance downstream. These structures are the result of loosening the flow boundaries. Despite such a dramatic change, predictions of LE models remain unverified by measurements of the fully developed jet. We compared predictions of momentum transfer using an LE model with measurements of size and velocity of a fully developed jet/vortex detached from an SJ. Our SJ device operated with air as an active fluid. Comparing measurements and predictions, we found a constant difference for the higher sound pressures. However, the predictions and the measurements follow similar trends. Additionally, we found that the decay rate of the flow regime given by the relationship between the Reynolds and the Strouhal numbers differs significantly when the flow is studied within the neck and downstream the cavity.

Rectified Flow offers a simple and effective approach to high-quality generative modeling by learning a velocity field. However, we identify a limitation in directly modeling the velocity with an unconstrained neural network: the learned velocity often fails to satisfy certain boundary conditions, leading to inaccurate velocity field estimations that deviate from the desired ODE. This issue is particularly critical during stochastic sampling at inference, as the score function's errors are amplified near the boundary. To mitigate this, we propose a Boundary-enforced Rectified Flow Model (Boundary RF Model), in which we enforce boundary conditions with a minimal code modification. Boundary RF Model improves performance over vanilla RF model, demonstrating 8.01% improvement in FID score on ImageNet using ODE sampling and 8.98% improvement using SDE sampling.

This paper explores the relationship between the condition number of a neural network's weight tensor and the extent of information encoded by the associated processing unit, viewed through the lens of information theory. It argues that a high condition number, though not sufficient for effective knowledge encoding, may indicate that the unit has learned to selectively amplify and compress information. This intuition is formalized for linear units with Gaussian inputs, linking the condition number and the transformation's log-volume scaling factor to the characteristics of the output entropy and the geometric properties of the learned transformation. The analysis demonstrates that for a fixed weight norm, a concentrated distribution of singular values (high condition number) corresponds to reduced overall information transfer, indicating a specialized and efficient encoding strategy. Furthermore, the linear stage entropy bound provides an upper limit on post-activation information for contractive, element-wise nonlinearities, supporting the condition number as a scale-invariant proxy for encoding capacity in practical neural networks. An empirical case study applies these principles to guide selective fine-tuning of Large Language Models for both a new task and a new input modality. The experiments show that the proposed method, named KappaTune, effectively mitigates catastrophic forgetting. Unlike many existing catastrophic forgetting mitigation methods that rely on access to pre-training statistics, which are often unavailable, this selective fine-tuning approach offers a way to bypass this common requirement.

We show that every n-dimensional, kappa-noncollapsed, noncompact, complete ancient solution to the Ricci flow with uniformly PIC for n=4 or nge 12 has weakly PIC_2 and bounded curvature. Combining this with earlier results, we prove that any such solution is isometric to either a family of shrinking cylinders (or a quotient thereof) or the Bryant soliton. Also, we classify all complex 2-dimensional, kappa-noncollapsed, complete ancient solutions to the K\"ahler Ricci flow with weakly PIC.

We consider the scattering of acoustic perturbations in a presence of a flow. We suppose that the space can be split into a zone where the flow is uniform and a zone where the flow is potential. In the first zone, we apply a Prandtl-Glauert transformation to recover the Helmholtz equation. The well-known setting of boundary element method for the Helmholtz equation is available. In the second zone, the flow quantities are space dependent, we have to consider a local resolution, namely the finite element method. Herein, we carry out the coupling of these two methods and present various applications and validation test cases. The source term is given through the decomposition of an incident acoustic field on a section of the computational domain's boundary.

It is demonstrated that self-diffusion and shear viscosity data for the TIP4P/Ice water model reported recently [L. Baran, W. Rzysko and L. MacDowell, J. Chem. Phys. {\bf 158}, 064503 (2023)] obey the microscopic version of the Stokes-Einstein relation without the hydrodynamic diameter.