New method estimates velocity fields for minimizing f-divergences without overfitting.
problem Minimizing statistical discrepancies between target and particle distributions.
method Directly estimate velocity fields using interpolation techniques, proving consistency under mild conditions.
result Consistent estimators of velocity fields improve accuracy in applications like domain adaptation and missing data imputation.
RFM improves CNFs by adding a boundary constraint term and matching velocity fields.
problem Flow matching on constrained domains leads to unnatural samples.
method RFM adds a boundary constraint term and matches velocity fields in a simulation-free manner.
result RFM achieves comparable or better results on standard image benchmarks and produces high-quality samples.
LFIS uses a time-dependent velocity field to sample from complex distributions.
problem Sampling from unnormalized density functions.
method LFIS learns a time-dependent velocity field to transport samples from a simple initial distribution to a complex target distribution.
result LFIS achieves state-of-the-art performance on various benchmark problems.
Develops scalable model for learning velocity fields in complex traffic scenarios.
problem Learning heterogeneous and dynamic velocity fields in complex traffic scenarios.
method Nonparametric Bayesian modeling with hierarchical Dirichlet process and infinite hidden Markov model, Gaussian process prior, and scalable approximate inference.
result Demonstrates effective scalability and applicability to real-world traffic data.
NN-Turb generates turbulent velocity statistics using neural networks.
problem Creating a 1D field with turbulent velocity statistics.
method Fully-convolutional neural network (NN-Turb) to generate the field.
result NN-Turb generates a 1D field that satisfies Kolmogorov's 2/3 and 4/5 laws, exhibiting intermittency.
Neural solver computes Wasserstein geodesics and velocity fields efficiently.
problem Computing Wasserstein geodesics and velocity fields efficiently.
method Sample-based neural network approach to solve the minimax problem.
result Directly samples from target distribution and estimates velocity field.
We prove that, in a space-time of dimension n>3 with a velocity field that is shear-free, vorticity-free and acceleration-free, the covariant divergence of the Weyl tensor is zero if the contraction of the Weyl tensor with the velocity is zero. The other way, if the covariant divergence of the Weyl tensor is zero, then…
Study uses neural networks to predict wall quantities in turbulent flows.
problem Predicting wall quantities in turbulent open channel flows.
method Training convolutional neural networks (FCN) and a proposed R-Net architecture to predict wall-shear-stress and wall pressure.
result R-Net architecture performs better and predicts wall quantities with around 10% error.
Neural net reconstructs dark matter density from halo velocities.
problem Reconstructing local dark matter density from halo velocities.
method Hybrid architecture combining U-Net and DeepSets.
result Hybrid network recovers density amplitudes and phases better than U-Net.
We introduce a measure for estimating the best risk-return relation of power production in wind farms within a given time-lag, conditioned to the velocity field. The velocity field is represented by a scalar that weighs the influence of the velocity at each wind turbine at present and previous time-steps for the presen…
Vortex induced vibrations of bluff bodies occur when the vortex shedding frequency is close to the natural frequency of the structure. Of interest is the prediction of the lift and drag forces on the structure given some limited and scattered information on the velocity field. This is an inverse problem that is not str…
A new method interprets astrophysical spectra using geometric paths to distinguish line profiles.
problem Tackling the indistinguishability of spectral line profiles under scalar summaries.
method Introduces a geometric representation of line profiles using rough path theory, mapping profiles to a common velocity grid and defining descriptors from path properties.
result Compact descriptors separate morphologies with similar scalar summaries, revealing ordered line structures.
Generative sampler learns velocity fields for efficient posterior inference.
problem Sampling from complex posterior distributions in high dimensions.
method Generative multivariate posterior sampler via flow matching, learning a velocity field for a deterministic transport map.
result Conditional Brenier map enables fast generation of credible sets with theoretical consistency guarantees.
SAGE generates subsurface velocity models from sparse well logs and seismic images.
problem Lack of high-quality subsurface velocity models due to limited data availability.
method Subsurface AI-driven geostatistical extraction using proxy posterior.
result SAGE produces geologically plausible and statistically accurate velocity realizations.
The paper explores rectified flows and their relation to optimal transport.
problem Understanding the connection between rectified flows and optimal transport.
method Investigates invariance properties, explicit constructions, and analysis of rectified flows in various settings.
result Rectified flows, when gradient constrained, do not generally solve optimal transport problems.
New sampling method uses gradient-free IPS with RKHS velocity field.
problem Efficient sampling from unnormalized target densities.
method Gradient-free interacting particle systems (IPS) with RKHS velocity field.
result IPS produce high-quality samples from various target distributions.
Flow Matching models help generative models stay within the subspace of real data.
problem How do generative models stay within the subspace of real data?
method Flow Matching models using a learned velocity field to transform a simple prior into a complex target distribution.
result Generated samples memorize real data points and represent the sample data subspace exactly.
In the present report, by using the Stokes-Helmholtz decomposition theorem the 3-dimensional Navier-Stokes equation (NSE) is uncoupled and transformed into a scalar equation for the velocity potential when the flow field is toroidal. The dynamics of the velocity potential is independent of the vector potential. The red…
A conservative drifting method improves generative modeling by using KDE gradients, proving convergence rates.
problem Improving generative modeling by addressing non-conservatism issues.
method Proposes a conservative drifting method using kernel density estimator gradients to address non-conservatism.
result Proves finite-particle convergence rates for the conservative method, providing explicit quadrature constants.
Study of k-almost Yamabe solitons in perfect fluid spacetimes.
problem Analyzing k-almost Yamabe solitons in perfect fluid spacetimes. method Examined perfect fluid spacetimes and k-almost Yamabe solitons using Einstein field equations. result Characterized properties of k-almost Yamabe solitons in perfect fluid spacetimes. A perfect-fluid space-time of dimension n>3 with 1) irrotational velocity vector field, 2) null divergence of the Weyl tensor, is a generalised Robertson-Walker space-time with Einstein fiber. Condition 1) is verified whenever pressure and energy density are related by an equation of state. The contraction of the Weyl …
Neural networks predict flow and elastic stresses in viscoelastic turbulence.
problem Predicting flow and elastic stresses in viscoelastic turbulent flows using limited experimental data.
method Convolutional neural networks trained on wall-normal velocity and pressure data.
result Neural networks accurately predict flow and elastic stresses, especially during low-drag events.
Neural network predicts turbulence near-wall regions efficiently.
problem Reducing computational cost in turbulent flow simulations.
method Fully-convolutional neural network trained on DNS data.
result FCN predicts velocity fluctuations at y+=50 with less than 20% error. Develops a method for non-equilibrium importance sampling to estimate expectations and constants.
problem Estimating expectations and normalization constants for complex high-dimensional distributions.
method Generates samples from a base distribution, transports them using a velocity field, and averages along flowlines.
result The method can achieve zero-variance estimation and significantly reduces variance compared to vanilla estimators.
New method uses neural ODEs to approximate complex distributions efficiently.
problem Approximating complex probability distributions efficiently.
method Neural ODEs with minimum energy regularization for distribution approximation.
result Deep neural network representations can achieve accurate distribution approximation.
The purpose of this paper is to derive the anisotropic averaged Euler equations and to study their geometric and analytic properties. These new equations involve the evolution of a mean velocity field and an advected symmetric tensor that captures the fluctuation effects. Besides the derivation of these equations, the …
Optimal self-distillation improves generative models' velocity risk and mode recovery.
problem Improving generative models' velocity risk and mode recovery.
method Proved optimal self-distillation for rectified flow via linear probing, derived mixing coefficient, and provided validation tuning.
result Optimal self-distillation improves velocity risk and mode recovery.
This paper presents a novel generative model to synthesize fluid simulations from a set of reduced parameters. A convolutional neural network is trained on a collection of discrete, parameterizable fluid simulation velocity fields. Due to the capability of deep learning architectures to learn representative features of…
We consider billiard ball motion in a convex domain on a constant curvature surface influenced by the constant magnetic field. We examine the existence of integral of motion which is polynomial in velocities. We prove that if such an integral exists then the boundary curve of the domain determines an algebraic curve in…
A time schedule simplifies learning in flow-based models for high-dimensional data.
problem Disappearance of relative probability phase in high-dimensional Gaussian mixture sampling.
method Introduces a time dilation schedule to characterize phases of learning.
result Autoencoder learns to simplify by focusing on relevant parameters for each phase.
Deep learning predicts fluid flow in porous media, accelerating simulations by orders of magnitude.
problem Accurate simulation of fluid flow in complex porous media requires excessive computational resources.
method Combining deep learning with direct simulation, using Gated U-Net CNNs trained on datasets of 2D and 3D porous media.
result Deep learning predictions can reach over 90% accuracy for permeability estimation and accelerate simulations by orders of magnitude.
Proposes a method combining CNFs and rejection-resampling for sampling from unnormalized densities.
problem Sampling from unnormalized probability densities, especially multimodal ones.
method Combines continuous normalizing flows with rejection-resampling steps based on importance weights.
result The method improves sampling accuracy and performance compared to state-of-the-art methods.
Two non-local asymptotic invariants of magnetic fields for the ideal magnetohydrodynamics are introduced. The velocity of variation of the invariants for a non-ideal magnetohydrodynamics with a small magnetic dissipation is estimated. By means of the invariants the spectra of electromagnetic fields are investigated. A …
Jointly estimates flow fields and particle properties from Lagrangian data.
problem Estimating flow fields and particle properties from sparse, noisy Lagrangian data.
method Data assimilation framework coupling Eulerian and Lagrangian models.
result Joint estimation of flow fields and particle properties in various flow regimes.
Sharp stability threshold found for deep residual architectures.
problem Ensuring stable training and inference in deep residual networks.
method Sublinear-growth principle and optimal-control analysis.
result Stable training condition: input-magnitude exponent q ≤ 1.
Develops Hamiltonian Score Matching and Generative Flows for machine learning.
problem Estimating score functions and designing generative models.
method Introduces Hamiltonian velocity predictors (HVPs) for score matching and generative flows.
result Hamiltonian Generative Flows (HGFs) rival leading generative modeling techniques.
This work proposes a novel method for estimating the influence that unknown static objects might have over mobile agents. Since the motion of agents can be affected by the presence of fixed objects, it is possible use the information about trajectories deviations to infer the presence of obstacles and estimate the forc…
DFM models are analyzed for generating distributions with provable convergence.
problem Training DFM models to generate distributions that match true data.
method Theoretical analysis decomposes error into approximation and estimation errors.
result DFM models converge to true data distribution as training set size increases.
New geometric structures that relate the lagrangian and hamiltonian formalisms defined upon a singular lagrangian are presented. Several vector fields are constructed in velocity space that give new and precise answers to several topics like the projectability of a vector field to a hamiltonian vector field, the comput…
We extend Routh's reduction procedure to an arbitrary Lagrangian system (that is, one whose Lagrangian is not necessarily the difference of kinetic and potential energies) with a symmetry group which is not necessarily Abelian. To do so we analyse the restriction of the Euler-Lagrange field to a level set of momentum i…
Flow matching adapts to manifold structures without diffusion.
problem Theoretical understanding of flow matching in manifold-supported settings.
method Flow matching with linear interpolation on smooth manifolds, analyzing velocity field and density estimator.
result Non-asymptotic convergence guarantee and statistical consistency of flow matching on manifolds.
Study shows polynomial-width neural networks can closely approximate infinite-width networks in polynomial time.
problem Approximating dynamics of polynomial-width neural networks with infinite-width networks.
method Bounding approximation gap through a differential equation governed by mean-field dynamics, considering local Hessian.
result Polynomially many neurons are sufficient to closely approximate mean-field dynamics.
This paper presents a methodology that aims at the incremental representation of areas inside environments in terms of attractive forces. It is proposed a parametric representation of velocity fields ruling the dynamics of moving agents. It is assumed that attractive spots in the environment are responsible for modifyi…
The paper proposes a method to infer differentiation trees from RNA velocity data.
problem Reconstructing dynamic cellular processes from sequencing data.
method Defining varifold distances between RNA velocity curves to approximate shortest-path distances in a tree.
result The varifold distance method approximates the shortest-path distance in a tree isomorphic to the target differentiation tree.
In this note we first set up an analogy between spin and vorticity of a perfect 2d-fluid flow, based on the Borel-Weil contruction of the irreducible unitary representations of SU(2), and looking at the Madelung-Bohm velocity attached to the ensuing spin wave functions. We also show that, in the framework of finite dim…
A theorem proves a surface evolution graph satisfies a PDE under specific conditions.
problem Prove a surface evolution graph satisfies a PDE under specific conditions.
method Use Brakke's formulation of velocity and analyze the distributional time derivative of the graph.
result The graph satisfies the PDE pointwise under the given conditions.
MeanFlow training is unstable due to misusing conditional velocity, leading to variance issues.
problem Unstable training of MeanFlow due to variance problems.
method Theoretical analysis and derivation of optimal coefficient in closed form.
result The optimal coefficient in MeanFlow training minimizes variance but not necessarily quality.
The correspondence between Riemann-Finsler geometries and effective field theories with spin-independent Lorentz violation is explored. We obtain the general quadratic action for effective scalar field theories in any spacetime dimension with Lorentz-violating operators of arbitrary mass dimension. Classical relativist…