Modified curve shortening flow constructs -Angenent curve.
problem Constructing -Angenent curve.
method Modified curve shortening flow
result Constructs -Angenent curve.
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48 results for “flow methods”
New method shortens and straightens curves, proving convergence and well-posedness.
problem Shortening and straightening of curves.
method Conceptual shift in curve shortening to tangent aligning, variational study of geometric flows.
result Proves convergence to a straight line and global well-posedness for various geometric flows.
Improved sampling method using regularized Stein Variational Gradient Flow.
problem Improving the accuracy of sampling methods in machine learning.
method Proposed Regularized Stein Variational Gradient Flow to interpolate between SVGD and Wasserstein Gradient Flow.
result Established theoretical properties and provided preliminary numerical evidence of improved performance.
New method constructs Birkhoff sections for pseudo-Anosov flows with controlled complexity.
problem Constructing Birkhoff sections for pseudo-Anosov flows with specific properties.
method Uses connection between pseudo-Anosov flows and veering triangulations to explicitly construct sections with controlled complexity.
result Shows that any transitive pseudo-Anosov flow has a Birkhoff section with two boundary components.
Method extracts taint flows to classify Bitcoin mining pools.
problem Understanding pseudonymous Bitcoin actors and their transactions.
method Taint analysis and graph embedding methods applied to taint flows.
result Taint flows from the same period show high similarity.
By the method of discrete Morse flows, we construct an energy reducing multiple-valued function flow. The flow we get is Holder continuous with respect to the L-2 norm. We also give another way of constructing flows in some special cases, where the flow we get behaves like ordinary heat flow.
A new method for reconstructing flows from perturbed distributions.
problem Reconstructing flows from perturbed probability distributions.
method Integrable vector fields and Green's functions.
result A nonparametric flow can be computed to generate samples from a perturbed distribution.
Method for conditional sampling with pre-trained normalizing flows.
problem Conditional sampling for incomplete observations.
method Variational Schur conditional sampling with normalizing flows.
result Successfully applied to invertible residual networks for inference and classification.
A discrete method approximates hyperbolic curvature flow in the plane.
problem Modeling wave phenomena in solid-liquid interfaces.
method Semidiscrete finite difference method for hyperbolic curvature flow.
result Error bounds for natural discrete norms are proven.
Method learns PDE dynamics via evolving latent manifold using Ricci flow.
problem Learning dynamics in time, especially PDEs, with low-dimensional representations.
method Parameterizes latent manifold, simulates Ricci flow physics-informedly, matching manifold quantities.
result Ricci flow facilitates learning for out-of-distribution data and adversarial robustness.
Proposes a new method for high-dimensional density estimation.
problem Estimating high-dimensional probability density functions efficiently.
method Tensorizing flow method combining tensor-train and flow-based generative modeling.
result Efficiently constructs an approximate density in tensor-train form and trains a flow model to match empirical distribution.
In general, gradient estimates are very important and necessary for deriving convergence results in different geometric flows, and most of them are obtained by analytic methods. In this paper, we will apply a stochastic approach to systematically give gradient estimates for some important geometric quantities under the…
Modeling bone microarchitecture adaptation using geometric flows.
problem Bone microarchitecture adaptation modeling.
method Advection and mean curvature flow model with a sphere as a test case.
result Closed-form solution for sphere under advection and mean curvature flow.
Christoffel-Minkowski flowsmath.DG
New flow method solves Christoffel-Minkowski problem.
problem Solving Christoffel-Minkowski problem.
method Entropy preserving curvature flow with global term.
result Entropy preserving flow solves Christoffel-Minkowski problem.
We consider four extended Ricci flow systems---that is, Ricci flow coupled with other geometric flows---and prove dynamical stability of certain classes of stationary solutions of these flows. The systems include Ricci flow coupled with harmonic map flow (studied abstractly and in the context of Ricci flow on warped pr…
Localizes curvature estimates for evolving hypersurfaces under various flows.
problem Establishing curvature estimates for evolving hypersurfaces under different flow conditions.
method Adapted localization of Huisken--Stampacchia iteration method to fully nonlinear flows.
result Asymptotically sharp curvature pinching estimates for general flows.
Urban spatial-temporal flows prediction is of great importance to traffic management, land use, public safety, etc. Urban flows are affected by several complex and dynamic factors, such as patterns of human activities, weather, events and holidays. Datasets evaluated the flows come from various sources in different dom…
New error bounds for flow matching methods using deterministic sampling.
problem Improving the accuracy of flow matching methods for generating probability distributions.
method Derived error bounds for flow matching methods under deterministic sampling conditions.
result Presented error bounds for flow matching methods using loss and regularity conditions.
New method reduces discrete flow transitions, improving perplexity estimation.
problem Stochasticity in discrete paths makes rectification strategies ineffective.
method Dynamic-optimal-transport-like minimization objective with minibatch strategies.
result 32 times reduction in transitions for same perplexity.
Combines normalizing flows and quasi-Monte Carlo for improved numerical integration.
problem Improving the efficiency of numerical integration methods.
method Uses normalizing flows to approximate distributions and quasi-Monte Carlo for sampling.
result Demonstrates an estimator with significantly lower variance.
Study proves a new flow method for mean curvature with volume change analysis.
problem Existence of BV flow via mean curvature flow.
method Elliptic regularization to prove existence of generalized BV flow.
result Proves existence of generalized BV flow with volume change expression.
A new method speeds up sampling of Boltzmann distribution in high-dimensional systems.
problem High computational cost of obtaining Jacobian of flow-based models in high dimensions.
method Flow perturbation method that incorporates stochastic perturbations and reweighting.
result Achieves unbiased sampling of Boltzmann distribution with orders of magnitude speedup.
A new method learns straight trajectories in one step for optimal flow matching.
problem Learning flows with straight trajectories for fast inference.
method Optimal Flow Matching (OFM) approach using convex functions for vector fields.
result Recovering straight OT displacements in just one FM step for quadratic transport.
In many fields of science, high-dimensional integration is required. Numerical methods have been developed to evaluate these complex integrals. We introduce the code i-flow, a python package that performs high-dimensional numerical integration utilizing normalizing flows. Normalizing flows are machine-learned, bijectiv…
Flow-based generative models are a family of exact log-likelihood models with tractable sampling and latent-variable inference, hence conceptually attractive for modeling complex distributions. However, flow-based models are limited by density estimation performance issues as compared to state-of-the-art autoregressive…
Study of twisted Calabi flow connecting J-flow and Calabi flow on Kähler manifolds.
problem Existence and convergence of twisted Calabi flow on compact Kähler manifolds.
method Analysis of a family of twisted Calabi flows connecting J-flow and Calabi flow, showing long-time existence and convergence to cscK metrics.
result Long-time existence and convergence of twisted Calabi flow to cscK metrics, implying openness of continuity method.
Paper introduces geometry-aware normalizing flows for improved causal inference.
problem Disparity between sample and population distributions in causal inference.
method Integrates continuous normalizing flows with parametric submodels, employing Wasserstein gradient flows and optimal transport.
result Significantly reduces parameter estimation bias and variance in finite-sample settings.
CFMI improves missing data imputation across various data types and dimensions.
problem Imputing missing data in complex, high-dimensional datasets.
method Combines normalising flows, flow-matching, and shared conditional modelling.
result Outperforms traditional and modern imputation methods across multiple metrics.
RC flow learns molecular kinetics in low dimensions.
problem Discovering interpretable low-dimensional models of molecular kinetics.
method Normalizing flow for coordinate transformation and Brownian dynamics for kinetics approximation.
result Tractable and trainable model of reduced kinetics in continuous time and space.
A new method for normalizing flows using stochastic interpolants simplifies likelihood estimation and improves efficiency.
problem Efficient and scalable likelihood estimation for complex probability distributions.
method Inference of velocity field from time-dependent density interpolating between base and target densities.
result Simplified quadratic loss for velocity estimation, leading to faster and more efficient training.
A training-free method for conditional sampling using flow matching.
problem Weight degeneracy in high-dimensional importance sampling.
method Sequential Monte Carlo with resampling and stochastic flow.
result Significantly outperforms existing methods on MNIST and CIFAR-10.
A new method for Gaussian filtering using gradient flows and Wasserstein metrics.
problem Approximating Gaussian and mixture-of-Gaussians filtering for complex systems.
method Variational approximation via gradient-flow representation on Wasserstein metric space.
result Competitive performance in posterior representation and parameter estimation for systems with multiplicative noise and multi-modal distributions.
This paper studies a training method to jointly estimate an energy-based model and a flow-based model, in which the two models are iteratively updated based on a shared adversarial value function. This joint training method has the following traits. (1) The update of the energy-based model is based on noise contrastive…
Remarks on Kahler Ricci Flowmath.DG
We study some estimates along the Kahler Ricci flow on Fano manifolds. Using these estimates, we show the convergence of Kahler Ricci flow directly if the -invariant of the canonical class is greater than . Applying these convergence theorems, we can give a flow proof of Calabi conjecture on such Fano…
Flow AIS Bootstrap improves flow training by generating samples in hard-to-reach regions.
problem Training flows with high variance and mode-seeking behavior.
method Augment flows with AIS and minimize -divergence with .
result FAB learns Boltzmann distribution of alanine dipeptide without MD samples.
Flows with surgery revisitedmath.AP
New method for geometric flows with surgery without smooth estimates.
problem Existence of geometric flows with surgery.
method Hybrid compactness theorem for weak limits.
result Existence of geometric flows with surgery in mean-convex surfaces.
The study examines the long-term behavior of mean curvature flows in closed 3-manifolds.
problem Understanding the long-term behavior of mean curvature flows in closed 3-manifolds.
method The approach involves constructing piecewise almost regular flows and applying perturbative arguments.
result The study constructs minimal surfaces in 3-manifolds via parabolic methods.
Paper explores Fisher-Rao gradient flows and their kernel approximations.
problem Understanding and analyzing approximations of Fisher-Rao gradient flows.
method Rigorous investigation of Fisher-Rao and Wasserstein type gradient flows, focusing on kernel approximations.
result Proves evolutionary Γ-convergence for kernel-approximated Fisher-Rao flows, providing theoretical guarantees.
New method shows pseudo-Anosov flows on graph manifolds can be simplified.
problem Understanding pseudo-Anosov flows on graph manifolds.
method Constructing a partial Birkhoff section with genus one components that misses finitely many closed orbits.
result Every pseudo-Anosov flow on a graph manifold is almost equivalent to a totally periodic flow or a suspension Anosov flow.
New method solves generalized Minkowski problem for torsional rigidity.
problem Generalized Minkowski problem for torsional rigidity.
method Flow method
result Existence of solutions for general measures.
CRAFT improves on existing methods for sampling complex distributions.
problem Sampling from complex probability distributions.
method Combines SMC with variational inference using normalizing flows.
result Improves on Annealed Flow Transport Monte Carlo and MCMC-based Stochastic Normalizing Flows.
Study complex Monge-Ampère flows on Kähler manifolds using Perron method.
problem Complex Monge-Ampère flows in big cohomology classes.
method Perron method for pluripotential subsolutions.
result Upper envelope of subsolutions is a unique pluripotential solution with regularity.
Improved stock price prediction model using generalized order flow imbalance.
problem Improving stock price prediction models using new order flow imbalance indicators.
method Proposed a generalized order flow imbalance construction method and applied it to CSI 500 stocks.
result Generalized Stationarized Order Flow Imbalance (log-GOFI) shows significant improvement in explaining stock price changes.
We convert deterministic flow models to stochastic samplers.
problem Deterministic flow models are sensitive to errors and cannot condition on intermediate states.
method Transform ODEs into SDEs with the same marginal distributions.
result Empirically outperforms deterministic samplers and controls generation diversity.
New Ricci flow solutions found with rotational symmetry and cone-like singularities.
problem Finding Ricci flow solutions with specific symmetry and singularity properties.
method Rotationally symmetric Ricci flow with scaling-invariant curvature bounds, using approximation method.
result Complete Ricci flow solution with cone-like singularity at the origin.
Symmetries of Ricci Flowsmath.DG
Researchers discover symmetries in Ricci flows and use them to find invariant solutions.
problem Finding symmetries in Ricci flows on manifolds.
method Developed a method to find Lie point symmetries of Ricci flows and particular metrics.
result Invariant solutions of Ricci flow for specific metric families were obtained.
The rectified flow method is analyzed for its statistical properties.
problem Theoretical support for rectified flow methods is lacking.
method Empirical analysis of rectified flow's statistical properties using regression and density estimation.
result Convergence rates for rectified flow estimators are faster than for nonparametric regression and density estimation.
Rod flow models Adam's behavior at the edge of stability.
problem Modeling adaptive gradient methods like Adam at the edge of stability.
method Extended rod flow to Adam, considering parameters, first moment, and second moment as variables.
result Rod flow accurately tracks Adam's behavior through the edge-of-stability regime.