Related papers: Critically-Damped Higher-Order Langevin Dynamics

Related papers

Wasserstein Convergence of Critically Damped Langevin Diffusions [9.063081094420044]
Critically-damped Langevin Diffusions (CLDs) have been shown to outperform standard diffusion-based samplers numerically.<n>We derive a novel upper bound on the sampling error of CLD-based generative models in the Wasserstein metric.
arXiv Detail & Related papers (2025-11-04T09:49:07Z)
Langevin Flows for Modeling Neural Latent Dynamics [81.81271685018284]
We introduce LangevinFlow, a sequential Variational Auto-Encoder where the time evolution of latent variables is governed by the underdamped Langevin equation.<n>Our approach incorporates physical priors -- such as inertia, damping, a learned potential function, and forces -- to represent both autonomous and non-autonomous processes in neural systems.<n>Our method outperforms state-of-the-art baselines on synthetic neural populations generated by a Lorenz attractor.
arXiv Detail & Related papers (2025-07-15T17:57:48Z)
Advanced long-term earth system forecasting by learning the small-scale nature [74.19833913539053]
We present Triton, an AI framework designed to address this fundamental challenge.<n>Inspired by increasing grids to explicitly resolve small scales in numerical models, Triton employs a hierarchical architecture processing information across multiple resolutions to mitigate spectral bias.<n>We demonstrate Triton's superior performance on challenging forecast tasks, achieving stable year-long global temperature forecasts, skillful Kuroshio eddy predictions till 120 days, and high-fidelity turbulence simulations.
arXiv Detail & Related papers (2025-05-26T02:49:00Z)
Generative emulation of chaotic dynamics with coherent prior [0.129182926254119]
We present an efficient generative framework for dynamics emulation, unifying principles of turbulence with diffusion-based modeling: Cohesion.<n>Specifically, our method estimates large-scale coherent structure of the underlying dynamics as guidance during the denoising process.<n>Cohesion superior long-range forecasting skill can efficiently generate physically-consistent simulations, even in the presence of partially-observed guidance.
arXiv Detail & Related papers (2025-04-19T11:14:40Z)
Critically Damped Third-Order Langevin Dynamics [0.0]
This work describes a novel improvement to Third- Order Langevin Dynamics (TOLD) It is carried out by critically damping the TOLD forward transition matrix similarly to Dockhorn's Critically-Damped Langevin Dynamics (CLD)
arXiv Detail & Related papers (2024-09-12T01:59:58Z)
Unfolding Time: Generative Modeling for Turbulent Flows in 4D [49.843505326598596]
This work introduces a 4D generative diffusion model and a physics-informed guidance technique that enables the generation of realistic sequences of flow states. Our findings indicate that the proposed method can successfully sample entire subsequences from the turbulent manifold. This advancement opens doors for the application of generative modeling in analyzing the temporal evolution of turbulent flows.
arXiv Detail & Related papers (2024-06-17T10:21:01Z)
AdjointDPM: Adjoint Sensitivity Method for Gradient Backpropagation of Diffusion Probabilistic Models [103.41269503488546]
Existing customization methods require access to multiple reference examples to align pre-trained diffusion probabilistic models with user-provided concepts. This paper aims to address the challenge of DPM customization when the only available supervision is a differentiable metric defined on the generated contents. We propose a novel method AdjointDPM, which first generates new samples from diffusion models by solving the corresponding probability-flow ODEs. It then uses the adjoint sensitivity method to backpropagate the gradients of the loss to the models' parameters.
arXiv Detail & Related papers (2023-07-20T09:06:21Z)
Convergence of mean-field Langevin dynamics: Time and space discretization, stochastic gradient, and variance reduction [49.66486092259376]
The mean-field Langevin dynamics (MFLD) is a nonlinear generalization of the Langevin dynamics that incorporates a distribution-dependent drift. Recent works have shown that MFLD globally minimizes an entropy-regularized convex functional in the space of measures. We provide a framework to prove a uniform-in-time propagation of chaos for MFLD that takes into account the errors due to finite-particle approximation, time-discretization, and gradient approximation.
arXiv Detail & Related papers (2023-06-12T16:28:11Z)
A Geometric Perspective on Diffusion Models [57.27857591493788]
We inspect the ODE-based sampling of a popular variance-exploding SDE. We establish a theoretical relationship between the optimal ODE-based sampling and the classic mean-shift (mode-seeking) algorithm.
arXiv Detail & Related papers (2023-05-31T15:33:16Z)
Score-based Diffusion Models in Function Space [137.70916238028306]
Diffusion models have recently emerged as a powerful framework for generative modeling.<n>This work introduces a mathematically rigorous framework called Denoising Diffusion Operators (DDOs) for training diffusion models in function space.<n>We show that the corresponding discretized algorithm generates accurate samples at a fixed cost independent of the data resolution.
arXiv Detail & Related papers (2023-02-14T23:50:53Z)
Weak Collocation Regression method: fast reveal hidden stochastic dynamics from high-dimensional aggregate data [10.195461345970541]
We show an approach to effectively modeling the dynamics of the data without trajectories based on the weak form of the Fokker-Planck (FP) equation. We name the method with the Weak Collocation Regression (WCR) method for its three key components: weak form, collocation of Gaussian kernels, and regression.
arXiv Detail & Related papers (2022-09-06T16:29:49Z)
Learning and Inference in Sparse Coding Models with Langevin Dynamics [3.0600309122672726]
We describe a system capable of inference and learning in a probabilistic latent variable model. We demonstrate this idea for a sparse coding model by deriving a continuous-time equation for inferring its latent variables via Langevin dynamics. We show that Langevin dynamics lead to an efficient procedure for sampling from the posterior distribution in the 'L0 sparse' regime, where latent variables are encouraged to be set to zero as opposed to having a small L1 norm.
arXiv Detail & Related papers (2022-04-23T23:16:47Z)
Improved Convergence Rate of Stochastic Gradient Langevin Dynamics with Variance Reduction and its Application to Optimization [50.83356836818667]
gradient Langevin Dynamics is one of the most fundamental algorithms to solve non-eps optimization problems. In this paper, we show two variants of this kind, namely the Variance Reduced Langevin Dynamics and the Recursive Gradient Langevin Dynamics.
arXiv Detail & Related papers (2022-03-30T11:39:00Z)
Extension of Dynamic Mode Decomposition for dynamic systems with incomplete information based on t-model of optimal prediction [69.81996031777717]
The Dynamic Mode Decomposition has proved to be a very efficient technique to study dynamic data. The application of this approach becomes problematic if the available data is incomplete because some dimensions of smaller scale either missing or unmeasured. We consider a first-order approximation of the Mori-Zwanzig decomposition, state the corresponding optimization problem and solve it with the gradient-based optimization method.
arXiv Detail & Related papers (2022-02-23T11:23:59Z)
Convex Analysis of the Mean Field Langevin Dynamics [49.66486092259375]
convergence rate analysis of the mean field Langevin dynamics is presented. $p_q$ associated with the dynamics allows us to develop a convergence theory parallel to classical results in convex optimization.
arXiv Detail & Related papers (2022-01-25T17:13:56Z)
Neural Ordinary Differential Equations for Data-Driven Reduced Order Modeling of Environmental Hydrodynamics [4.547988283172179]
We explore the use of Neural Ordinary Differential Equations for fluid flow simulation. Test problems we consider include incompressible flow around a cylinder and real-world applications of shallow water hydrodynamics in riverine and estuarine systems. Our findings indicate that Neural ODEs provide an elegant framework for stable and accurate evolution of latent-space dynamics with a promising potential of extrapolatory predictions.
arXiv Detail & Related papers (2021-04-22T19:20:47Z)
Fast Mixing of Multi-Scale Langevin Dynamics under the Manifold Hypothesis [85.65870661645823]
We show how the Langevin dimension algorithm allows for the considerable reduction of time depending on the (much) smaller data. Second, the high of the sampling space significantly hurts the performance of Langevin Dynamics.
arXiv Detail & Related papers (2020-06-19T14:52:40Z)
Hessian-Free High-Resolution Nesterov Acceleration for Sampling [55.498092486970364]
Nesterov's Accelerated Gradient (NAG) for optimization has better performance than its continuous time limit (noiseless kinetic Langevin) when a finite step-size is employed. This work explores the sampling counterpart of this phenonemon and proposes a diffusion process, whose discretizations can yield accelerated gradient-based MCMC methods.
arXiv Detail & Related papers (2020-06-16T15:07:37Z)
Non-Convex Optimization via Non-Reversible Stochastic Gradient Langevin Dynamics [27.097121544378528]
Gradient Langevin Dynamics (SGLD) is a powerful algorithm for optimizing a non- objective gradient. NSGLD is based on discretization of the non-reversible diffusion.
arXiv Detail & Related papers (2020-04-06T17:11:03Z)

This list is automatically generated from the titles and abstracts of the papers in this site.