Variational Inference via Smoothed Particle Hydrodynamics

• URL: http://arxiv.org/abs/2407.09186v2
• Date: Fri, 26 Jul 2024 17:26:45 GMT
• Title: Variational Inference via Smoothed Particle Hydrodynamics
• Authors: Yongchao Huang,
• Abstract summary: A new variational inference method is proposed, based on smoothed particle hydrodynamics. It offers fast, flexible, scalable and deterministic sampling and inference for a class of probabilistic models.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: A new variational inference method, SPH-ParVI, based on smoothed particle hydrodynamics (SPH), is proposed for sampling partially known densities (e.g. up to a constant) or sampling using gradients. SPH-ParVI simulates the flow of a fluid under external effects driven by the target density; transient or steady state of the fluid approximates the target density. The continuum fluid is modelled as an interacting particle system (IPS) via SPH, where each particle carries smoothed properties, interacts and evolves as per the Navier-Stokes equations. This mesh-free, Lagrangian simulation method offers fast, flexible, scalable and deterministic sampling and inference for a class of probabilistic models such as those encountered in Bayesian inference and generative modelling.

Related papers

• Tunneling in a Lorenz-like model for an active wave-particle entity [0.0]
  Active wave-particle entities (WPEs) emerge as self-propelled oil droplets on the free surface of a vibrating oil bath. We numerically explore a dynamical analog of tunneling by considering the setup of a one-dimensional WPE incident on an isolated Gaussian potential barrier. Our work highlights that velocity fluctuations of the WPE at high memories that are rooted in non-equilibrium features of the Lorenz system, such as spiraling motion towards equilibrium points and transient chaos, give rise to - (i) sensitivity and unpredictability in barrier crossing.
  arXiv  Detail & Related papers  (2024-08-25T08:09:32Z)
• Variational Inference Using Material Point Method [0.0]
  MPM-ParVI is a gradient-based particle sampling method for variational inference. It offers deterministic sampling and inference for a class of probabilistic models.
  arXiv  Detail & Related papers  (2024-07-26T17:19:50Z)
• Dynamical Measure Transport and Neural PDE Solvers for Sampling [77.38204731939273]
  We tackle the task of sampling from a probability density as transporting a tractable density function to the target. We employ physics-informed neural networks (PINNs) to approximate the respective partial differential equations (PDEs) solutions. PINNs allow for simulation- and discretization-free optimization and can be trained very efficiently.
  arXiv  Detail & Related papers  (2024-07-10T17:39:50Z)
• Electrostatics-based particle sampling and approximate inference [0.0]
  A new particle-based sampling and approximate inference method, based on electrostatics and Newton mechanics principles, is introduced. A discrete-time, discrete-space algorithmic design is provided for usage in more general inference problems.
  arXiv  Detail & Related papers  (2024-06-28T16:53:06Z)
• Sampling in Unit Time with Kernel Fisher-Rao Flow [0.0]
  We introduce a new mean-field ODE and corresponding interacting particle systems (IPS) for sampling from an unnormalized target density. The IPS are gradient-free, available in closed form, and only require the ability to sample from a reference density and compute the (unnormalized) target-to-reference density ratio.
  arXiv  Detail & Related papers  (2024-01-08T13:43:56Z)
• Equivariant Flow Matching with Hybrid Probability Transport [69.11915545210393]
  Diffusion Models (DMs) have demonstrated effectiveness in generating feature-rich geometries. DMs typically suffer from unstable probability dynamics with inefficient sampling speed. We introduce geometric flow matching, which enjoys the advantages of both equivariant modeling and stabilized probability dynamics.
  arXiv  Detail & Related papers  (2023-12-12T11:13:13Z)
• 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)
• NeuroFluid: Fluid Dynamics Grounding with Particle-Driven Neural Radiance Fields [65.07940731309856]
  Deep learning has shown great potential for modeling the physical dynamics of complex particle systems such as fluids. In this paper, we consider a partially observable scenario known as fluid dynamics grounding. We propose a differentiable two-stage network named NeuroFluid. It is shown to reasonably estimate the underlying physics of fluids with different initial shapes, viscosity, and densities.
  arXiv  Detail & Related papers  (2022-03-03T15:13:29Z)
• Fast Gravitational Approach for Rigid Point Set Registration with Ordinary Differential Equations [79.71184760864507]
  This article introduces a new physics-based method for rigid point set alignment called Fast Gravitational Approach (FGA) In FGA, the source and target point sets are interpreted as rigid particle swarms with masses interacting in a globally multiply-linked manner while moving in a simulated gravitational force field. We show that the new method class has characteristics not found in previous alignment methods.
  arXiv  Detail & Related papers  (2020-09-28T15:05:39Z)
• A Near-Optimal Gradient Flow for Learning Neural Energy-Based Models [93.24030378630175]
  We propose a novel numerical scheme to optimize the gradient flows for learning energy-based models (EBMs) We derive a second-order Wasserstein gradient flow of the global relative entropy from Fokker-Planck equation. Compared with existing schemes, Wasserstein gradient flow is a smoother and near-optimal numerical scheme to approximate real data densities.
  arXiv  Detail & Related papers  (2019-10-31T02:26:20Z)

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

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.