# Particle-based Energetic Variational Inference

arXiv: https://arxiv.org/abs/2004.06443 · HTML: https://mlsanity.com/paper/2004.06443/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Apr 2020.

## Built on by (most cited first, 14 of 14)

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- [Learning interacting particle systems from unlabeled data](https://mlsanity.com/paper/2604.02581/) (2026)
- [DeePN2: A deep learning-based non-Newtonian hydrodynamic model](https://mlsanity.com/paper/2112.14798/) (2021)
- [Variational Inference via Smoothed Particle Hydrodynamics](https://mlsanity.com/paper/2407.09186/) (2024)
- [A Dirac-Frenkel-Onsager principle: Instantaneous residual minimization with gauge momentum for nonlinear parametrizations of PDE solutions](https://mlsanity.com/paper/2605.00284/) (2026)
- [Variational Inference Using Material Point Method](https://mlsanity.com/paper/2407.20287/) (2024)
- [Accelerating Particle-based Energetic Variational Inference](https://mlsanity.com/paper/2504.03158/) (2025)
- [Dirac-Frenkel dynamics with inertia for nonlinearly parametrized solutions of evolution problems](https://mlsanity.com/paper/2606.24769/) (2026)

## Abstract (arXiv)

We introduce a new variational inference (VI) framework, called energetic variational inference (EVI). It minimizes the VI objective function based on a prescribed energy-dissipation law. Using the EVI framework, we can derive many existing Particle-based Variational Inference (ParVI) methods, including the popular Stein Variational Gradient Descent (SVGD) approach. More importantly, many new ParVI schemes can be created under this framework. For illustration, we propose a new particle-based EVI scheme, which performs the particle-based approximation of the density first and then uses the approximated density in the variational procedure, or "Approximation-then-Variation" for short. Thanks to this order of approximation and variation, the new scheme can maintain the variational structure at the particle level, and can significantly decrease the KL-divergence in each iteration. Numerical experiments show the proposed method outperforms some existing ParVI methods in terms of fidelity to the target distribution.