# Sampling from Boltzmann densities with physics informed low-rank formats

arXiv: https://arxiv.org/abs/2412.07637 · HTML: https://mlsanity.com/paper/2412.07637/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 37 references that are in the map.
- First posted on arXiv 10 Dec 2024.

## Builds on (most cited first, 21 of 21)

- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Stochastic Normalizing Flows](https://mlsanity.com/paper/2002.06707/) (2020)
- [Flow-based generative models for Markov chain Monte Carlo in lattice field theory](https://mlsanity.com/paper/1904.12072/) (2019)
- [An optimal control perspective on diffusion-based generative modeling](https://mlsanity.com/paper/2211.01364/) (2022)
- [Flow Annealed Importance Sampling Bootstrap](https://mlsanity.com/paper/2208.01893/) (2022)
- [User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradient](https://mlsanity.com/paper/1710.00095/) (2017)
- [Annealed Flow Transport Monte Carlo](https://mlsanity.com/paper/2102.07501/) (2021)
- [Continual Repeated Annealed Flow Transport Monte Carlo](https://mlsanity.com/paper/2201.13117/) (2022)
- [Learning Interpolations between Boltzmann Densities](https://mlsanity.com/paper/2301.07388/) (2023)
- [Nonasymptotic estimates for Stochastic Gradient Langevin Dynamics under local conditions in nonconvex optimization](https://mlsanity.com/paper/1910.02008/) (2019)
- [Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpoint](https://mlsanity.com/paper/2109.11375/) (2021)
- [Experience report of physics-informed neural networks in fluid simulations: pitfalls and frustration](https://mlsanity.com/paper/2205.14249/) (2022)
- [Dynamical Measure Transport and Neural PDE Solvers for Sampling](https://mlsanity.com/paper/2407.07873/) (2024)
- [Solving high-dimensional parabolic PDEs using the tensor train format](https://mlsanity.com/paper/2102.11830/) (2021)
- [Functional Tensor Decompositions for Physics-Informed Neural Networks](https://mlsanity.com/paper/2408.13101/) (2024)
- [Neural Sampling from Boltzmann Densities: Fisher-Rao Curves in the Wasserstein Geometry](https://mlsanity.com/paper/2410.03282/) (2024)
- [Importance Corrected Neural JKO Sampling](https://mlsanity.com/paper/2407.20444/) (2024)
- [On free energy barriers in Gaussian priors and failure of cold start MCMC for high-dimensional unimodal distributions](https://mlsanity.com/paper/2209.02001/) (2022)
- [Generative Modelling with Tensor Train approximations of Hamilton--Jacobi--Bellman equations](https://mlsanity.com/paper/2402.15285/) (2024)
- [Dynamical low-rank approximations of solutions to the Hamilton-Jacobi-Bellman equation](https://mlsanity.com/paper/2111.14540/) (2021)
- [Approximating Langevin Monte Carlo with ResNet-like Neural Network architectures](https://mlsanity.com/paper/2311.03242/) (2023)

## Abstract (arXiv)

Our method proposes the efficient generation of samples from an unnormalized Boltzmann density by solving the underlying continuity equation in the low-rank tensor train (TT) format. It is based on the annealing path commonly used in MCMC literature, which is given by the linear interpolation in the space of energies. Inspired by Sequential Monte Carlo, we alternate between deterministic time steps from the TT representation of the flow field and stochastic steps, which include Langevin and resampling steps. These adjust the relative weights of the different modes of the target distribution and anneal to the correct path distribution. We showcase the efficiency of our method on multiple numerical examples.