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Sampling from Boltzmann densities with physics informed low-rank formats

arXiv 2412.07637 ↗First posted 10 Dec 2024cs.LG math.OCcited by 0

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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.

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.

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21 of 37 references.

References · 21

  1. 2019Normalizing Flows for Probabilistic Modeling and Inferencecited by 1,323
  2. 2020Stochastic Normalizing Flowscited by 157
  3. 2019Flow-based generative models for Markov chain Monte Carlo in lattice field theorycited by 148
  4. 2022An optimal control perspective on diffusion-based generative modelingcited by 147
  5. 2022Flow Annealed Importance Sampling Bootstrapcited by 127
  6. 2017User-friendly guarantees for the Langevin Monte Carlo with inaccurate gradientcited by 116
  7. 2021Annealed Flow Transport Monte Carlocited by 90
  8. 2022Continual Repeated Annealed Flow Transport Monte Carlocited by 66
  9. 2023Learning Interpolations between Boltzmann Densitiescited by 43
  10. 2019Nonasymptotic estimates for Stochastic Gradient Langevin Dynamics under local conditions in nonconvex optimizationcited by 38
  11. 2021Stochastic Normalizing Flows for Inverse Problems: a Markov Chains Viewpointcited by 32
  12. 2022Experience report of physics-informed neural networks in fluid simulations: pitfalls and frustrationcited by 21
9 more
  1. 2024Dynamical Measure Transport and Neural PDE Solvers for Samplingcited by 20
  2. 2021Solving high-dimensional parabolic PDEs using the tensor train formatcited by 17
  3. 2024Functional Tensor Decompositions for Physics-Informed Neural Networkscited by 13
  4. 2024Neural Sampling from Boltzmann Densities: Fisher-Rao Curves in the Wasserstein Geometrycited by 13
  5. 2024Importance Corrected Neural JKO Samplingcited by 7
  6. 2022On free energy barriers in Gaussian priors and failure of cold start MCMC for high-dimensional unimodal distributionscited by 6
  7. 2024Generative Modelling with Tensor Train approximations of Hamilton--Jacobi--Bellman equationscited by 3
  8. 2021Dynamical low-rank approximations of solutions to the Hamilton-Jacobi-Bellman equationcited by 2
  9. 2023Approximating Langevin Monte Carlo with ResNet-like Neural Network architecturescited by 2

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