Algorithm improves sampling from complex physical system models
FUND: Density Flow for Sampling Unnormalised Distributions
Machine Learning
Summary
Sampling accurately from complex distributions is important to model physical systems, but traditional methods like MCMC can be very slow and get stuck. The authors develop a new algorithm that learns to sample from complicated distributions without needing any real examples beforehand. Their method reshapes the distribution iteratively, helping it cover all important modes and improve sampling quality. They tested it on multiple standard problems, showing better performance and accuracy than existing techniques.
What this means in practice
- •For simulation engineers: Improve sampling of energy landscapes in physical and chemical simulations for faster and more accurate modeling of complex systems.
- •For machine learning engineers: Develop generative models that learn complex distributions without requiring costly training samples, enabling more efficient probabilistic modeling.
Authors
Vikas Kanaujia, Vipul Arora
Abstract
Efficient sampling from Boltzmann distributions is central to modelling complex physical systems. Markov Chain Monte Carlo (MCMC) methods suffer from critical slowing down, high autocorrelation, and poor mode-mixing, limiting their scalability. Recent advances, like Boltzmann Generators, offer a promising alternative but remain constrained by costly MCMC-based training, inefficient sampling, and poor ergodicity. We introduce an algorithm for learning Boltzmann distributions that does not require any true samples for training. Our approach draws inspiration from flow matching but departs fundamentally from sample-trajectory matching to distribution-trajectory matching. The algorithm iteratively reshapes the target distribution, using model generated samples to guide learning and ensure comprehensive mode coverage. We validate our method on standard benchmarks, including a 2D Gaussian mixture, Many-Well distributions, and high-dimensional scalar $φ^4$ theory. The proposed approach not only improves sampling performance and accuracy over traditional MCMC and flow-based baselines but also establishes a new method for sample-free learning of complex physical distributions.