# Machine Learning of Thermodynamic Observables in the Presence of Mode Collapse

arXiv: https://arxiv.org/abs/2111.11303 · HTML: https://mlsanity.com/paper/2111.11303/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 28 references that are in the map.
- First posted on arXiv 22 Nov 2021.

## Builds on (most cited first, 11 of 11)

- [Flow-based generative models for Markov chain Monte Carlo in lattice field theory](https://mlsanity.com/paper/1904.12072/) (2019)
- [Equivariant flow-based sampling for lattice gauge theory](https://mlsanity.com/paper/2003.06413/) (2020)
- [Solving Statistical Mechanics Using Variational Autoregressive Networks](https://mlsanity.com/paper/1809.10606/) (2018)
- [Targeted free energy estimation via learned mappings](https://mlsanity.com/paper/2002.04913/) (2020)
- [Normalizing flows for atomic solids](https://mlsanity.com/paper/2111.08696/) (2021)
- [Flow-based sampling for multimodal and extended-mode distributions in lattice field theory](https://mlsanity.com/paper/2107.00734/) (2021)
- [Scaling Up Machine Learning For Quantum Field Theory with Equivariant Continuous Flows](https://mlsanity.com/paper/2110.02673/) (2021)
- [Generalization capabilities of translationally equivariant neural networks](https://mlsanity.com/paper/2103.14686/) (2021)
- [Quantum field-theoretic machine learning](https://mlsanity.com/paper/2102.09449/) (2021)
- [Towards reduction of autocorrelation in HMC by machine learning](https://mlsanity.com/paper/1712.03893/) (2017)
- [Comment on "Solving Statistical Mechanics Using VANs": Introducing saVANt - VANs Enhanced by Importance and MCMC Sampling](https://mlsanity.com/paper/1903.11048/) (2019)

## Built on by (most cited first, 10 of 10)

- [Learning Lattice Quantum Field Theories with Equivariant Continuous Flows](https://mlsanity.com/paper/2207.00283/) (2022)
- [Detecting and Mitigating Mode-Collapse for Flow-based Sampling of Lattice Field Theories](https://mlsanity.com/paper/2302.14082/) (2023)
- [Gradients should stay on Path: Better Estimators of the Reverse- and Forward KL Divergence for Normalizing Flows](https://mlsanity.com/paper/2207.08219/) (2022)
- [On Sampling with Approximate Transport Maps](https://mlsanity.com/paper/2302.04763/) (2023)
- [A theoretical perspective on mode collapse in variational inference](https://mlsanity.com/paper/2410.13300/) (2024)
- [Applications of flow models to the generation of correlated lattice QCD ensembles](https://mlsanity.com/paper/2401.10874/) (2024)
- [AdvNF: Reducing Mode Collapse in Conditional Normalising Flows using Adversarial Learning](https://mlsanity.com/paper/2401.15948/) (2024)
- [Flow-based density of states for complex actions](https://mlsanity.com/paper/2203.01243/) (2022)
- [Multi-Lattice Sampling of Quantum Field Theories via Neural Operator-based Flows](https://mlsanity.com/paper/2401.00828/) (2024)
- [Simulating the Hubbard Model with Equivariant Normalizing Flows](https://mlsanity.com/paper/2501.07371/) (2025)

## Abstract (arXiv)

Estimating the free energy, as well as other thermodynamic observables, is a key task in lattice field theories. Recently, it has been pointed out that deep generative models can be used in this context [1]. Crucially, these models allow for the direct estimation of the free energy at a given point in parameter space. This is in contrast to existing methods based on Markov chains which generically require integration through parameter space. In this contribution, we will review this novel machine-learning-based estimation method. We will in detail discuss the issue of mode collapse and outline mitigation techniques which are particularly suited for applications at finite temperature.