# Physics-Driven Learning for Inverse Problems in Quantum Chromodynamics

arXiv: https://arxiv.org/abs/2501.05580 · HTML: https://mlsanity.com/paper/2501.05580/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 34 of its 118 references that are in the map.
- First posted on arXiv 9 Jan 2025.

## Builds on (most cited first, 30 of 34)

- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Deep Unsupervised Learning using Nonequilibrium Thermodynamics](https://mlsanity.com/paper/1503.03585/) (2015)
- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Group Equivariant Convolutional Networks](https://mlsanity.com/paper/1602.07576/) (2016)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [Deep Neural Networks as Gaussian Processes](https://mlsanity.com/paper/1711.00165/) (2017)
- [The frontier of simulation-based inference](https://mlsanity.com/paper/1911.01429/) (2019)
- [Deep Convolutional Neural Network for Inverse Problems in Imaging](https://mlsanity.com/paper/1611.03679/) (2016)
- [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://mlsanity.com/paper/1711.10561/) (2017)
- [Invertible Residual Networks](https://mlsanity.com/paper/1811.00995/) (2018)
- [Gauge Equivariant Convolutional Networks and the Icosahedral CNN](https://mlsanity.com/paper/1902.04615/) (2019)
- [e3nn: Euclidean Neural Networks](https://mlsanity.com/paper/2207.09453/) (2022)
- [Neural Importance Sampling](https://mlsanity.com/paper/1808.03856/) (2018)
- [Equivariant flow-based sampling for lattice gauge theory](https://mlsanity.com/paper/2003.06413/) (2020)
- [A Living Review of Machine Learning for Particle Physics](https://mlsanity.com/paper/2102.02770/) (2021)
- [Physics-based Deep Learning](https://mlsanity.com/paper/2109.05237/) (2021)
- [Neural Networks and Quantum Field Theory](https://mlsanity.com/paper/2008.08601/) (2020)
- [Lattice gauge equivariant convolutional neural networks](https://mlsanity.com/paper/2012.12901/) (2020)
- [Physical Symmetries Embedded in Neural Networks](https://mlsanity.com/paper/1904.08991/) (2019)
- [Advances in machine-learning-based sampling motivated by lattice quantum chromodynamics](https://mlsanity.com/paper/2309.01156/) (2023)
- [Enabling real-time multi-messenger astrophysics discoveries with deep learning](https://mlsanity.com/paper/1911.11779/) (2019)
- [Quantum field-theoretic machine learning](https://mlsanity.com/paper/2102.09449/) (2021)
- [Renormalizing Diffusion Models](https://mlsanity.com/paper/2308.12355/) (2023)
- [Applications of Machine Learning to Lattice Quantum Field Theory](https://mlsanity.com/paper/2202.05838/) (2022)
- [Towards Novel Insights in Lattice Field Theory with Explainable Machine Learning](https://mlsanity.com/paper/2003.01504/) (2020)
- [Stochastic weight matrix dynamics during learning and Dyson Brownian motion](https://mlsanity.com/paper/2407.16427/) (2024)
- [Geometrical aspects of lattice gauge equivariant convolutional neural networks](https://mlsanity.com/paper/2303.11448/) (2023)
- [Gauge-equivariant pooling layers for preconditioners in lattice QCD](https://mlsanity.com/paper/2304.10438/) (2023)
- [Reconstructing spectral functions via automatic differentiation](https://mlsanity.com/paper/2111.14760/) (2021)
- [Extensive Studies of the Neutron Star Equation of State from the Deep Learning Inference with the Observational Data Augmentation](https://mlsanity.com/paper/2101.08156/) (2021)

## Built on by (most cited first, 7 of 7)

- [Physics-Conditioned Diffusion Models for Lattice Gauge Theory](https://mlsanity.com/paper/2502.05504/) (2025)
- [Machine Learning - Driven Materials Discovery: Unlocking Next-Generation Functional Materials - A review](https://mlsanity.com/paper/2503.18975/) (2025)
- [Phase diagram and eigenvalue dynamics of stochastic gradient descent in multilayer neural networks](https://mlsanity.com/paper/2509.01349/) (2025)
- [Latent Representation Learning in Heavy-Ion Collisions with MaskPoint Transformer](https://mlsanity.com/paper/2510.06691/) (2025)
- [How unconstrained machine-learning models learn physical symmetries](https://mlsanity.com/paper/2603.24638/) (2026)
- [Starter-Iterator Neural Operator: A Unified Architecture for High-Fidelity Forward and Inverse PDE Problems](https://mlsanity.com/paper/2606.18305/) (2026)
- [Machine Learning Meets High-Energy Nuclear Physics: From Pattern Recognition to Physics-Integrated Discovery](https://mlsanity.com/paper/2610.12293/) (2026)

## Abstract (arXiv)

The integration of deep learning techniques and physics-driven designs is reforming the way we address inverse problems, in which accurate physical properties are extracted from complex data sets. This is particularly relevant for quantum chromodynamics (QCD), the theory of strong interactions, with its inherent limitations in observational data and demanding computational approaches. This perspective highlights advances and potential of physics-driven learning methods, focusing on predictions of physical quantities towards QCD physics, and drawing connections to machine learning(ML). It is shown that the fusion of ML and physics can lead to more efficient and reliable problem-solving strategies. Key ideas of ML, methodology of embedding physics priors, and generative models as inverse modelling of physical probability distributions are introduced. Specific applications cover first-principle lattice calculations, and QCD physics of hadrons, neutron stars, and heavy-ion collisions. These examples provide a structured and concise overview of how incorporating prior knowledge such as symmetry, continuity and equations into deep learning designs can address diverse inverse problems across different physical sciences.