# Learning thermodynamic master equations for open quantum systems

arXiv: https://arxiv.org/abs/2506.01882 · HTML: https://mlsanity.com/paper/2506.01882/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 61 references that are in the map.
- First posted on arXiv 2 Jun 2025.

## Builds on (most cited first, 14 of 14)

- [Scientific Machine Learning through Physics-Informed Neural Networks: Where we are and What's next](https://mlsanity.com/paper/2201.05624/) (2022)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Machine learning structure preserving brackets for forecasting irreversible processes](https://mlsanity.com/paper/2106.12619/) (2021)
- [GFINNs: GENERIC Formalism Informed Neural Networks for Deterministic and Stochastic Dynamical Systems](https://mlsanity.com/paper/2109.00092/) (2021)
- [Deep learning of thermodynamics-aware reduced-order models from data](https://mlsanity.com/paper/2007.03758/) (2020)
- [Learning to predict arbitrary quantum processes](https://mlsanity.com/paper/2210.14894/) (2022)
- [Thermodynamics-informed graph neural networks](https://mlsanity.com/paper/2203.01874/) (2022)
- [Reversible and irreversible bracket-based dynamics for deep graph neural networks](https://mlsanity.com/paper/2305.15616/) (2023)
- [Partial Differential Equations Meet Deep Neural Networks: A Survey](https://mlsanity.com/paper/2211.05567/) (2022)
- [Physics-Guided, Physics-Informed, and Physics-Encoded Neural Networks in Scientific Computing](https://mlsanity.com/paper/2211.07377/) (2022)
- [Improved machine learning algorithm for predicting ground state properties](https://mlsanity.com/paper/2301.13169/) (2023)
- [Port-metriplectic neural networks: thermodynamics-informed machine learning of complex physical systems](https://mlsanity.com/paper/2211.01873/) (2022)
- [Thermodynamics of learning physical phenomena](https://mlsanity.com/paper/2207.12749/) (2022)
- [Solving The Quantum Many-Body Hamiltonian Learning Problem with Neural Differential Equations](https://mlsanity.com/paper/2408.08639/) (2024)

## Abstract (arXiv)

The characterization of Hamiltonians and other components of open quantum dynamical systems plays a crucial role in quantum computing and other applications. Scientific machine learning techniques have been applied to this problem in a variety of ways, including by modeling with deep neural networks. However, the majority of mathematical models describing open quantum systems are linear, and the natural nonlinearities in learnable models have not been incorporated using physical principles. We present a data-driven model for open quantum systems that includes learnable, thermodynamically consistent terms. The trained model is interpretable, as it directly estimates the system Hamiltonian and linear components of coupling to the environment. We validate the model on synthetic two and three-level data, as well as experimental two-level data collected from a quantum device at Lawrence Livermore National Laboratory.