Physically-consistent quantum dissipative dynamics simulations with neural networks

The work “Physics-Informed Neural Networks and Beyond: Enforcing Physical Constraints in Quantum Dissipative Dynamics” performed in collaboration of Professor Pavlo O. Dral (Xiamen University) and Assistant Professor Arif Ullah (Anhui University) was published in Digital Discovery. In this blog, Arif Ullah highlights this recent work which addresses the issue of trace conservation in machine learning-based quantum dissipative dynamics. In this work, we demonstrate that existing machine learning approaches often violate trace conservation, leading to inaccurate results. To address this, we propose a Physics-informed neural network and a novel uncertainty-aware hard coded constraint approach that enforces perfect trace conservation by design.

Let me start with the open quantum systems which are ubiquitous in nature, and have applications from quantum information to photosynthesis. Simulating these systems is crucial for understanding fundamental quantum phenomena.

However, the exact characterization of open quantum systems poses significant challenges due to the exponential growth in Hilbert space dimension and the complexity of environmental interactions. Traditional methods have limitations in accurately capturing quantum effects and computational efficiency. That’s where machine learning comes into play.

Machine learning, particularly neural networks, has shown great promise in learning spatio-temporal dynamics. They can efficiently predict the future evolution of quantum states. 

While neural networks are powerful tools, their reliance on data-driven approximations can lead to limitations. In the context of quantum dissipative dynamics, purely data-driven models often fail to capture underlying physical laws such as trace conservation which should remain equal to 1. As shown in this figure, existing ML approaches do not conserve trace in the case of spin-boson model and FMO complex. 

To address the issue of trace conservation, they developed physics-informed neural networks (PINNs). PINNs incorporate physical constraints directly into the loss function. In their case, they integrated the trace conservation constraint into the model. While PINNs significantly improve trace conservation, they can still exhibit minor violations as we see in the figure shown here.

To overcome this limitation, they introduced the uncertainty-aware hard coded constraint which unlike PINNs, enforces trace conservation by design, guaranteeing perfect adherence to physical laws during simulations. It utilizes uncertainty quantification techniques to redistribute residual errors and ensure rigorous compliance with the trace conservation principle.

To summarize, they evaluated the effectiveness of PINNs and U-aware HC constraint in enforcing trace conservation for both the spin-boson model and the FMO complex. Their results demonstrate that PINNs significantly outperform pure data-driven models in terms of trace conservation. However, the U-aware HC approach, when combined with PINNs, achieves perfect trace conservation throughout the simulations. This highlights the importance of enforcing physical constraints rigorously.

Publication

• Arif Ullah*, Yu Huang, Ming Yang, Pavlo O. Dral*. Physics-Informed Neural Networks and Beyond: Enforcing Physical Constraints in Quantum Dissipative Dynamics. Digit. Discov. 2024. DOI: 10.1039/D4DD00153B
  Preprint on arXiv: https://arxiv.org/abs/2404.14021.