Physics-Informed Neural Networks and Beyond: Enforcing Physical Constraints in Quantum Dissipative Dynamics

TL;DR

This paper introduces physics-informed neural networks (PINNs) and an uncertainty-aware method to improve the physical accuracy of quantum dissipative dynamics simulations, ensuring trace conservation and adherence to fundamental laws.

Contribution

The paper develops PINNs for quantum dynamics and proposes a novel uncertainty-aware approach that guarantees perfect trace conservation, advancing the fidelity of neural network simulations.

Findings

PINNs reduce violations of trace conservation in quantum simulations.

The uncertainty-aware method enforces perfect trace conservation by design.

Proposed approaches outperform existing NN methods in physical accuracy.

Abstract

Neural networks (NNs) accelerate simulations of quantum dissipative dynamics. Ensuring that these simulations adhere to fundamental physical laws is crucial, but has been largely ignored in the state-of-the-art NN approaches. We show that this may lead to implausible results measured by violation of the trace conservation. To recover the correct physical behavior, we develop physics-informed NNs (PINNs) that mitigate the violations to a good extend. Beyond that, we propose a novel uncertainty-aware approach that enforces perfect trace conservation by design, surpassing PINNs.