On physics-informed neural networks for quantum computers

Abstract

Physics-Informed Neural Networks (PINN) emerged as a powerful tool for solving scientific computing problems, ranging from the solution of Partial Differential Equations to data assimilation tasks. One of the advantages of using PINN is to leverage the usage of Machine Learning computational frameworks relying on the combined usage of CPUs and co-processors, such as accelerators, to achieve maximum performance. This work investigates the design, implementation, and performance of PINNs, using the Quantum Processing Unit (QPU) co-processor. We design a simple Quantum PINN to solve the one-dimensional Poisson problem using a Continuous Variable (CV) quantum computing framework. We discuss the impact of different optimizers, PINN residual formulation, and quantum neural network depth on the quantum PINN accuracy. We show that the optimizer exploration of the training landscape in the case of quantum PINN is not as effective as in classical PINN, and basic Stochastic Gradient Descent (SGD) optimizers outperform adaptive and high-order optimizers. Finally, we highlight the difference in methods and algorithms between quantum and classical PINNs and outline future research challenges for quantum PINN development.

Programming Quantum Neural Networks on NISQ Systems: An Overview of Technologies and Methodologies

“…Because of the continuous approach, CV QPC is regarded as an excellent fit for QNN regression-like tasks. In addition, CV QNNs are a critical building block for developing quantum Physics Informed Neural Networks (PINN) using CV gates [ 31 ]. The most established technology to implement CV quantum gates is photonics.…”

Quantum Computing for Climate Change Detection, Climate Modeling, and Climate Digital Twin

“…The third approach is to integrate physics laws and models with practical datasets and QML models when a physical model for an event is known, and data is scarce in nature. Here, Quantum Physics-Informed Neural Networks (QPINNs) proposed by the authors of the articles [50,51] can be applied to, e.g., a rainfall-runoff model that is used for the prediction of flooding and drought analysis [52]. Here, PINNs are ML and DL models imposed by physics laws and PDEs [53,54], and QPINNs refer to PINNs whose conventional NNs are replaced by QML models.…”

“…Due to the limitation of the memory capacity of computing devices and large-scale climate datasets, we need to train conventional DL models on a small subset of climate datasets, and however, they do not generalize well on small-scale datasets compared to large-scale ones [64]. To overcome the small dataset challenge, QPINNs can be utilized for predicting and projecting some climate states [50,51,61]. 3.…”