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QI: Fachverband Quanteninformation
QI 2: Quantum Machine Learning I
QI 2.1: Vortrag
Montag, 10. März 2025, 11:00–11:15, HS VIII
Self-Adaptive Physics-Informed Quantum Machine Learning for Solving Differential Equations — •Abhishek Setty1,2,3, Rasul Abdusalamov1, and Felix Motzoi2,3 — 1Department of Continuum Mechanics, RWTH Aachen University, Germany — 2Forschungszentrum Jülich, Institute of Quantum Control (PGI-8), D-52425 Jülich, Germany — 3Institute for Theoretical Physics, University of Cologne, D-50937 Cologne, Germany
Chebyshev polynomials have shown significant promise as an efficient tool for both classical and quantum neural networks to solve linear and nonlinear differential equations. In this work, we adapt and generalize this framework in a quantum machine learning setting for a variety of problems, including the 2D Poisson's equation, second-order linear differential equation, system of differential equations, nonlinear Duffing and Riccati equation. In particular, we propose in the quantum setting a modified Self-Adaptive Physics-Informed Neural Network (SAPINN) approach, where self-adaptive weights are applied to problems with multi-objective loss functions. We further explore capturing correlations in our loss function using a quantum-correlated measurement, resulting in improved accuracy for initial value problems. We analyse also the use of entangling layers and their impact on the solution accuracy for second-order differential equations. The results indicate a promising approach to the near-term evaluation of differential equations on quantum devices.
Keywords: Quantum Machine Learning; Differential Equations; Variational Quantum Algorithms; Physics Informed Neural Networks