Harmonic (Quantum) Neural Networks
This work addresses a gap in machine learning for applications like industrial optimization and robotics by introducing harmonic function biases, though it appears incremental as it builds on existing physics-informed neural network methods.
The paper tackled the problem of incorporating inductive biases towards harmonic functions in machine learning, demonstrating effective neural network representations and extending them to quantum neural networks, with results showing favorable performance against physics-informed neural networks in benchmarks.
Harmonic functions are abundant in nature, appearing in limiting cases of Maxwell's, Navier-Stokes equations, the heat and the wave equation. Consequently, there are many applications of harmonic functions from industrial process optimisation to robotic path planning and the calculation of first exit times of random walks. Despite their ubiquity and relevance, there have been few attempts to incorporate inductive biases towards harmonic functions in machine learning contexts. In this work, we demonstrate effective means of representing harmonic functions in neural networks and extend such results also to quantum neural networks to demonstrate the generality of our approach. We benchmark our approaches against (quantum) physics-informed neural networks, where we show favourable performance.