mlsanityData to 7 Oct 2026

Harmonic (Quantum) Neural Networks

arXiv 2212.07462 ↗First posted 14 Dec 2022cs.LG quant-phcited by 1

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Abstract (arXiv)

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.

Key facts. Cited by 1 paper in the map (data through 7 Oct 2026). Builds on 27 of its 90 references that are in the map. First posted on arXiv 14 Dec 2022.

Builds on

27 of 90 references.

References · 27

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15 more
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Cited by year

Citing papers per year: 2023: 1.

1 paper.

  1. 2023Let Quantum Neural Networks Choose Their Own Frequenciescited by 22