Evaluating Artificial Neural Networks and Quantum Computing for Solving Mechanical Boundary Value Problems
A. Mielke, und T. Ricken. Advances in Engineering Materials, Structures and Systems: Innovations, Mechanics and Applications, Seite 537-542. PO box 11320, Leiden, 2301 EH, Netherlands, Natl Res Fdn S Africa; S African Natl Roads Agcy Ltd; ADINA R & D Inc, CRC Press-Balkema, (2019)7th International Conference on Structural Engineering, Mechanics and Computation (SEMC), Cape Town, SOUTH AFRICA, SEP 02-04, 2019.
Artificial neural networks (ANNs) and quantum computing (QC) have both received rapidly increasing interest in recent years for several reasons. Their roles in the mechanics community remain a subject of ongoing debate and research. ANNs have successfully been employed on problems previously considered unsolvable (Silver et al. 2016), as well as on practical and illustrative problems especially in the image recognition domain (Szegedy et al. 2013, among others). The most straightforward way to interpret the behavior of ANNs is focusing on their ability to approximate any continuous function to arbitrary precision (Kreinovich 1991). The adjustment to a given function happens automatically except for hyperparameters, such as the number of hidden layers or the learning rate, which remain constant during training. This makes them a perfect tool for reducing computational cost in otherwise time-consuming simulations.
Quantum computing on the other hand has received some publicity in 2018 mainly because of a paper published by Google Quantum A.I. Lab scientists defining quantum supremacy (Boixo & Isakov 2018), where it is shown that a fully working universal quantum computer with only 50 qubits will outperform any near-term realizable classical supercomputer on certain tasks. This publicationwas followed up by Google revealing Bristlecone (Kelly 2018), a quantum processor consisting of 72 qubits.
While many interesting quantum algorithms have proven to run polynomially or even exponentially faster than their classical analogons (Montanaro 2016), these results only hold true for a decoherence-free machine. Therefore, to actually achieve quantum supremacy, quantum error correction schemes need to be implemented, requiring several physical qubits to make up a single logical qubit suitable for computation.