The scaling of physics-informed machine learning with data and dimensions. (March 2020)

• Record Type: Journal Article
• Authors: Miller, Scott T.; Lindner, John F.; Choudhary, Anshul; Sinha, Sudeshna; Ditto, William L.
• Is Part Of: Chaos, solitons & fractals. Volume 5(2020)
• Publication Date: 2020-03
• Subjects: Machine learning -- Neural networks -- Hamiltonian dynamics -- High dimensions; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Solitons; Fractals; Chaotic behavior in systems; Periodicals; Electronic journals; 003.7
• DOI: 10.1016/j.csfx.2020.100046
• Languages: English
• ISSNs: 2590-0544

Abstract

Highlights: Physics-informed machine learning scales well with dimensions and data. Hamiltonian surpasses conventional neural networks when forecasting dynamics. Advantage of neural-network inductive (learning) bias persists for complex systems. Forecasting error decreases as a power-law with increasing training pairs. Map-building perspective elucidates the superiority of Hamiltonian neural networks. Abstract: We quantify how incorporating physics into neural network design can significantly improve the learning and forecasting of dynamical systems, even nonlinear systems of many dimensions. We train conventional and Hamiltonian neural networks on increasingly difficult dynamical systems and compute their forecasting errors as the number of training data and number of system dimensions vary. A map-building perspective elucidates the superiority of Hamiltonian neural networks. The results clarify the critical relation among data, dimension, and neural network learning performance.