English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

The partial differential equation (PDE) plays a significantly important rolein many fields of science and engineering. The conventional case of thederivation of PDE mainly relies on first principles and empirical observation.However, the development of machine learning technology allows us to minepotential control equations from the massive amounts of stored data in a freshway. Although there has been considerable progress in the data-driven discoveryof PDE, the extant literature mostly focuses on the improvements of discoverymethods, without substantial breakthroughs in the discovery process itself,including the principles for the construction of candidates and how toincorporate physical priors. In this paper, through rigorous derivation offormulas, novel physically enhanced machining learning discovery methods forcontrol equations: GSNN (Galileo Symbolic Neural Network) and LSNN (LorentzSymbolic Neural Network) are firstly proposed based on Galileo invariance andLorentz invariance respectively, setting forth guidelines for building thecandidates of discovering equations. The adoption of mandatory embedding ofphysical constraints is fundamentally different from PINN in the form of theloss function, thus ensuring that the designed Neural Network strictly obeysthe physical prior of invariance and enhancing the interpretability of thenetwork. By comparing the results with PDE-NET in numerical experiments ofBurgers equation and Sine-Gordon equation, it shows that the method presentedin this study has better accuracy, parsimony, and interpretability.

Discovering Governing Equations by Machine Learning implemented with Invariance