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

Rapid evolution of sensor technology, advances in instrumentation, andprogress in devising data-acquisition softwares/hardwares are providing vastamounts of data for various complex phenomena, ranging from those inatomospheric environment, to large-scale porous formations, and biologicalsystems. The tremendous increase in the speed of scientific computing has alsomade it possible to emulate diverse high-dimensional, multiscale andmultiphysics phenomena that contain elements of stochasticity, and to generatelarge volumes of numerical data for them in heterogeneous systems. Thedifficulty is, however, that often the governing equations for such phenomenaare not known. A prime example is flow, transport, and deformation processes inmacroscopically-heterogeneous materials and geomedia. In other cases, thegoverning equations are only partially known, in the sense that they eithercontain various coefficients that must be evaluated based on data, or that theyrequire constitutive relations, such as the relationship between the stresstensor and the velocity gradients for non-Newtonian fluids in the momentumconservation equation, in order for them to be useful to the modeling. Severalclasses of approaches are emerging to address such problems that are based onmachine learning, symbolic regression, the Mori-Zwanzig projection operatorformulation, sparse identification of nonlinear dynamics, data assimilation,and stochastic optimization and analysis, or a combination of two or more ofsuch approaches. This Perspective describes the latest developments in thishighly important area, and discusses possible future directions.

Physics-Informed and Data-Driven Discovery of Governing Equations for Complex Phenomena in Heterogeneous Media