Abstract Scope |
Discovering the governing equations for various phenomena involving heterogeneity or stochasticity, has dominated the physical sciences and engineering. The classical approach has been based on the fundamental conservation laws, which are averaged over an ensemble of possible realizations. This is valid only if there is a well-defined representative elementary volume, which might not exist. At the same time, rapid advances in various technologies for data-acquisition software/hardware have also opened new fields of exploration for which the governing equations are difficult to derive. The most obvious examples are biological, and nano- and neurosciences where first-principle derivations are very difficult to carry out, while data are becoming abundant. How do we discover the governing equations that not only honor and better explain the data, but also provide predictions for either the future, or over larger length scales? This presentation describes advances in this new field and discusses two examples in detail. |