Zhang Pin

on the 4 May 2023
Data-Driven Modelling for Discovery and Solution of Partial Differential Equations

Identifying governing equations from data and solving them to acquire spatio-temporal responses is desirable, yet highly challenging, for many practical problems. Machine learning (ML) has emerged as an alternative to influence knowledge discovery in complex geotechnical processes. To demonstrate feasibility, this study develops an ML-assisted data-driven approach to automatically recover Terzaghi’s consolidation theory from measured data and obtain the corresponding solutions. This process incorporates several algorithms including sparse regression and prior information based neural network (PiNet), transformed weak-form partial differential equations (PDEs) (to reduce sensitivity to noisy measurement), and Monte Carlo dropout to achieve a measure of prediction uncertainty. The results indicate that consolidation PDEs can be accurately extracted using the proposed approach which is also shown to be robust to noisy measurements. PDEs solved by PiNet are also shown to provide excellent agreement with actual results thus highlighting its potential for inverse analysis. The proposed approach is generic and provides an auxiliary method to verify heuristic interpretations of data or to directly identify patterns and obtain solutions without the need for expert intervention.


Galilée room 011
Mis à jour le 21 April 2023