Mathematics of Digital Twins and Transfer Learning for PDE Models

The paper presents a digital twin (DT) framework for physical systems governed by partial differential equations (PDEs), using a Karhunen-Loève Neural Network (KL-NN) surrogate model and transfer learning (TL). The KL-NN model enables fast inference and differentiability for optimization and control, while TL allows efficient retraining with minimal data for new conditions. The study analyzes TL using moment equations to identify transferable parameters and optimize control variable selection. For linear PDEs, one-shot TL is shown to be exact, while for nonlinear PDEs, errors are introduced, and parameter estimation requires additional methods such as mean-field equations and least square approaches for accurate adaptation.

Read the full paper here:
Mathematics of Digital Twins and Transfer Learning for PDE Models