Physics-informed ML Modeling in Digital Twin

- Physics-informed Loss Function. This approach modifies the loss function of a data-driven ML model by adding a physics informed loss term that penalizes model predictions not compliant with first principles (or physics), thus constraining the training of the ML model toward solutions that comply with physics  
- Data Augmentation. This second approach first runs first-principle simulations to generate data at various states an operating conditions of a physical system.  
- Transfer Learning. It first pre-trains an ML model using a large quantity of data from first-principle simulations. It then fine-tunes the model using a small quantity of real data (e.g., data from physical system experiments).  
- Delta Learning (Missing Physics). The basic idea of this delta learning approach is to add a data-driven ML model, co-existing with a first-principle simulation model, that learns to recover the unmodeled physics.  
- Delta Learning (ML Prediction). In this approach, an ML model learns residuals on top of initial predictions by another ML model, trained using data generated by a physics-based model. The final predictions are the sum of the initial predictions and residuals. The initial predictions can also be made directly by a physics-based model.  
- ML-Assisted Prediction. This sixth approach to physics-informed ML uses a data-driven ML model to predict the input x or parameters θ of a first-principle model.