Learning goals¶
Name major SciML families used for power-system dynamics and TSA
Say what each family learns (trajectory, vector field, operator, …)
Avoid treating every neural method as “a PINN”
Reading¶
Physics-informed machine learning overview Karniadakis et al., 2021
Overview and models chapter of Thuerey et al. (2021)
Plain-words map¶
SciML here means: neural models with physics structure for dynamics or margins — not only black-box stable/unstable classifiers.
| Family | Learns (roughly) | Teaching role in this book |
|---|---|---|
| Supervised surrogate | Map features → trajectories / labels | Mandatory baseline (Lab 2) |
| PINN (collocation) | with residual loss | Core forward / inverse path |
| Neural ODE / hybrid | Vector field (+ optional known physics) | Lab 4 option |
| Operator learning (DeepONet / FNO) | Function → function | Advanced / Lab 4 option; not inverse named- default |
| Differentiable simulator | Sensitivities through a solver | Identification (differentiable simulation); Lab 3 option |
| Classical simulation | Reference trajectories | Lab 1 and all baselines |
For transient stability, families differ mainly by whether they output trajectories, decisions, or operators — and how CCT search sits on top. Details: Stability pillar.
How tightly is physics coupled?¶
A second way to sort the same families is by how tightly the physics is built into training. This ordering follows the method textbook by Thuerey et al. (2021). Here it is restated for the SMIB swing equation.
| Level | Where the swing equation enters | Gradient comes from | In this book |
|---|---|---|---|
| 1. Supervised surrogate | Only through simulator-generated labels | Data mismatch | Data and surrogates, Lab 2 baseline |
| 2. Physics loss (PINN) | Residual at collocation points | Data mismatch + residual (soft constraint) | Forward PINN, inverse PINN, Labs 2–3 |
| 3. Differentiable simulator | A numerical integrator (e.g. RK4) rolled out in an AD framework | Mismatch of the simulated trajectory, differentiated through every solver step | Differentiable simulation, Lab 3 option; hybrid models in Neural ODE / hybrid |
Plain words: moving down the table, the model is allowed to break the physics less, but each training step costs more and needs a solver you can differentiate.
Tighter coupling is not automatically better. Pick the level from the engineering question and the data contract, not from the ladder.
Further reading¶
Neural ODEs Chen et al., 2018 and universal differential equations Rackauckas et al., 2020, developed in Neural ODEs and hybrid models
Common misconceptions¶
“DeepONet is a PINN variant”
Ranking methods by hype instead of task fit
Skipping classical simulation because a neural method exists
“The most tightly coupled method is always the best one”
- Karniadakis, G. E., Kevrekidis, I. G., Lu, L., Perdikaris, P., Wang, S., & Yang, L. (2021). Physics-informed machine learning. Nature Reviews Physics, 3(6), 422–440. 10.1038/s42254-021-00314-5
- Thuerey, N., Holzschuh, B., Holl, P., Kohl, G., Lino, M., Liu, Q., Schnell, P., & Trost, F. (2021). Physics-based Deep Learning. arXiv. 10.48550/arXiv.2109.05237
- Chen, R. T. Q., Rubanova, Y., Bettencourt, J., & Duvenaud, D. (2018). Neural Ordinary Differential Equations. arXiv. 10.48550/arXiv.1806.07366
- Rackauckas, C., Ma, Y., Martensen, J., Warner, C., Zubov, K., Supekar, R., Skinner, D., Ramadhan, A., & Edelman, A. (2020). Universal Differential Equations for Scientific Machine Learning. arXiv. 10.48550/arXiv.2001.04385