Learning goals¶
Define matched input/output contracts for a supervised trajectory surrogate
Separate scenario splits from within-trajectory splits
State what a surrogate can and cannot claim about physics and stability
Reading¶
Lab 2 — surrogate versus PINN; neural-network training basics Bishop & Bishop, 2024
Supervised surrogate¶
Given features (e.g. time, operating point, clearing time, or a parameter vector) predict trajectories or a reduced output. Training uses labeled simulator data only — no residual term unless you add one (then you are moving toward a PINN).
| Strength | Limitation |
|---|---|
| Simple baseline; clear budget | Needs enough labeled scenarios |
| Fast evaluation | Extrapolation outside the training distribution is unsafe |
| Easy ablation | Does not enforce physics unless you add constraints |
Data contracts¶
Document:
Channels: which states/outputs are supervised
Normalization fit on training scenarios only
Held-out scenarios chosen before training
Worked example¶
Train a small MLP to predict on a grid of clearing times. Report error on a held-out clearing time near the stability boundary vs far from it.
Lab¶
Lab 2 — Surrogate versus PINN (after Lab 1)
Further reading¶
Supervised training discussion in Thuerey et al. (2021) as method background
Data-driven dynamics Brunton & Kutz, 2022
Common misconceptions¶
Low average trajectory error implies correct CCT decisions
More capacity always fixes distribution shift
Using test events to tune architecture without saying so
- Bishop, C. M., & Bishop, H. (2024). Deep Learning: Foundations and Concepts. Springer. 10.1007/978-3-031-45468-4
- 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
- Brunton, S. L., & Kutz, J. N. (2022). Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control (Second). Cambridge University Press. 10.1017/9781009089517