When does a physics-based model outperform machine learning, when does ML win, and how can hybrid approaches combine both for better robustness and interpretability? System to Model (Simple but Powerful)
We intentionally choose a system that is:
- physically interpretable
- time-dependent
- sensor-like
Chosen System: # Thermal system (1st-order dynamic system) → analogous to many real sensors (temperature, drift, latency, noise)
Physical model: 𝑑𝑇(𝑡)𝑑𝑡=−𝑘(𝑇(𝑡)−𝑇𝑒𝑛𝑣)+𝑢(𝑡)dt/dT(t)=−k⋅(T(t)−Tenv)+u(t)
Where:
T(t) = system state (measured) T_env = environment k = system constant u(t) = external input / disturbance
Modeling Approach: Physics model → baseline prediction ML model → predicts residual error
Evaluation & Validation: compare: RMSE MAE robustness to noise behavior under missing data generalization to unseen inputs
Also include: qualitative plots error breakdowns failure cases
Tools: Python numpy pandas scikit-learn matplotlib
scipy