Hybrid-Modeling-of-Sensor-Time-Series-Physics-Based-vs-Machine-Learning-Approaches

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:

1. physically interpretable
2. time-dependent
3. 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