Chemometrics Hybrid Modeling

Use hybrid modeling when:

• You have partial mechanistic knowledge of the system
• Pure mechanistic models are inaccurate (missing phenomena)
• Pure ML models violate physical laws
• Need interpretable predictions that respect physics
• Want to extrapolate beyond training data safely
• Have limited data but know underlying physics
• Modeling chemical processes, reactions, or thermodynamics
• Dealing with Beer-Lambert law deviations in spectroscopy

Core Hybrid Modeling Approaches

Residual Modeling: y_pred = y_mechanistic + ML(x, residual). Simplest hybrid -- start here. Details: references/approaches.md

Parallel Hybrid: y_pred = w1 * y_mech + w2 * y_ML. Weighted ensemble of both worlds. Details: references/approaches.md

Physics-Informed NN: Add physics loss terms (non-negativity, mass balance, PDEs) to training. Details: references/approaches.md

Mechanistic Features: Compute Arrhenius rates, dimensionless numbers, etc. as ML inputs. Details: references/approaches.md

Constrained Optimization: Post-process ML predictions with NMF, NNLS, or scipy constraints. Details: references/approaches.md

When to Use What

Application Examples

Full worked examples with code comparing pure ML, pure mechanistic, and hybrid approaches. Details: references/application-examples.md

• NIR Spectroscopy: Beer-Lambert deviations corrected via residual modeling
• Chemical Reactor: Arrhenius kinetics augmented with NN correction
• Spectral Unmixing: PLS with mass balance enforcement (normalization + non-negativity)

Best Practices, Pitfalls, and Advanced Topics

Guidance on validation, interpretation, extrapolation testing, common mistakes, transfer learning, and multi-fidelity modeling. Details: references/approaches.md

Key points:

• Always compare pure mechanistic, pure ML, and hybrid (choose hybrid only if it wins)
• Validate physics constraints on predictions (non-negativity, mass balance, range)
• Interpret residual importance to find where physics breaks down
• Test extrapolation performance -- hybrid should degrade gracefully
• Avoid model mismatch (validate mechanistic component first, R2 > 0)
• Balance lambda_physics to avoid over-constraining

See Also

• ML method selection: ../chemometrics-ml-selection/SKILL.md
• Validation strategies: ../chemometrics-shared/references/validation-strategies.md
• Performance metrics: ../chemometrics-shared/references/performance-metrics.md

References

• Trinh et al. (2021). Machine Learning in Chemical Product Engineering. Processes, 9(8), 1456.
• von Stosch et al. (2014). Hybrid semi-parametric modeling in process systems engineering. Computers & Chemical Engineering, 60, 86-101.
• Psichogios & Ungar (1992). A hybrid neural network-first principles approach to process modeling. AIChE Journal, 38(10), 1499-1511.
• Raissi et al. (2019). Physics-informed neural networks. Journal of Computational Physics, 378, 686-707.