AgentSkillsCN

chemometrics-hybrid-modeling

化学计量学与化学工程领域中，关于如何将机理模型与机器学习相结合（混合建模）的指南。涵盖物理信息驱动的机器学习、残差建模、模型增强，以及约束引入等方法，以提升预测精度与模型可解释性。

SKILL.md
--- frontmatter
name: chemometrics-hybrid-modeling
description: Guide for combining mechanistic models with machine learning (hybrid modeling) in chemometrics and chemical engineering. Covers physics-informed ML, residual modeling, model augmentation, and constraint incorporation for improved predictions and interpretability.
license: MIT
metadata:
  skill-author: Alban Ott
  based-on: Trinh et al. 2021 - Machine Learning in Chemical Product Engineering

Chemometrics Hybrid Modeling

Hybrid modeling combines mechanistic (first-principles) models with machine learning. Use physics/chemistry knowledge where available; use ML to learn what is unknown or too complex.

Why Hybrid Models?

AspectPure MechanisticPure Data-DrivenHybrid
InterpretabilityHighLow (black box)Moderate-High
ExtrapolationGood within physicsPoorBetter than pure ML
Data requirementsLowHighModerate
FlexibilityLimited to known physicsLearns any patternPhysics + data flexibility
Physical validityGuaranteedMay violate lawsConstrained by design
Development effortHigh (needs domain)Low (needs data)Moderate

When to Use This Skill

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

#ApproachFormula / IdeaBest For
1Residual Modeling (Serial)y = y_mech + ML(x, residual)Decent mech. model with systematic bias
2Parallel Hybrid (Ensemble)y = w1*y_mech + w2*y_MLBoth models have merits; uncertain form
3Physics-Informed NN (PINNs)Physics laws as loss constraintsPDE-governed systems (diffusion, flow)
4Mechanistic Features for MLEngineer physics features as ML inputsPartial domain knowledge available
5Constrained OptimizationML predictions post-processed for feasibilityML violates known inequality bounds

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

SituationRecommended Approach
Good mech. model, systematic residuals1 - Residual Modeling
Two decent models, want best of both2 - Parallel Hybrid
PDEs / differential equations govern system3 - Physics-Informed NN
Know relevant dimensionless numbers / rates4 - Mechanistic Features
ML predictions violate physical constraints5 - Constrained Optimization
Not sure where to start1 - Residual Modeling (simplest)

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

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.