Physics-Constrained Neural Identification of Thermal Kinetic Parameters from Multi-Rate Thermogravimetric Data

Technical Summary: Physics-Constrained Neural Identification of Thermal Kinetic Parameters

Problem Statement
Reliable estimation of thermal kinetic parameters (activation energy $E_a$, pre-exponential factor $A$, and reaction order $n$) is critical for the safe design and scale-up of biomass pyrolysis, waste-to-energy conversion, and thermal recycling. However, extracting these parameters from Thermogravimetric Analysis (TGA) data is an ill-conditioned inverse problem. Conventional methods face three primary challenges:

1. Strong Correlation: The Arrhenius parameters $A$ and $E_a$ are highly correlated, leading to non-unique solutions.
2. Noise Amplification: Derivative-based methods (e.g., Friedman analysis) amplify measurement noise, degrading accuracy.
3. Limited Generalizability: Parameters inferred at a single heating rate often fail to predict conversion curves at other, unseen heating rates.

While machine learning offers new pattern-recognition capabilities, purely data-driven models often violate physical consistency, failing to represent admissible thermal processes or extrapolate reliably.

Methodology
The authors propose a physics-constrained neural identification framework that simultaneously reconstructs conversion curves and estimates the Arrhenius triplet from multi-rate non-isothermal TGA data. The approach integrates the governing differential equations directly into the neural network's training objective.

• Neural Surrogate: A feedforward neural network, $z_\theta(\tilde{T}, \tilde{\beta})$, maps normalized temperature and heating rate to an unconstrained scalar. The conversion $\alpha$ is represented as a bounded function using a sigmoid activation: $\alpha_\theta(T, \beta) = \sigma(z_\theta)$. This ensures physically admissible conversion values ($0 \le \alpha \le 1$).
• Differentiable Physics: Automatic differentiation is used to evaluate the temperature derivative $\partial \alpha_\theta / \partial T$ required by the kinetic equation, avoiding finite-difference noise amplification.
• Parameterization: To enforce positivity and improve conditioning, kinetic parameters are reparameterized using unconstrained trainable variables ($q_E, q_A, q_n$) mapped through sigmoid functions to specific physical bounds (e.g., $E_a \in [50, 300]$ kJ mol$^{-1}$).
• Composite Objective Function: The training loss ($L$) combines five components:
  1. Data Mismatch ($L_{data}$): Mean squared error between predicted and observed conversion.
  2. Physics Residual ($L_{phys}$): Mean squared error of the kinetic equation residual: $\beta \frac{\partial \alpha}{\partial T} - A \exp(-E_a/RT)(1-\alpha)^n$.
  3. Initial Condition ($L_0$): Penalty for non-zero conversion at the start temperature.
  4. Monotonicity ($L_{mono}$): Penalty ensuring the decomposition rate is non-negative.
  5. Regularization: Weight decay on network weights.
     An adaptive weighting strategy balances the data and physics terms during optimization.

Experimental Design (Benchmark)
The study utilizes a controlled computational benchmark rather than experimental data to establish a reproducible baseline.

• Reference Model: A generalized $n$-th order decomposition law ($f(\alpha) = (1-\alpha)^n$) with known parameters ($E_a = 155$ kJ mol$^{-1}$, $A = 2.50 \times 10^{10}$ s$^{-1}$, $n = 1.35$).
• Data Generation: Synthetic TGA curves were generated at four heating rates (5, 10, 15, 20 K min$^{-1}$) for training.
• Blind Prediction: Intermediate rates (7.5 and 12.5 K min$^{-1}$) were withheld to test extrapolation capabilities.
• Noise Injection: Gaussian noise was added to conversion data at standard deviations of 0%, 0.25%, and 0.5%.

Key Results

• Parameter Recovery: At a noise level of 0.25% (0.0025 standard deviation), the method recovered the kinetic parameters with high precision:
  • $E_a$: 155.08 kJ mol$^{-1}$ (Reference: 155; Error $\approx 0.05\%$)
  • $A$: $2.551 \times 10^{10}$ s$^{-1}$ (Reference: $2.50 \times 10^{10}$; Error $\approx 2.0\%$)
  • $n$: 1.356 (Reference: 1.35; Error $\approx 0.47\%$)
• Blind Prediction: The model accurately predicted conversion curves at unseen heating rates (7.5 and 12.5 K min$^{-1}$), achieving an RMSE of $2.39 \times 10^{-4}$ and an $R^2 > 0.999999$.
• Ablation Analysis: Comparisons with "data-only" neural regression and direct kinetic least squares demonstrated that:
  • Data-only models fit sampled curves but fail to identify a consistent kinetic triplet and perform poorly on unseen rates.
  • The physics-constrained approach is essential for stable parameter identification and cross-rate prediction.
  • Monotonicity constraints prevent local derivative violations near conversion plateaus.

Significance and Claims
The paper claims to provide an interpretable route for AI-assisted kinetic analysis. By embedding the Arrhenius law as a residual constraint, the method ensures that the learned model represents a physically admissible thermal process rather than a mere curve-fitting exercise.

The authors emphasize that this work serves as a controlled computational benchmark. They explicitly state that no laboratory measurements are claimed in this study. The significance lies in establishing a reproducible baseline that can be transferred to experimental TGA data after necessary preprocessing (e.g., buoyancy correction, baseline treatment).

The framework is presented as directly extendable to complex, multi-step systems (e.g., biomass pyrolysis involving hemicellulose, cellulose, and lignin; polymer decomposition; battery material degradation) by replacing the single-step law with a weighted sum of parallel reactions. However, the authors caution that for real-world applications, the method requires validation against replicate experimental data and should be accompanied by uncertainty quantification (e.g., Bayesian analysis) to address structural non-identifiability and model discrepancies.