Synthetic Dataset Generator for
Time-Resolved Spectroscopy
A rigorous framework implementing 18 first-order reaction mechanisms across 7 topological superclasses, bridging theoretical chemical kinetics and practical machine learning for automated mechanism identification from spectroscopic data.
Authors
Bermúdez, S., Noriega Cedeño, J. R., Pavel, J. A., and Fernández-Terán, R.
Faculty of Applied Science & Technology, Humber Polytechnic, Toronto • Department of Physical Chemistry, University of Geneva
Abstract
We present the architecture, methodology, and practical implementation of a synthetic dataset generator for time-resolved UV-visible spectroscopy designed for training and evaluating machine learning models. The generator implements the rigorous mathematical framework established by Fernández-Terán and colleagues, incorporating the bilinear model of spectrokinetics, matrix exponential kinetics, analytical instrument response function convolution, and realistic multi-component noise injection.
The system encompasses a curated catalogue of 18 first-order reaction mechanisms organized into seven topological superclasses, enabling generation of physically grounded synthetic spectra that capture the full diversity of kinetic behaviours observed in experimental systems. Key methodological advances include eigenvalue decomposition for computational efficiency (50–100× speedup), mechanism-aware quality scoring, and comprehensive numerical stability safeguards.
Theoretical Foundations
Mathematical Framework
Built upon rigorous spectrokinetic theory, the generator implements analytical solutions for computational efficiency and numerical precision.
Bilinear Model of Spectrokinetics
Time-resolved spectra decompose into the product of concentration and spectral matrices, assuming spectral time-invariance and well-defined chemical intermediates.
C ∈ ℝ^{n_t × N} contains time-dependent concentrations of N species; S ∈ ℝ^{N × n_λ} contains species-associated spectra.
Matrix Exponential Kinetics
Coupled first-order reactions are governed by a system of linear ODEs with the rate matrix K, solved analytically via the matrix exponential.
Mass conservation enforced: each column of K sums to zero. Off-diagonal K_{ij} represent interconversion rates.
Eigenvalue Decomposition Solver
The matrix exponential is computed efficiently via eigendecomposition, providing 50–100× speedup over direct methods for batch generation.
Where V contains eigenvectors, α = V⁻¹C(0) are modal amplitudes. One-time O(N³) cost amortized over all time evaluations.
Analytical IRF Convolution
Gaussian instrument response function convolution evaluated analytically, avoiding numerical artefacts on logarithmic time grids.
σ is the Gaussian IRF width (FWHM = 2σ√(2ln2)). 10–20× faster than numerical convolution.
Mechanism-Aware Quality Scoring
A composite quality score that accounts for mechanistic topology. Traditional metrics based solely on condition number inappropriately penalize mechanisms with inherent collinearity. For parallel and branched pathways, the spectral overlap penalty is relaxed with a floor of 0.3 rather than 0.0, reflecting the physical reality that product concentrations are inherently collinear.
Mechanism Catalogue
18 Reaction Mechanisms, 7 Superclasses
A curated catalogue organized by kinetic topology and distinguishability, from simple direct decay to complex hub networks with branching and exchange.
DIRECT_DECAY
Simple direct decay or equilibrium
SEQUENTIAL_3SP
Linear three-species chains with optional reversibility
BRANCHED_3SP
Competitive or parallel pathways converging to product
LINEAR_4SP_IRR
Fully irreversible four-species linear chain
LINEAR_4SP_PARTIAL
Linear chains with partial reversibility
LINEAR_4SP_FULL
Fully reversible linear four-species systems
HUB_TOPOLOGY
Hub-like networks with branching or exchange
System Design
Architecture & Pipeline
A modular Python framework with six primary components, designed for extensibility and batch generation efficiency.
Mechanism Selection
Sample from 18 mechanisms across 7 superclasses with configurable distribution weights
Rate Constant Sampling
Log-uniform distribution over [10⁻⁴, 10] s⁻¹ with kinetic separation enforcement (β = 2.0)
Spectral Generation
1–4 Gaussian peaks per species, 350–750 nm range, 250 channels, enforced spectral distinguishability
Kinetic Solving
Eigenvalue decomposition with vectorized exponential evaluation, O(N³ + N·n_t) complexity
IRF Convolution
Analytical Gaussian convolution (FWHM 0.05–1.0 s), 10–20× faster than numerical methods
Quality Assessment & Export
Mechanism-aware scoring, spectral overlap filtering (> 0.5 rejected), NPZ/CSV/JSON export
Core Modules
18 mechanisms, 7 superclasses, rate matrix builders
Parametric Gaussian peak generation with diversity constraints
Eigenvalue decomposition with condition number monitoring
5-component model: shot, read, drift, artefacts, cosmic rays
Mechanism-aware composite scoring with topology awareness
NPZ, CSV, JSON with complete provenance metadata
Performance Characteristics
Validation
Chameleon Reaction Benchmark
Validated against the oxidation of reducing sugars by permanganate, a well-characterized experimental system with known rate constants and species-associated spectra.
Quantitative Agreement with Experimental Data
KMnO\u2084 + Sugar substrates in basic solution
| Substrate | Mechanism | R\u00B2 | Pearson r |
|---|---|---|---|
| Fructose | M4.1 | 0.9857 | 0.9929 |
| Glucose | M2.1 | 0.9657 | 0.9827 |
| Sucrose | M2.1 | 0.9945 | 0.9974 |
Correlation with Experimental Data
All correlations exceed r = 0.98, confirming deterministic, physically accurate generation across three independent experimental systems.
Additional Accuracy Metrics
Machine Learning Results
Initial Approaches (Modest Performance)
Classical ML (Random Forest, XGBoost, Logistic Regression) and sequential deep learning (GRUs, LSTMs) yielded top-1 validation accuracies in the range of 0.30–0.60, initially suggesting fundamental limits from spectrokinetic degeneracy.
Breakthrough: 2D CNN Architecture
Treating D(t, \u03BB) as a 2D image with a convolutional neural network exploited the inherent spatial structure of spectrokinetic data. Combined with scaled dataset (120K initial, 15K filtered), the 2D CNN achieved consistently accurate top-1 predictions across all mechanism superclasses.
Production Dataset
Dataset Statistics & Structure
119,988 initial spectra generated with balanced sampling, aggressively filtered to 15,192 high-quality samples (12.7% pass rate).
Superclass Distribution
Aggressive filtering disproportionately removed samples from LINEAR_4SP_IRR (M4.1). Fully irreversible linear chains are particularly susceptible to kinetic degeneracy when rate constants approach similar values.
Export Format
Data matrices D, concentration profiles C, species-associated spectra S
n_samples × n_t × n_λ | n_samples × n_t × N | n_samples × N × n_λ
Per-sample parameters, mechanism IDs, quality metrics (SNR, condition number, kinetic separation, spectral overlap)
n_samples rows × 12+ columns
All rate constants, spectral component parameters, K-matrix eigenvalues, DAS fingerprints
Full TRSpectrumLabel dictionaries
Wavelength (350–750 nm) and time (0.001–1000 s) vectors
n_λ = 250 | n_t = 250
Compute Grant Request
Help Us Scale Continuum
We have validated the synthetic data pipeline and demonstrated that 2D CNNs can classify reaction mechanisms from spectrokinetic data. To reach production-grade accuracy and extend to real experimental data, we need compute resources.
Why This Research Matters
Traditional spectrokinetic analysis requires deep expertise in both spectroscopy and chemical kinetics. Our ML approach automates mechanism identification, democratizing access to these analytical capabilities.
Synthetic data with complete ground truth labels enables rigorous benchmarking impossible with experimental data alone. Transfer learning will extend these models to real laboratory measurements.
The generator, datasets, and trained models will be released open-source, providing the spectroscopy community with validated tools for automated kinetic analysis across chemistry, biochemistry, and materials science.
Dataset Generation at Scale
- •Scale from 15K to 500K+ filtered samples
- •Full 18-mechanism balanced coverage
- •Multi-noise-level augmentation
- •Estimated: ~200 GPU-hours on A100
CNN Model Training & Optimization
- •2D CNN architecture for D(t,λ) image classification
- •Hyperparameter search across 7 superclasses
- •Cross-validation with stratified splits
- •Estimated: ~500 GPU-hours on A100/H100
Physics-Informed Neural Networks
- •PINNs leveraging analytical structure of kinetic equations
- •Embedding eigenvalue constraints as physics losses
- •Transfer learning from synthetic to experimental data
- •Estimated: ~800 GPU-hours on H100
Mixed-Order Kinetics Extension
- •Extend beyond first-order to second/mixed-order kinetics
- •Hybrid analytical-numerical ODE solvers
- •Concentration-dependent kinetic models
- •Estimated: ~400 GPU-hours on A100
Estimated Resource Requirements
| Resource | Quantity | Estimated Cost |
|---|---|---|
| GPU Compute (A100/H100) | 2,000 | $6,000–$10,000 |
| Storage (Datasets + Checkpoints) | 5 TB | $500 |
| CPU Compute (Data Generation) | 500 hours | $250 |
| Experiment Tracking (W&B Pro) | 12 months | $600 |
| Total Estimated | $7,350–$11,350 |
Support This Research
A compute grant would enable us to scale dataset generation, train production-grade models, and validate transfer learning from synthetic to experimental spectrokinetic data.
Prof. Ricardo Fernández-Terán • University of Geneva • Ricardo.FernandezTeran@unige.ch
Team & Affiliations
Research Team
Simón Bermúdez
Project Manager & Lead Developer
Humber Polytechnic
System architecture, ML pipeline, and data engineering
José Rafael Noriega Cedeño
Chemistry Subject Matter Expert
Humber Polytechnic
Mechanism catalogue design, kinetic validation, and chemical accuracy
Julie Anne Pavel
Data Analyst
Humber Polytechnic
Statistical analysis, quality metrics, and dataset characterization
Prof. Ricardo Fernández-Terán
Principal Investigator & Supervisor
University of Geneva
Theoretical framework, spectrokinetic methods, and experimental validation
Institutions
Foundational Reference
Fernández-Terán, R. et al. (2022). "A sweet introduction to the mathematical analysis of time-resolved spectra and complex kinetic mechanisms." J. Chem. Educ., 99(6), 2327–2337.
We thank Dr. Ricardo Fernández-Terán for insightful discussions on spectrokinetic analysis and for providing the theoretical framework. We acknowledge the support of Humber Polytechnic's Faculty of Applied Science and Technology. This work was inspired by the treatment of the chameleon reaction published in the Journal of Chemical Education.