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Autonomous Discovery of Unknown Reaction Pathways from Data by Chemical Reaction Neural Network
Weiqi Ji, Sili Deng
TL;DR
Complex reaction systems remain difficult to analyze because species, reactions, and usable reaction templates may be unknown. This paper introduces a physics-informed Chemical Reaction Neural Network that learns pathways and kinetic parameters from time-resolved concentration data. Demonstrations in chemical engineering and biochemical systems show that the approach can autonomously infer reaction systems and support generalization to similar systems.
Problem
Inferring reaction pathways in complex systems is difficult when the involved species and reactions are unknown, while ab initio calculation is computationally intractable and reaction-template knowledge is limited.
Method
The Chemical Reaction Neural Network learns reaction pathways from time-resolved species concentration data by encoding fundamental chemical physics laws and training with stochastic gradient descent.
Results
The CRNN accurately learns reaction pathways and kinetic parameters in demonstrated chemical engineering and biochemical systems.
Takeaways & Limitations
The approach supports autonomous inference of new chemical reaction systems without prior reaction templates and can formulate templates transferable to similar systems.
Takeaways & Limitations
The current approach assumes conditions that can make systems with wide ranges of time scales and concentration levels challenging.
Abstract
from arXiv · showhide
Chemical reactions occur in energy, environmental, biological, and many other natural systems, and the inference of the reaction networks is essential to understand and design the chemical processes in engineering and life sciences. Yet, revealing the reaction pathways for complex systems and processes is still challenging due to the lack of knowledge of the involved species and reactions. Here, we present a neural network approach that autonomously discovers reaction pathways from the time-resolved species concentration data. The proposed Chemical Reaction Neural Network (CRNN), by design, satisfies the fundamental physics laws, including the Law of Mass Action and the Arrhenius Law. Consequently, the CRNN is physically interpretable such that the reaction pathways can be interpreted, and the kinetic parameters can be quantified simultaneously from the weights of the neural network. The inference of the chemical pathways is accomplished by training the CRNN with species concentration data via stochastic gradient descent. We demonstrate the successful implementations and the robustness of the approach in elucidating the chemical reaction pathways of several chemical engineering and biochemical systems. The autonomous inference by the CRNN approach precludes the need for expert knowledge in proposing candidate networks and addresses the curse of dimensionality in complex systems. The physical interpretability also makes the CRNN capable of not only fitting the data for a given system but also developing knowledge of unknown pathways that could be generalized to similar chemical systems.
1. Introduction
Inferring reaction pathways and kinetic parameters from concentration data is difficult because complex systems lack known species and reactions, while candidate enumeration grows rapidly with system size. The CRNN addresses this by embedding chemical physics in a neural-network architecture so pathways and parameters remain interpretable while being learned from data.
- Complex systems are difficult to model because ab initio calculations are computationally intractable and reaction-template knowledge is limited.
- Reaction-network inference must recover both reaction pathways and kinetic parameters from species concentration data.
- Candidate reaction pathways become impractical to propose as the number of species increases because possible interactions grow rapidly.
- Traditional neural networks can approximate unknown reaction pathways, but their weights are difficult to interpret as chemical pathways and rate constants.
- The proposed Chemical Reaction Neural Network identifies reaction pathways without prior chemical-system knowledge by encoding governing physics into its architecture.
- CRNN training uses stochastic gradient descent, while interpretable weights connect learned reaction pathways with kinetic parameters and support generalized reaction templates.
2. Methods
The CRNN embeds chemical reaction laws into an interpretable neural-network structure, allowing reaction pathways and kinetic parameters to be inferred from concentration data. CRNN-ODE training fits integrated concentration trajectories, while node selection and pruning convert the learned model into reaction equations.
- CRNN construction: The Law of Mass Action becomes a logarithmic weighted-sum and exponential operation, matching the neural-neuron form.The reaction rate is expressed using rate constants and reactant concentrations raised to their reaction orders.
- CRNN construction: The CRNN represents each elementary reaction as a neuron whose inputs are species concentrations and outputs are species production rates.Input weights encode reaction orders, and output weights encode stoichiometric coefficients.
- CRNN construction: Multiple elementary reactions are modeled by stacking neurons in one hidden layer, with hidden-node count corresponding to the number of reactions.The network is designed for multi-step reaction systems.
- Temperature dependence: The CRNN incorporates Arrhenius temperature dependence by representing the rate constant through temperature and prefactor-related parameters.The logarithmic form provides a linear operation involving temperature and the prefactor.
- Network inference: Physically interpretable weights and biases make the CRNN a digital twin of a classical chemical reaction network that can be inferred from measurements.Training uses concentration data to learn the reaction-network parameters.
- CRNN-ODE training: CRNN-ODE integrates the learned reaction model and minimizes mean absolute error between measured and predicted concentration time series.Backpropagation through ODE integrators supports stochastic-gradient optimization of the CRNN parameters.
- Model selection and interpretation: Grid search selects the number of hidden nodes and the pruning threshold, after which small input and output weights are clipped and the model is translated into reaction equations.Pruning targets reaction orders and stoichiometric coefficients to encourage sparsity.
3. Results
CRNN-ODE training on synthetic noisy concentration data learned reaction pathways and kinetic parameters across chemical and biochemical systems. In Case I, four reactions described the kinetics, learned pathways and parameters closely matched ground truth, and predictions agreed well with noisy profiles.
- Experimental setup: CRNN-ODE was trained on synthetic noisy data to discover reaction pathways and learn kinetic parameters, including settings with complete and missing species measurements.The implementation used an ODE solver and stochastic optimization; the code was made open source.
- Experimental setup: The Case I datasets comprised 30 simulations with randomly sampled initial conditions and 5% Gaussian concentration noise.Each dataset contained 100 evenly distributed temporal data points, and the data were split 20:10 between training and validation.
- Model selection: Training typically converged at around 5000 epochs, while training and validation losses plateaued after four proposed reactions, indicating that four reactions described the kinetics.The model used four hidden nodes for the learned Case I network.
- Pathway interpretation: The CRNN weights were physically interpretable: input weights represented reaction orders, output weights represented stoichiometric coefficients and participation, and biases represented rate constants.Rows corresponded to reactions, with positive and negative output weights indicating production and consumption.
- Sparsity and robustness: Hard-threshold pruning encouraged sparsity without materially changing performance when the threshold was much smaller than unity; 0.01 and 0.5 produced no difference in model performance.Under 1% noise, learned stoichiometric coefficients were closer to ground truth than under 5% noise.
- Case I results: The learned pathways, stoichiometric coefficients, and rate constants were close to ground truth, with maximum relative error within 10%, and predictions agreed very well with noisy concentration profiles.Learned reaction orders and stoichiometric coefficients were close to integers, while nonparticipating species had values close to zero.
4. Discussion
The discussion presents a physics-informed neural-network design that preserves physical constraints while fitting chemical data, but identifies important scope and generality limitations.
- The approach encodes fundamental physics laws into the neural-network structure while maintaining fitting accuracy.
- Physically interpretable models are expected to generalize across regimes and enable knowledge transfer among similar chemical systems.
- Further studies are needed to improve the robustness and generality of the approach.
- The current approach assumes that the chemical system is not very stiff and that species concentrations have similar orders of magnitude.
- Wide ranges of time scales and concentration levels can challenge the current fitness representation, though adaptive loss weighting could help.
- Encoding additional physical laws is challenging because integer stoichiometric constraints are difficult to enforce with stochastic gradient descent.
- Element conservation and collision limits could be incorporated into the loss function to reduce training data requirements and improve generality.
5. Conclusions
The conclusions present CRNN as a physics-based framework for discovering reaction pathways and kinetic parameters from concentration time series. Demonstrations in chemical engineering and biochemistry accurately learned both quantities and suggest broader discovery applications.
- CRNN autonomously discovers reaction pathways and kinetic parameters from concentration time series data.
- The model is formulated from the Law of Mass Action and Arrhenius Law as a digital twin of the classical chemical reaction network.
- Reaction pathways and rate constants are interpretable from CRNN weights and biases optimized with stochastic gradient descent.
- Demonstrations in three representative chemical engineering and biochemical systems accurately learned both reaction pathways and kinetic parameters.
- The demonstrations open the possibility of discovering hidden reaction pathways across life sciences, environmental sciences, and engineering.
6. Associated Contents
The associated contents provide supporting information on the governing equations, loss curves, and how model performance depends on the number of proposed reactions.
- Supporting information includes the governing ordinary differential equations and loss curves.
- Supporting information examines model performance as a function of the number of proposed reactions.
Supporting Information for
The supporting-information heading identifies the paper, authors, and their Massachusetts Institute of Technology affiliation.
- The paper is titled “Autonomous Discovery of Unknown Reaction Pathways from Data by Chemical Reaction Neural Network.”
- The authors are Weiqi Ji and Sili Deng.
- The authors are affiliated with the Department of Mechanical Engineering at the Massachusetts Institute of Technology.
- ORCID identifiers are provided for both authors.
1. Case I: An Elementary Reaction Network Without Temperature Dependence
Case I is documented through its governing equations, which are presented in Eq. S1.
- The section presents the governing equations for Case I.The equations are referenced as Eq. S1.
- Case I is associated with Eq. S1.
- Eq. S1 contains the governing equations used for Case I.
2. Case II: Bio-diesel Production with Temperature Dependence
Case II is presented through governing equations in Eq. S2 and training-related results involving loss functions and hidden-node counts.
- The governing equations for Case II are shown in Eq. S2.
- Figure S1 shows typical loss-function evolution across epochs for Case II.The results correspond to a CRNN with three hidden nodes.
- The Case II results in Figure S1 use three hidden nodes.
- Figure S2 presents the dependence of minimum training and validation losses on the number of hidden nodes.
3. Case III: An Enzyme Reaction Network
Case III is documented through governing equations in Eq. S3 and results concerning loss-function evolution, with results corresponding to eight hidden nodes.
- The governing equations for Case III are shown in Eq. S3.
- Figure S3 shows typical loss-function evolution across epochs for Case III.
- The Case III results correspond to a CRNN with eight hidden nodes.