Grzegorz Brus

Zofia Pizoń, Shinji Kimijima, Grzegorz Brus

Hydrogen's role is growing as an energy carrier, increasing the need for efficient production, with methane steam reforming being the most widely used technique. This process is crucial for applications like fuel cells, where hydrogen is converted into electricity, pushing for reactor miniaturization and optimized process control through numerical simulations. Existing models typically address either kinetic or equilibrium regimes, limiting their applicability. Here we show a surrogate model capable of unifying both regimes. An artificial neural network trained on a comprehensive dataset that includes experimental data from kinetic and equilibrium experiments, interpolated data, and theoretical data derived from theoretical models for each regime. Data augmentation and assigning appropriate weights to each data type enhanced training. After evaluating Bayesian Optimization and Random Sampling, the optimal model demonstrated high predictive accuracy for the composition of the post-reaction mixture under varying operating parameters, indicated by a mean squared error of 0.000498 and strong Pearson correlation coefficients of 0.927. The network's ability to provide continuous derivatives of its predictions makes it particularly useful for process modeling and optimization. The results confirm the surrogate model's robustness for simulating methane steam reforming in both kinetic and equilibrium regimes, making it a valuable tool for design and process optimization.

Szymon Buchaniec, Marek Gnatowski, Grzegorz Brus

One of the most common and universal problems in science is to investigate a function. The prediction can be made by an Artificial Neural Network (ANN) or a mathematical model. Both approaches have their advantages and disadvantages. Mathematical models were sought as more trustworthy as their prediction is based on the laws of physics expressed in the form of mathematical equations. However, the majority of existing mathematical models include different empirical parameters, and both approaches inherit inevitable experimental errors. At the same time, the approximation of neural networks can reproduce the solution extremely well if fed with a sufficient amount of data. The difference is that an ANN requires big data to build its accurate approximation whereas a typical mathematical model needs just several data points to estimate an empirical constant. Therefore, the common problem that developer meet is the inaccuracy of mathematical models and artificial neural network. An another common challenge is the computational complexity of the mathematical models, or lack of data for a sufficient precision of the Artificial Neural Networks. In the presented paper those problems are addressed using the integration of a mathematical model with an artificial neural network. In the presented analysis, an ANN predicts just a part of the mathematical model and its weights and biases are adjusted based on the output of the mathematical model. The performance of Integrated Mathematical modeling - Artificial Neural Network (IMANN) is compared to a Dense Neural Network (DNN) with the use of the benchmarking functions. The obtained calculation results indicate that such an approach could lead to an increase of precision as well as limiting the data-set required for learning.