Analytical and neural network modification of Heun's method for constructing a model of processes in a chemical reactor

Title	Analytical and neural network modification of Heun's method for constructing a model of processes in a chemical reactor
Authors	A. N. Vasilyev¹, D. A. Tarkhov¹, T. A. Shemyakina¹ ¹Peter the Great Saint Petersburg Polytechnic University
Annotation	The article explores new approaches to creating adaptive models that can fit to updated data. The proposed approach combines an analytical modification of classical numerical methods with physics informed neural networks (PINN). This approach builds a hierarchy of approximate solutions in the form of functions. The operation of the method is illustrated by an example of a process model in a chemical reactor. In this model, the task parameters are entered into a set of input variables. An analytical modification of Heun’s method is used to construct an approximate parametric solution. Numerical experiments at different levels of the neural network approach inclusion show that multilayer methods make it possible to build simpler models without losing accuracy, which simplifies their use and adaptation when new data is received.
Keywords	non-isothermal chemical reactor, Heun's method, neural networks, parametric solution.
Citation	Vasilyev A. N., Tarkhov D. A., Shemyakina T. A. ''Analytical and neural network modification of Heun's method for constructing a model of processes in a chemical reactor'' [Electronic resource]. Mathematical modeling, numerical methods, and software systems: Collection of materials from the 12th All‑Russian Scientific Youth School‑Seminar named after E. V. Voskresensky (Saransk, July 21–24, 2026). - pp. 33-36. Available at: https://conf.svmo.ru/files/2026/papers/paper68.pdf. - Date of access: 25.09.2026.

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Analytical and neural network modification of Heun's method for constructing a model of processes in a chemical reactor

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