Modeling the Immune Response with Machine Learning: Validation and Computational Cost Analysis of PINNs Compared to Neural Networks and Finite Volume Methods

• Thiago E. Fernandes UFJF
• Rodrigo W. dos Santos UFJF
• Marcelo Lobosco UFJF

DOI: https://doi.org/10.5753/sbcas_estendido.2026.21588

Resumo

This work investigates deep neural networks as surrogate models for simulating the spatiotemporal dynamics of the immune response in infectious myocarditis. A reduced PDE model describing pathogen–leukocyte interactions in myocardial tissue is solved using a finite volume method (FVM), whose solutions are used to train conventional neural networks (NNs) and physicsinformed neural networks (PINNs). The approaches are systematically compared in terms of predictive accuracy and computational performance. Results show that conventional NNs reproduce the reference FVM solution more accurately than PINNs, which exhibit excessive smoothing and reduced ability to capture sharp gradients. Despite these differences, neural networks enable significantly faster inference, achieving approximately 6.6× acceleration relative to the GPU-accelerated FVM. The computational advantage becomes most relevant in multi-execution scenarios such as parametric studies, sensitivity analyses, and inverse problems.

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