Modelagem da resposta imunológica com aprendizado de máquina: validação e analise de custo computacional de PINNs frente a redes neurais e volumes finitos

Abstract

Infectious myocarditis is an inammation of the cardiac muscle often associated with the development of myocardial edema, potentially leading to arrhythmias, heart failure, and sudden death. Epidemiological data indicate a 62.2% increase in the global incidence of the disease over the past three decades, culminating in 324,490 deaths in 2019. Despite advances in understanding the underlying pathophysiological mechanisms, challenges persist in eciently modeling the immune response to infection. This study focuses on evaluating deep neural networks as accelerated surrogates for the simulation of the immune response. To this end, a comparative analysis is proposed between Physics-Informed Neural Networks (PINNs) and conventional Neural Networks (NNs) for modeling the spatio-temporal dynamics of pathogen and leukocyte concentrations in myocardial tissue. A model based on partial dierential equations (PDEs), previously validated in the literature, is employed to describe the processes of diusion, chemotaxis, pathogen replication, and leukocyte recruitment in a saturated porous medium. PINNs tended to smooth the solution excessively, resulting in reduced local accuracy in regions with sharp gradients. In contrast, NNs demonstrated excellent capability in capturing localized phenomena and stationary structures, provided that an adequate sampling density was available. In terms of performance, both neural network approaches signicantly outperformed the Finite Volume Method (FVM), even in its GPU-parallelized version using CUDA, which achieved an average acceleration of 483 times. The neural networks reached an average computational acceleration of 6,66 times when compared to the GPU Version of FVM, a result attributed to their ability to evaluate the entire spatiotemporal domain in parallel, without the sequential dependency between time steps required by traditional solvers. In a context characterized by smooth solutions, uniform spatial coverage, and synthetic data, conventional neural networks demonstrated superior performance, striking a balance between delity to the reference solution and computational eciency. On the other hand, PINNs proved to be more robust in the face of data scarcity, thereby reinforcing their potential for applications in contexts with limited data availability, such as myocardial edema.