Otimização de Hiperparâmetros de Redes Neurais guiadas pela Física em Problema Convectivo-Difusivo
Resumo
Redes Neurais Guiadas pela Física (PINN) são uma técnica inovadora para resolver problemas governados por Equações Diferenciais, com aplicações em ciência e engenharia. Este estudo investiga a aplicação desse método em equações Convectivos-Difusivos Transientes. Através da biblioteca DeepXDE, que suporta frameworks como TensorFlow e PyTorch, analisou-se a otimização de hiperparâmetros no problema citado. Os experimentos realizados foram comparados com métodos numéricos de elementos finitos, e os resultados demonstram que essa abordagem é promissora, oferecendo um novo caminho em relação às técnicas tradicionais.Referências
Asrav, T. and Aydin, E. (2023). Physics-informed recurrent neural networks and hyperparameter optimization for dynamic process systems. Computers Chemical Engineering, 173:108195.
Atangana, A. (2018). Chapter 3 - groundwater pollution. In Atangana, A., editor, Fractional Operators with Constant and Variable Order with Application to Geo-Hydrology, pages 49–72. Academic Press.
Bhaumik, B., De, S., and Changdar, S. (2024). Deep learning based solution of nonlinear partial differential equations arising in the process of arterial blood flow. Mathematics and Computers in Simulation, 217:21 – 36. Cited by: 2.
Cranmer, M. D., Greydanus, S., Hoyer, S., Battaglia, P. W., Spergel, D. N., and Ho, S. (2020). Lagrangian neural networks. CoRR, abs/2003.04630.
Cuomo, S., Cola, V. S. D., Giampaolo, F., Rozza, G., Raissi, M., and Piccialli, F. (2022). Scientific machine learning through physics-informed neural networks: Where we are and what’s next. CoRR, abs/2201.05624.
Escapil-Inchauspé, P. and Ruz, G. A. (2023). Hyper-parameter tuning of physics-informed neural networks: Application to helmholtz problems. Neurocomputing, 561:126826.
Hansen, L. D., Stokholm-Bjerregaard, M., and Durdevic, P. (2022). Modeling phosphorous dynamics in a wastewater treatment process using bayesian optimized lstm. Computers Chemical Engineering, 160:107738.
Lu, L., Meng, X., Mao, Z., and Karniadakis, G. E. (2021). DeepXDE: A deep learning library for solving differential equations. SIAM Review, 63(1):208–228.
Markidis, S. (2021). The old and the new: Can physics-informed deep-learning replace traditional linear solvers? Frontiers in Big Data, 4.
Raissi, M., Perdikaris, P., and Karniadakis, G. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378:686–707.
Valli, A. M. P., Catabriga, L., Santos, I. P., Coutinho, A. L., and Almeida, R. C. (2015). Predictor-multicorrector scheme for the dynamic diffusion method. In Proceeding Series of the Brazilian Society of Applied and Computational Mathematics, Vol. 3, N. 2, 2015.
Wang, S., Teng, Y., and Perdikaris, P. (2021). Understanding and mitigating gradient flow pathologies in physics-informed neural networks. SIAM Journal on Scientific Computing, 43(5):A3055–A3081.
Zhang, A., Lipton, Z. C., Li, M., and Smola, A. J. (2023). Dive into Deep Learning. Cambridge University Press. [link].
Atangana, A. (2018). Chapter 3 - groundwater pollution. In Atangana, A., editor, Fractional Operators with Constant and Variable Order with Application to Geo-Hydrology, pages 49–72. Academic Press.
Bhaumik, B., De, S., and Changdar, S. (2024). Deep learning based solution of nonlinear partial differential equations arising in the process of arterial blood flow. Mathematics and Computers in Simulation, 217:21 – 36. Cited by: 2.
Cranmer, M. D., Greydanus, S., Hoyer, S., Battaglia, P. W., Spergel, D. N., and Ho, S. (2020). Lagrangian neural networks. CoRR, abs/2003.04630.
Cuomo, S., Cola, V. S. D., Giampaolo, F., Rozza, G., Raissi, M., and Piccialli, F. (2022). Scientific machine learning through physics-informed neural networks: Where we are and what’s next. CoRR, abs/2201.05624.
Escapil-Inchauspé, P. and Ruz, G. A. (2023). Hyper-parameter tuning of physics-informed neural networks: Application to helmholtz problems. Neurocomputing, 561:126826.
Hansen, L. D., Stokholm-Bjerregaard, M., and Durdevic, P. (2022). Modeling phosphorous dynamics in a wastewater treatment process using bayesian optimized lstm. Computers Chemical Engineering, 160:107738.
Lu, L., Meng, X., Mao, Z., and Karniadakis, G. E. (2021). DeepXDE: A deep learning library for solving differential equations. SIAM Review, 63(1):208–228.
Markidis, S. (2021). The old and the new: Can physics-informed deep-learning replace traditional linear solvers? Frontiers in Big Data, 4.
Raissi, M., Perdikaris, P., and Karniadakis, G. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378:686–707.
Valli, A. M. P., Catabriga, L., Santos, I. P., Coutinho, A. L., and Almeida, R. C. (2015). Predictor-multicorrector scheme for the dynamic diffusion method. In Proceeding Series of the Brazilian Society of Applied and Computational Mathematics, Vol. 3, N. 2, 2015.
Wang, S., Teng, Y., and Perdikaris, P. (2021). Understanding and mitigating gradient flow pathologies in physics-informed neural networks. SIAM Journal on Scientific Computing, 43(5):A3055–A3081.
Zhang, A., Lipton, Z. C., Li, M., and Smola, A. J. (2023). Dive into Deep Learning. Cambridge University Press. [link].
Publicado
23/10/2024
Como Citar
SILVA, Ricardo Ervilha; CAMATA, José J..
Otimização de Hiperparâmetros de Redes Neurais guiadas pela Física em Problema Convectivo-Difusivo. In: WORKSHOP DE INICIAÇÃO CIENTÍFICA - SIMPÓSIO EM SISTEMAS COMPUTACIONAIS DE ALTO DESEMPENHO (SSCAD), 25. , 2024, São Carlos/SP.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2024
.
p. 137-144.
DOI: https://doi.org/10.5753/sscad_estendido.2024.244373.
