TY - GEN
T1 - Physics Informed Neural Networks and Gaussian Processes-Hamiltonian Monte Carlo to Solve Ordinary Differential Equations
AU - Chachalo, Roberth
AU - Astudillo, Jaime
AU - Infante, Saba
AU - Pineda, Israel
N1 - Publisher Copyright:
© The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.
PY - 2025
Y1 - 2025
N2 - Non-linear systems of differential equations are vital in fields like biology, finance, ecology, and engineering for modeling dynamic systems. This paper explores two advanced function approximation techniques Physics Informed Neural Networks (PINNs) and Gaussian Processes (GPs) combined with Hamiltonian Monte Carlo (HMC) for solving Ordinary Differential Equations (ODEs) that represent complex physical phenomena. The proposed approach integrates PINNs and GP-HMC, demonstrated through two synthetic models (Lotka Volterra and Fitzhugh Nagumo) and a real dataset (COVID-19 SIR model). The results show that the methodology effectively estimates parameters with low Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE). For example, in the Lotka-Volterra model, GP-HMC achieved an RMSE of 0.044 and MAE of 0.041 for one state variable, while PINNs yielded an RMSE of 0.106 and MAE of 0.081. These results highlight the robustness of the methodology in accurately reconstructing system states across varying levels of variability.
AB - Non-linear systems of differential equations are vital in fields like biology, finance, ecology, and engineering for modeling dynamic systems. This paper explores two advanced function approximation techniques Physics Informed Neural Networks (PINNs) and Gaussian Processes (GPs) combined with Hamiltonian Monte Carlo (HMC) for solving Ordinary Differential Equations (ODEs) that represent complex physical phenomena. The proposed approach integrates PINNs and GP-HMC, demonstrated through two synthetic models (Lotka Volterra and Fitzhugh Nagumo) and a real dataset (COVID-19 SIR model). The results show that the methodology effectively estimates parameters with low Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE). For example, in the Lotka-Volterra model, GP-HMC achieved an RMSE of 0.044 and MAE of 0.041 for one state variable, while PINNs yielded an RMSE of 0.106 and MAE of 0.081. These results highlight the robustness of the methodology in accurately reconstructing system states across varying levels of variability.
KW - Bayesian Inference
KW - Gaussian Processes
KW - Halmitonian Monte Carlo
KW - Ordinary Differential Equations
KW - Physics-Informed Neural Networks
KW - Uncertainty Quantification
UR - https://www.scopus.com/pages/publications/85209778820
U2 - 10.1007/978-3-031-75431-9_17
DO - 10.1007/978-3-031-75431-9_17
M3 - Contribución a la conferencia
AN - SCOPUS:85209778820
SN - 9783031754302
T3 - Communications in Computer and Information Science
SP - 253
EP - 268
BT - Information and Communication Technologies - 12th Ecuadorian Conference, TICEC 2024, Proceedings
A2 - Berrezueta-Guzman, Santiago
A2 - Torres, Rommel
A2 - Zambrano-Martinez, Jorge Luis
A2 - Herrera-Tapia, Jorge
PB - Springer Science and Business Media Deutschland GmbH
T2 - 12th Ecuadorian Conference on Information and Communication Technologies, TICEC 2024
Y2 - 16 October 2024 through 18 October 2024
ER -