Euler iteration augmented physics-informed neural networks for time-varying parameter estimation of the epidemic compartmental model

Abstract

Introduction: Differential equations governed compartmental models are known for their ability to simulate epidemiological dynamics and provide highly accurate descriptive and predictive results. However, identifying the corresponding parameters of flow from one compartment to another in these models remains a challenging task. These parameters change over time due to the effect of interventions, virus variation and so on, thus time-varying compartmental models are required to reflect the dynamics of the epidemic and provide plausible results.Methods: In this paper, we propose an Euler iteration augmented physics-informed neural networks(called Euler-PINNs) to optimally integrates real-world reported data, epidemic laws and deep neural networks to capture the dynamics of COVID-19. The proposed Euler-PINNs method integrates the differential equations into deep neural networks by discretizing the compartmental model with suitable time-step and expressing the desired parameters as neural networks. We then define a robust and concise loss of the predicted data and the observed data for the epidemic in question and try to minimize it. In addition, a novel activation function based on Fourier theory is introduced for the Euler-PINNs method, which can deal with the inherently stochastic and noisy real-world data, leading to enhanced model performance.Results and Discussion: Furthermore, we verify the effectiveness of the Euler-PINNs method on 2020 COVID-19-related data in Minnesota, the United States, both qualitative and quantitative analyses of the simulation results demonstrate its accuracy and efficiency. Finally, we also perform predictions based on data from the early stages of the outbreak, and the experimental results demonstrate that the Euler-PINNs method remains robust on small dataset.

Epi-DNNs: Epidemiological priors informed deep neural networks for modeling COVID-19 dynamics

“…Since then, DNNs-based models are consistently used as the non-linear function approximation method and have shown their strong potential to address various science computing tasks in many fields. Additionally, several research efforts have attempted to apply the PINNs framework in modeling and analyzing the dynamics of COVID-19 [16] , [17] , [18] , [19] , [20] .…”

High Fidelity Fast Simulation of Human in the Loop Human in the Plant (HIL-HIP) systems

“…Time-varying system dynamics can be simulated by solving nonlinear ordinary differential equations (ODE) [15]. Recent advancements take advantage of data driven supervised learning, such as NeuralODE, [7] or Euler-physics induced neural networks [17]. Such methods are usually slow and depending on the simulation time step.…”

Neural networks for endemic measles dynamics: comparative analysis and integration with mechanistic models

“…PINN methods are able to preserve high predictive performance while incorporating and inferring scientific parameters, and have only recently been extended from physics differential equations to infectious disease mechanistic equations [6,22]. While previous pioneering work [6,[22][23][24] has demonstrated the ability of PINN methods to improve disease incidence forecasts, the applications have not focused on long-term prediction and inference of the transmission dynamics in the context of endemic childhood infections. We build a PINN model which integrates a machine learning model directly with a mechanistic S-I-R model, and is able to address these shortcomings by augmenting the measles transmission dynamics with reconstructed latent susceptible dynamics from the TSIR model.…”