Data-driven deep Neural Networks for epidemiological and biochemical models

Abstract

In recent years, the efficiency of deep neural networks to forward and inverse problems that have found applications in biochemical and epidemiological models has been demonstrated. In these systems, it has been observed that the system parameters fit unknown nonlinear functions. Classical models mostly assume these system parameters to be constants. Some researchers explicitly chose a form for these nonlinear parameters using intuition and good reasoning. In this work, we will study mathematical models with nonlinear dynamics that occur in biochemical and epidemiological models and we will develop data-driven deep learning approaches to learn the nonlinear parameters in these models and thereby detect hidden patterns in these complex systems. In our study, we will employ a modification of the physics-informed neural network. The modified network, which we call an epidemiology informed neural network, allows us to predict nonlinear system parameters. Here, multilayer perceptrons are connected to a larger multilayer perceptron that learns the solution to a system of partial differential equations or a system of ordinary differential equations. The Neural network approaches we present are suitable for partial differential equations and ordinary differential equations because they are meshless and can scale to high spatial dimensions. They can also solve forward and inverse problems with sparse data. We enforce the physics of our model in the objective function and device efficient methods that allows us to train with a small dataset. The adaptive neuro-fuzzy inference system, a widely used Neural network in time series forecast, is combined with an epidemiology informed neural network. We demonstrate that this hybrid network is an improvement over the adaptive neuro-fuzzy inference system. We also demonstrate that the epidemiology informed neural network combined with a recurrent neural network such as the long short-term memory network provides a more accurate short-term forecast than a plain recurrent neural network. Next, we develop an attention-based neural network that is capable of learning nonlinear dynamics from noisy data.