Related papers: Asymptotic-Preserving Neural Networks for multisca…
With the rapid advance of Machine Learning techniques and the deep increase of availability of scientific data, data-driven approaches have started to become progressively popular across science, causing a fundamental shift in the…
In this paper we develop a neural network for the numerical simulation of time-dependent linear transport equations with diffusive scaling and uncertainties. The goal of the network is to resolve the computational challenges of…
Compartmental models provide simple and efficient tools to analyze the relevant transmission processes during an outbreak, to produce short-term forecasts or transmission scenarios, and to assess the impact of vaccination campaigns.…
We develop a Macroscopic Auxiliary Asymptotic-Preserving Neural Network (MA-APNN) method to solve the time-dependent linear radiative transfer equations (LRTEs), which have a multi-scale nature and high dimensionality. To achieve this, we…
Forecasting temporal processes such as virus spreading in epidemics often requires more than just observed time-series data, especially at the beginning of a wave when data is limited. Traditional methods employ mechanistic models like the…
Accurate forecasting of contagious diseases is critical for public health policymaking and pandemic preparedness. We propose a new infectious disease forecasting model based on physics-informed neural networks (PINNs), an emerging…
Physics-Informed Neural Networks (PINNs) are machine learning tools that approximate the solution of general partial differential equations (PDEs) by adding them in some form as terms of the loss/cost function of a Neural Network. Most…
Reaction-diffusion epidemic models with vital dynamics are an important framework for describing the spatial and temporal spread of infectious diseases. In this work, we present a constraint-aware, physics-informed neural network (PINN)…
Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…
This work introduces a physics-informed neural networks (PINNs)-based model predictive control (MPC) framework for susceptible-infected-recovered ($SIR$) spreading models. Existing studies in MPC design for epidemic control often assume…
Physics-Informed Neural Network (PINN) is a deep learning framework that integrates the governing equations underlying data into a loss function. In this study, we consider the problem of estimating state variables and parameters in…
In this paper, we present two novel Asymptotic-Preserving Neural Networks (APNNs) for tackling multiscale time-dependent kinetic problems, encompassing the linear transport equation and Bhatnagar-Gross-Krook (BGK) equation with diffusive…
This paper introduces a novel approach to solve inverse problems by leveraging deep learning techniques. The objective is to infer unknown parameters that govern a physical system based on observed data. We focus on scenarios where the…
Physics-Informed Neural Networks (PINNs) frequently encounter difficulties in accurately resolving shock waves within high-speed compressible flows, a failure largely attributed to the "gradient pathology" arising from extreme stiffness at…
A physics-informed neural network (PINN) embedded with the susceptible-infected-removed (SIR) model is devised to understand the temporal evolution dynamics of infectious diseases. Firstly, the effectiveness of this approach is demonstrated…
Physics-Informed Neural Networks (PINNs) have enabled significant improvements in modelling physical processes described by partial differential equations (PDEs). PINNs are based on simple architectures, and learn the behavior of complex…
Physics-informed neural networks (PINNs) [31] use automatic differentiation to solve partial differential equations (PDEs) by penalizing the PDE in the loss function at a random set of points in the domain of interest. Here, we develop a…
Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the…
We propose a model-data asymptotic-preserving neural network(MD-APNN) method to solve the nonlinear gray radiative transfer equations(GRTEs). The system is challenging to be simulated with both the traditional numerical schemes and the…
Physics-Informed Neural Networks (PINN) are a machine learning tool that can be used to solve direct and inverse problems related to models described by Partial Differential Equations. This paper proposes an adaptive inverse PINN applied to…