Related papers: Hybrid PDE-Deep Neural Network Model for Calcium D…

Deep learning has revolutionized the field of computer vision by introducing large scale neural networks with millions of parameters. Training these networks requires massive datasets and leads to intransparent models that can fail to…

Graph neural networks (GNNs) leverage message passing mechanisms to learn the topological features of graph data. Traditional GNNs learns node features in a spatial domain unrelated to the topology, which can hardly ensure topological…

Deep neural networks (DNNs) have been widely used to solve partial differential equations (PDEs) in recent years. In this work, a novel deep learning-based framework named Particle Weak-form based Neural Networks (ParticleWNN) is developed…

In the field of pharmacokinetics and pharmacodynamics (PKPD) modeling, which plays a pivotal role in the drug development process, traditional models frequently encounter difficulties in fully encapsulating the complexities of drug…

Partial differential equations (PDEs) play a dominant role in the mathematical modeling of many complex dynamical processes. Solving these PDEs often requires prohibitively high computational costs, especially when multiple evaluations must…

In chemical reaction network theory, ordinary differential equations are used to model the temporal change of chemical species concentration. As the functional form of these ordinary differential equations systems is derived from an…

In this study, we propose parameter-varying neural ordinary differential equations (NODEs) where the evolution of model parameters is represented by partition-of-unity networks (POUNets), a mixture of experts architecture. The proposed…

Modeling the traffic dynamics is essential for understanding and predicting the traffic spatiotemporal evolution. However, deriving the partial differential equation (PDE) models that capture these dynamics is challenging due to their…

Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated…

Recently, Neural Ordinary Differential Equations has emerged as a powerful framework for modeling physical simulations without explicitly defining the ODEs governing the system, but instead learning them via machine learning. However, the…

Utilizing physics-informed neural networks (PINN) to solve partial differential equations (PDEs) becomes a hot issue and also shows its great powers, but still suffers from the dilemmas of limited predicted accuracy in the sampling domain…

We propose a unified framework for delay differential equations (DDEs) based on deep neural networks (DNNs) - the neural delay differential equations (NDDEs), aimed at solving the forward and inverse problems of delay differential…

Learning dynamics governed by differential equations is crucial for predicting and controlling the systems in science and engineering. Neural Ordinary Differential Equation (NODE), a deep learning model integrated with differential…

Deep Learning has emerged as one of the most significant innovations in machine learning. However, a notable limitation of this field lies in the ``black box" decision-making processes, which have led to skepticism within groups like…

We propose a new approach to learning the subgrid-scale model when simulating partial differential equations (PDEs) solved by the method of lines and their representation in chaotic ordinary differential equations, based on neural ordinary…

The robotic systems continuously interact with complex dynamical systems in the physical world. Reliable predictions of spatiotemporal evolution of these dynamical systems, with limited knowledge of system dynamics, are crucial for…

We propose a neural network-based meta-learning method to efficiently solve partial differential equation (PDE) problems. The proposed method is designed to meta-learn how to solve a wide variety of PDE problems, and uses the knowledge for…

We use elliptic partial differential equations (PDEs) as examples to show various properties and behaviors when shallow neural networks (SNNs) are used to represent the solutions. In particular, we study the numerical ill-conditioning,…

Partial differential equations (PDEs) are commonly derived based on empirical observations. However, recent advances of technology enable us to collect and store massive amount of data, which offers new opportunities for data-driven…

Differential equations in general and neural ODEs in particular are an essential technique in continuous-time system identification. While many deterministic learning algorithms have been designed based on numerical integration via the…