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Many physical processes such as weather phenomena or fluid mechanics are governed by partial differential equations (PDEs). Modelling such dynamical systems using Neural Networks is an active research field. However, current methods are…
Purpose: To develop a neural ordinary differential equation (ODE) model for visualizing deep neural network (DNN) behavior during multi-parametric MRI (mp-MRI) based glioma segmentation as a method to enhance deep learning explainability.…
Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with some representative datasets. Recently, an augmented framework has been…
Weather prediction is a quintessential problem involving the forecasting of a complex, nonlinear, and chaotic high-dimensional dynamical system. This work introduces an efficient reduced-order modeling (ROM) framework for short-range…
The great learning ability of deep learning models facilitates us to comprehend the real physical world, making learning to simulate complicated particle systems a promising endeavour. However, the complex laws of the physical world pose…
A novel convolutional autoencoder neural ODE (CAE-NODE) framework is proposed for a reduced-order model (ROM) of transient 2D counterflow flames, as an extension of AE-NODE methods in homogeneous reactive systems to spatially resolved…
Due to their dynamic properties such as irregular sampling rate and high-frequency sampling, Continuous Time Series (CTS) are found in many applications. Since CTS with irregular sampling rate are difficult to model with standard Recurrent…
Reasoning over an instance composed of a set of vectors, like a point cloud, requires that one accounts for intra-set dependent features among elements. However, since such instances are unordered, the elements' features should remain…
Obtaining accurate channel state information (CSI) is crucial and challenging for multiple-input multiple-output (MIMO) wireless communication systems. With the increasing antenna scale and user mobility, traditional channel estimation…
Neural ordinary differential equations (NODE) have been proposed as a continuous depth generalization to popular deep learning models such as Residual networks (ResNets). They provide parameter efficiency and automate the model selection…
Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with representative datasets. Recently, an augmented framework has been…
Neural ODEs (NODEs) are continuous-time neural networks (NNs) that can process data without the limitation of time intervals. They have advantages in learning and understanding the evolution of complex real dynamics. Many previous works…
The working mechanisms of complex natural systems tend to abide by concise and profound partial differential equations (PDEs). Methods that directly mine equations from data are called PDE discovery, which reveals consistent physical laws…
Humans gain an implicit understanding of physical laws through observing and interacting with the world. Endowing an autonomous agent with an understanding of physical laws through experience and observation is seldom practical: we should…
Differential equations are widely used to describe complex dynamical systems with evolving parameters in nature and engineering. Effectively learning a family of maps from the parameter function to the system dynamics is of great…
Neural differential equations are a promising new member in the neural network family. They show the potential of differential equations for time series data analysis. In this paper, the strength of the ordinary differential equation (ODE)…
Neural networks have recently been used to analyze diverse physical systems and to identify the underlying dynamics. While existing methods achieve impressive results, they are limited by their strong demand for training data and their weak…
This study presents a novel unsupervised convolutional Neural Network (NN) architecture with nonlocal interactions for solving Partial Differential Equations (PDEs). The nonlocal Peridynamic Differential Operator (PDDO) is employed as a…
Pneumatic artificial muscles (PAMs) enable compliant actuation for soft wearable, assistive, and interactive robots. When arranged antagonistically, PAMs can provide variable impedance through co-contraction but exhibit coupled, nonlinear,…
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…