Related papers: Hybrid Time-Domain Behavior Model Based on Neural …

Physics-Informed Neural Networks (PINNs) and Neural Ordinary Differential Equations (NODEs) represent two distinct machine learning frameworks for modeling nonlinear neuronal dynamics. This study systematically evaluates their performance…

We enhance machine learning algorithms for learning model parameters in complex systems represented by ordinary differential equations (ODEs) with domain decomposition methods. The study evaluates the performance of two approaches, namely…

Network embedding has recently emerged as a promising technique to embed nodes of a network into low-dimensional vectors. While fairly successful, most existing works focus on the embedding techniques for static networks. But in practice,…

A physics informed neural network (PINN) incorporates the physics of a system by satisfying its boundary value problem through a neural network's loss function. The PINN approach has shown great success in approximating the map between the…

Dosing models often use differential equations to model biological dynamics. Neural differential equations in particular can learn to predict the derivative of a process, which permits predictions at irregular points of time. However, this…

Recurrent neural networks (RNNs) with continuous-time hidden states are a natural fit for modeling irregularly-sampled time series. These models, however, face difficulties when the input data possess long-term dependencies. We prove that…

Irregularly measured time series are common in many of the applied settings in which time series modelling is a key statistical tool, including medicine. This provides challenges in model choice, often necessitating imputation or similar…

A classic approach for solving differential equations with neural networks builds upon neural forms, which employ the differential equation with a discretisation of the solution domain. Making use of neural forms for time-dependent…

Deep Recurrent Neural Network architectures, though remarkably capable at modeling sequences, lack an intuitive high-level spatio-temporal structure. That is while many problems in computer vision inherently have an underlying high-level…

Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…

Neural Ordinary Differential Equations (NODEs) have proven to be a powerful modeling tool for approximating (interpolation) and forecasting (extrapolation) irregularly sampled time series data. However, their performance degrades…

Neuron models built from experimental data have successfully predicted observed voltage oscillations within and beyond training range. A tantalising prospect is the possibility of estimating the unobserved dynamics of ion channels which is…

We introduce a real-time identification method for discrete-time state-dependent switching systems in both the input--output and state-space domains. In particular, we design a system of adaptive algorithms running in two timescales; a…

Anomaly detection in SDN using data flow prediction is a difficult task. This problem is included in the category of time series and regression problems. Machine learning approaches are challenging in this field due to the manual selection…

Deep learning is one of the most successful and far-reaching strategies used in machine learning today. However, the scale and utility of neural networks is still greatly limited by the current hardware used to train them. These concerns…

Nonlinear differential equations rarely admit closed-form solutions, thus requiring numerical time-stepping algorithms to approximate solutions. Further, many systems characterized by multiscale physics exhibit dynamics over a vast range of…

Increasing the layer number of on-chip photonic neural networks (PNNs) is essential to improve its model performance. However, the successively cascading of network hidden layers results in larger integrated photonic chip areas. To address…

This paper deals with the problem of finite-time learning for unknown discrete-time nonlinear systems' dynamics, without the requirement of the persistence of excitation. Two finite-time concurrent learning methods are presented to…

We introduce \emph{Dynamical Physics-Modeled Neural Networks} (DynPMNNs), a continuous-time deep learning architecture in which each hidden layer is defined as the solution of an ordinary differential equation. Unlike classical feed-forward…

Recurrent neural networks (RNNs) are widely used as a memory model for sequence-related problems. Many variants of RNN have been proposed to solve the gradient problems of training RNNs and process long sequences. Although some classical…