Related papers: Continuous-Time Piecewise-Linear Recurrent Neural …

In many scientific disciplines, we are interested in inferring the nonlinear dynamical system underlying a set of observed time series, a challenging task in the face of chaotic behavior and noise. Previous deep learning approaches toward…

Dynamical systems (DS) theory is fundamental for many areas of science and engineering. It can provide deep insights into the behavior of systems evolving in time, as typically described by differential or recursive equations. A common…

We introduce a deep residual recurrent neural network (DR-RNN) as an efficient model reduction technique for nonlinear dynamical systems. The developed DR-RNN is inspired by the iterative steps of line search methods in finding the residual…

The computational properties of neural systems are often thought to be implemented in terms of their network dynamics. Hence, recovering the system dynamics from experimentally observed neuronal time series, like multiple single-unit (MSU)…

Recent work in deep learning focuses on solving physical systems in the Ordinary Differential Equation or Partial Differential Equation. This current work proposed a variant of Convolutional Neural Networks (CNNs) that can learn the hidden…

We present a new model, Predictive State Recurrent Neural Networks (PSRNNs), for filtering and prediction in dynamical systems. PSRNNs draw on insights from both Recurrent Neural Networks (RNNs) and Predictive State Representations (PSRs),…

Neural networks are a popular tool for modeling sequential data but they generally do not treat time as a continuous variable. Neural ODEs represent an important exception: they parameterize the time derivative of a hidden state with a…

Continuous-depth neural networks, such as the Neural Ordinary Differential Equations (ODEs), have aroused a great deal of interest from the communities of machine learning and data science in recent years, which bridge the connection…

Today, it is more important than ever before for users to have trust in the models they use. As Machine Learning models fall under increased regulatory scrutiny and begin to see more applications in high-stakes situations, it becomes…

Chaotic dynamical systems (DS) are ubiquitous in nature and society. Often we are interested in reconstructing such systems from observed time series for prediction or mechanistic insight, where by reconstruction we mean learning…

This work proposes a novel neural network architecture, called the Dynamically Controlled Recurrent Neural Network (DCRNN), specifically designed to model dynamical systems that are governed by ordinary differential equations (ODEs). The…

Classical methods of solving spatiotemporal dynamical systems include statistical approaches such as autoregressive integrated moving average, which assume linear and stationary relationships between systems' previous outputs. Development…

As a powerful modelling method, PieceWise Linear Neural Networks (PWLNNs) have proven successful in various fields, most recently in deep learning. To apply PWLNN methods, both the representation and the learning have long been studied. In…

Learning models for dynamical systems in continuous time is significant for understanding complex phenomena and making accurate predictions. This study presents a novel approach utilizing differential neural networks (DNNs) to model…

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…

Recurrent neural networks (RNN) as used in machine learning are commonly formulated in discrete time, i.e. as recursive maps. This brings a lot of advantages for training models on data, e.g. for the purpose of time series prediction or…

We present a novel layerwise optimization algorithm for the learning objective of Piecewise-Linear Convolutional Neural Networks (PL-CNNs), a large class of convolutional neural networks. Specifically, PL-CNNs employ piecewise linear…

Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…

Discrete-time modeling of acoustic, mechanical and electrical systems is a prominent topic in the musical signal processing literature. Such models are mostly derived by discretizing a mathematical model, given in terms of ordinary or…

In dynamical systems reconstruction (DSR) we seek to infer from time series measurements a generative model of the underlying dynamical process. This is a prime objective in any scientific discipline, where we are particularly interested in…