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A convolutional neural network can be constructed using numerical methods for solving dynamical systems, since the forward pass of the network can be regarded as a trajectory of a dynamical system. However, existing models based on…

Data-driven modeling and machine learning are widely used to model the behavior of dynamic systems. One application is the residual evaluation of technical systems where model predictions are compared with measurement data to create…

Recent work has attempted to interpret residual networks (ResNets) as one step of a forward Euler discretization of an ordinary differential equation, focusing mainly on syntactic algebraic similarities between the two systems. Discrete…

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…

Data-driven modeling of nonlinear dynamical systems is often hampered by measurement noise. We propose a denoising framework, called Runge-Kutta and Total Variation Based Implicit Neural Representation (RKTV-INR), that represents the state…

The forecasting and reconstruction of ocean and atmosphere dynamics from satellite observation time series are key challenges. While model-driven representations remain the classic approaches, data-driven representations become more and…

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…

In this paper, we introduce a novel architecture to connecting adaptive learning and neural networks into an arbitrary machine's control system paradigm. Two consecutive Recurrent Neural Networks (RNNs) are used together to accurately model…

We present a method that connects a well-established nonlinear (bilinear) identification method from time-domain data with neural network (NNs) advantages. The main challenge for fitting bilinear systems is the accurate recovery of the…

The use of deep neural network (DNN) models as surrogates for linear and nonlinear structural dynamical systems is explored. The goal is to develop DNN based surrogates to predict structural response, i.e., displacements and accelerations,…

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),…

Discovering dynamical models to describe underlying dynamical behavior is essential to draw decisive conclusions and engineering studies, e.g., optimizing a process. Experimental data availability notwithstanding has increased…

Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. More recently, as deep…

Data-driven models for predicting dynamic responses of linear and nonlinear systems are of great importance due to their wide application from probabilistic analysis to inverse problems such as system identification and damage diagnosis. In…

While trade-offs between modeling effort and model accuracy remain a major concern with system identification, resorting to data-driven methods often leads to a complete disregard for physical plausibility. To address this issue, we propose…

Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential…

Machine learning algorithms, and more in particular neural networks, arguably experience a revolution in terms of performance. Currently, the best systems we have for speech recognition, computer vision and similar problems are based on…

Neural dynamical systems are dynamical systems that are described at least in part by neural networks. The class of continuous-time neural dynamical systems must, however, be numerically integrated for simulation and learning. Here, we…

We present a general numerical approach for learning unknown dynamical systems using deep neural networks (DNNs). Our method is built upon recent studies that identified the residue network (ResNet) as an effective neural network structure.…

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…