Related papers: Identification of Continuous-Time Dynamical System…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
Sequential models, such as Recurrent Neural Networks and Neural Ordinary Differential Equations, have long suffered from slow training due to their inherent sequential nature. For many years this bottleneck has persisted, as many thought…
Multiscale is a hallmark feature of complex nonlinear systems. While the simulation using the classical numerical methods is restricted by the local \textit{Taylor} series constraints, the multiscale techniques are often limited by finding…
A novel procedure for the online identification of a class of discrete-time switched linear systems, which simultaneously estimates the parameters and switching manifolds of the systems, is proposed in this paper. Firstly, to estimate the…
When identifying electrical, mechanical, or biological systems, parametric continuous-time identification methods can lead to interpretable and parsimonious models when the model structure aligns with the physical properties of the system.…
Classical network embeddings create a low dimensional representation of the learned relationships between features across nodes. Such embeddings are important for tasks such as link prediction and node classification. In the current paper,…
This article introduces two Tensor Network-based iterative algorithms for the identification of high-order discrete-time nonlinear multiple-input multiple-output (MIMO) Volterra systems. The system identification problem is rewritten in…
The identification of electrical, mechanical, and biological systems using data can benefit greatly from prior knowledge extracted from physical modeling. Parametric continuous-time identification methods can naturally incorporate this…
In this paper we show that neural ODE analogs of recurrent (ODE-RNN) and Long Short-Term Memory (ODE-LSTM) networks can be algorithmically embeddeded into the class of polynomial systems. This embedding preserves input-output behavior and…
As neural networks grow in scale, their training becomes both computationally demanding and rich in dynamics. Amidst the flourishing interest in these training dynamics, we present a novel observation: Parameters during training exhibit…
One of the main problems encountered so far with recurrent neural networks is that they struggle to retain long-time information dependencies in their recurrent connections. Neural Turing Machines (NTMs) attempt to mitigate this issue by…
Data-driven approaches are increasingly popular for identifying dynamical systems due to improved accuracy and availability of sensor data. However, relying solely on data for identification does not guarantee that the identified systems…
In this paper, we present a new kind of learning implementation to recognize the patterns using the concept of Mirroring Neural Network (MNN) which can extract information from distinct sensory input patterns and perform pattern recognition…
We develop a formal framework for the behavioral comparison of linear systems across different time domains. We accomplish this by introducing the notion of system interpolation, which determines whether the input-state trajectories of a…
Continuous-time models are a natural choice for irregular and asynchronous data. A central design choice is how to embed discrete observations into continuous time. Interpolation- and imputation-based embeddings reconstruct a continuous…
Model predictive control (MPC) is a powerful framework for optimal control of dynamical systems. However, MPC solvers suffer from a high computational burden that restricts their application to systems with low sampling frequency. This…
Data-enabled predictive control (DeePC) for linear systems utilizes data matrices of recorded trajectories to directly predict new system trajectories, which is very appealing for real-life applications. In this paper we leverage the…
While discrete-event simulators are essential tools for architecture research, design, and development, their practicality is limited by an extremely long time-to-solution for realistic applications under investigation. This work describes…
The accurate assembly of the system matrix is an important step in any code that solves partial differential equations on a mesh. We either explicitly set up a matrix, or we work in a matrix-free environment where we have to be able to…
Koopman spectral analysis has attracted attention for nonlinear dynamical systems since we can analyze nonlinear dynamics with a linear regime by embedding data into a Koopman space by a nonlinear function. For the analysis, we need to find…