Related papers: Identifying Systems with Symmetries using Equivari…
The unknown inputs in a dynamical system may represent unknown external drivers, input uncertainty, state uncertainty, or instrument faults and thus unknown-input reconstruction has several wide-spread applications. In this paper we…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
We study how the degree of nonlinearity in the input data affects the optimal design of reservoir computers, focusing on how closely the model's nonlinearity should align with that of the data. By reducing minimal RCs to a single tunable…
Symmetry is a fundamental tool in the exploration of a broad range of complex systems. In machine learning symmetry has been explored in both models and data. In this paper we seek to connect the symmetries arising from the architecture of…
We demonstrate that matching the symmetry properties of a reservoir computer (RC) to the data being processed dramatically increases its processing power. We apply our method to the parity task, a challenging benchmark problem that…
Structural symmetries of linear dynamical systems can be exploited for decoupling the dynamics and reducing the computational complexity of the controller implementation. However, in practical applications, inexact structural symmetries…
Nonlinear manifold learning algorithms, such as diffusion maps, have been fruitfully applied in recent years to the analysis of large and complex data sets. However, such algorithms still encounter challenges when faced with real data. One…
We describe several algorithms for matrix completion and matrix approximation when only some of its entries are known. The approximation constraint can be any whose approximated solution is known for the full matrix. For low rank…
Datasets often have their intrinsic symmetries, and particular deep-learning models called equivariant or invariant models have been developed to exploit these symmetries. However, if some or all of these symmetries are only approximate,…
This paper presents a novel online identification algorithm for nonlinear regression models. The online identification problem is challenging due to the presence of nonlinear structure in the models. Previous works usually ignore the…
When computing the eigenstructure of matrix pencils associated with the passivity analysis of perturbed port-Hamiltonian descriptor system using a structured generalized eigenvalue method, one should make sure that the computed spectrum…
We are concerned with an approximation problem for a symmetric positive semidefinite matrix due to motivation from a class of nonlinear machine learning methods. We discuss an approximation approach that we call {matrix ridge…
We present a framework that enables estimation of low-dimensional sub-resolution reservoir properties directly from seismic data, without requiring the solution of a high dimensional seismic inverse problem. Our workflow is based on the…
The paper intends to offer a general overview on what the concept of integrability means for a nonlinear dynamical system and how the symmetry method can be applied for approaching it. After a general part where key problems as direct and…
A reservoir computer is a complex nonlinear dynamical system that has been shown to be useful for solving certain problems, such as prediction of chaotic signals, speech recognition or control of robotic systems. Typically a reservoir…
One of the fundamental problems of interest for discrete-time linear systems is whether its input sequence may be recovered given its output sequence, a.k.a. the left inversion problem. Many conditions on the state space geometry, dynamics,…
Reservoir computing (RC), is a class of computational methods such as Echo State Networks (ESN) and Liquid State Machines (LSM) describe a generic method to perform pattern recognition and temporal analysis with any non-linear system. This…
The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic…
Lie symmetry analysis is applied to study the nonlinear rotating shallow water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow water equations are related…
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…