Related papers: Theoretical Foundations for the Dynamic Mode Decom…
Dynamic Mode Decomposition (DMD) has emerged as a powerful tool for analyzing the dynamics of non-linear systems from experimental datasets. Recently, several attempts have extended DMD to the context of low-rank approximations. This…
Improved performance in higher-order spectral density estimation is achieved using a general class of infinite-order kernels. These estimates are asymptotically less biased but with the same order of variance as compared to the classical…
The regulation of the cell state is a complex process involving several components. These complex dynamics can be modeled using Boolean networks, allowing us to explain the existence of different cell states and the transition between them.…
Dissipative partial differential equations that exhibit chaotic dynamics tend to evolve to attractors that exist on finite-dimensional manifolds. We present a data-driven reduced order modeling method that capitalizes on this fact by…
Consider a higher order state space system and the aim of this paper is to linearize the system preserving system characteristics. That is, linearization preserving system characteristics(e.g, controllability, observability, various zeros…
A review of the authors's results is given. Several methods are discussed for solving nonlinear equations $F(u)=f$, where $F$ is a monotone operator in a Hilbert space, and noisy data are given in place of the exact data. A discrepancy…
New families of fourth-order composition methods for the numerical integration of initial value problems defined by ordinary differential equations are proposed. They are designed when the problem can be separated into three parts in such a…
Higher-order interactions play a key role for the stability and function of a complex system. However, how to identify them is still an open problem. Here, we propose a method to fully reconstruct the structural connectivity of a system of…
This manuscript is aimed at addressing several long standing limitations of dynamic mode decompositions in the application of Koopman analysis. Principle among these limitations are the convergence of associated Dynamic Mode Decomposition…
A variety of complex biological, natural and man-made systems exhibit non-Markovian dynamics that can be modeled through fractional order differential equations, yet, we lack sample comlexity aware system identification strategies. Towards…
The behaviour of solutions to fourth order problems is studied through the decomposition into a system of second order ones, which leads to relaxed formulations with the introduction of measure terms. This allows to solve a shape…
Many physical phenomena, governed by partial differential equations (PDEs), are second order in nature. This makes sense to pose the control on the second order derivatives of the field solution, in addition to zero and first order ones, to…
We consider a network of identical, first-order linear systems, and investigate how replacing a subset of the systems composing the network with higher-order ones, either taken to be generic or specifically designed, may affect its…
This letter presents a method to reduce the computational demands of including second-order dynamics sensitivity information into the Differential Dynamic Programming (DDP) trajectory optimization algorithm. An approach to DDP is developed…
In this thesis we introduce the concept of a guided dynamical system, and exploit this idea to solve various problems in functional equations and PDE's. Our main results are 1) a necessary and sufficient condition for unique-solvability of…
The aim of this work is to study fiber derivatives associated to Lagrangian and Hamiltonian functions describing the dynamics of a higher-order autonomous dynamical system. More precisely, given a function in $T^*T^{(k-1)}Q$, we find…
In this paper we investigate the effectiveness of direct statistical simulation (DSS) for two low-order models of dynamo action. The first model, which is a simple model of solar and stellar dynamo action, is third-order and has cubic…
Traditional solvable optimal control theory predominantly focuses on quadratic costs due to their analytical tractability, yet they often fail to capture critical non-linearities inherent in real-world systems including water, energy,…
We introduce algebraic approach for superoperators that might be useful tool for investigation of quantum (bosonic) multi-mode systems and its dynamics. In order to demonstrate potential of proposed method we consider multi-mode Liouvillian…
A novel data-driven method of modal analysis for complex flow dynamics, termed as reduced-order variational mode decomposition (RVMD), has been proposed, combining the idea of the separation of variables and a state-of-the-art nonstationary…