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A method for the quantitative analysis of the degree and parameters of synchronization of the chaotic oscillations in two coupled oscillators is proposed, which makes it possible to reveal a change in the structure of attractors. The…
We unify and extend the semigroup and the PDE approaches to stochastic maximal regularity of time-dependent semilinear parabolic problems with noise given by a cylindrical Brownian motion. We treat random coefficients that are only…
This paper focuses on the efficient numerical algorithms of a three-field Biot's consolidation model. The approach begins with the introduction of innovative monolithic and global-in-time iterative decoupled algorithms, which incorporate…
Recently, significant connections between compressed sensing problems and optimization of a particular class of functions relating to solutions of Hamilton-Jacobi equation was discovered. In this paper we introduce a fast approximate…
Combinatorial optimization is a promising area for achieving quantum speedup. Quantum approximate optimization algorithm (QAOA) is designed to search for low-energy states of the Ising model, which correspond to near-optimal solutions of…
We consider distributed stochastic optimization problems that are solved with master/workers computation architecture. Statistical arguments allow to exploit statistical similarity and approximate this problem by a finite-sum problem, for…
This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…
The reconstruction from observations of high-dimensional chaotic dynamics such as geophysical flows is hampered by (i) the partial and noisy observations that can realistically be obtained, (ii) the need to learn from long time series of…
Model order reduction is a technique that is used to construct low-order approximations of large-scale dynamical systems. In this paper, we investigate a balancing based model order reduction method for dynamical systems with a linear…
The synchronization of coupled chaotic systems represents a fundamental example of self organization and collective behavior. This well-studied phenomenon is classically characterized in terms of macroscopic parameters, such as Lyapunov…
Spatiotemporal chaotic systems are difficult to characterize in a model-free manner because of their high dimensionality, strong nonlinearity, and sensitivity to initial conditions. Coupled map lattices, as a representative class of…
Time-reversible symplectic methods, which are precisely compatible with Liouville's phase-volume-conservation theorem, are often recommended for computational simulations of Hamiltonian mechanics. Lack of energy drift is an apparent…
We study nonlinear constrained optimization problems in which only function evaluations of the objective and constraints are available. Existing zeroth-order methods rely on noisy gradient and Jacobian surrogates in high dimensions, making…
Zeroth-order (derivative-free) optimization attracts a lot of attention in machine learning, because explicit gradient calculations may be computationally expensive or infeasible. To handle large scale problems both in volume and dimension,…
As a core part of autonomous driving systems, motion planning has received extensive attention from academia and industry. However, real-time trajectory planning capable of spatial-temporal joint optimization is challenged by nonholonomic…
In this paper, we address the reduced-order synchronization problem between two chaotic memristive Hindmarsh-Rose (HR) neurons of different orders using two distinct methods. The first method employs the Lyapunov active control technique.…
Distributed optimization problems have received much attention due to their privacy preservation, parallel computation, less communication, and strong robustness. This paper presents and studies the time-varying distributed optimization…
A mass-conservative high-order unfitted finite element method for convection-diffusion equations in evolving domains is proposed. The space-time method presented in [P. Hansbo, M. G. Larson, S. Zahedi, Comput. Methods Appl. Mech. Engrg. 307…
We propose a general strategy for reduced order modeling of systems that display highly nonlinear oscillations. By considering a continuous family of forced periodic orbits defined in relation to a stable fixed point and subsequently…
In this paper we propose local approximation spaces for localized model order reduction procedures such as domain decomposition and multiscale methods. Those spaces are constructed from local solutions of the partial differential equation…