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We consider covariance control problems for nonlinear stochastic systems. Our objective is to find an optimal control strategy to steer the state from an initial distribution to a terminal one with specified mean and covariance. This…
This paper explores backward error analysis for numerical solutions of ordinary differential equations, particularly focusing on chaotic systems. Three approaches are examined: residual assessment, the method of modified equations, and…
In this work, to efficiently help escape the stationary and saddle points, we propose, analyze, and generalize a stochastic strategy performed as an operator for a first-order gradient descent algorithm in order to increase the target…
This paper examines restart strategies for algorithms whose successful termination depends on an unknown parameter $\lambda$. After each restart, $\lambda$ is increased, until the algorithm terminates successfully. It is assumed that there…
Accurately solving partial differential equations (PDEs) is essential across many scientific disciplines. However, high-fidelity solvers can be computationally prohibitive, motivating the development of reduced-order models (ROMs).…
This work concerns about forward-backward multivalued stochastic systems. First of all, we prove one average principle for general stochastic differential equations in the $L^{2p}$ ($p\geq 1$) sense. Moreover, for $p=1$ a convergence rate…
In this paper we study the problem of inferring the initial conditions of a dynamical system under incomplete information. Studying several model systems, we infer the latent microstates that best reproduce an observed time series when the…
Modeling and predicting the dynamics of complex multiscale systems remains a significant challenge due to their inherent nonlinearities and sensitivity to initial conditions, as well as limitations of traditional machine learning methods…
Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many…
Many recently introduced enhanced sampling techniques are based on biasing coarse descriptors (collective variables) of a molecular system on the fly. Sometimes the calculation of such collective variables is expensive and becomes a…
Stochastic gradient methods are scalable for solving large-scale optimization problems that involve empirical expectations of loss functions. Existing results mainly apply to optimization problems where the objectives are one- or two-level…
A multi-step extended maximum residual Kaczmarz method is presented for the solution of the large inconsistent linear system of equations by using the multi-step iterations technique. Theoretical analysis proves the proposed method is…
The long-time behaviour of many dynamical systems may be effectively predicted by a low-dimensional model that describes the evolution of a reduced set of variables. We consider the question of how to equip such a low-dimensional model with…
A minimal requirement for simulating multi-scale systems is to reproduce the statistical behavior of the slow variables. In particular, a good numerical method should accurately aproximate the probability density function of the…
To operate process engineering systems in a safe and reliable manner, predictive models are often used in decision making. In many cases, these are mechanistic first principles models which aim to accurately describe the process. In…
Reliable preparation of many-body ground states is an essential task in quantum computing, with applications spanning areas from chemistry and materials modeling to quantum optimization and benchmarking. A variety of approaches have been…
Learning-based control methods typically assume stationary system dynamics, an assumption often violated in real-world systems due to drift, wear, or changing operating conditions. We study reinforcement learning for control under…
A general, variational approach to derive low-order reduced systems is presented. The approach is based on the concept of optimal parameterizing manifold (OPM) that substitutes the more classical notions of invariant or slow manifold when…
The recently developed technique of DOC kernels has been a great success in the stability and convergence analysis for BDF2 scheme with variable time steps. However, such an analysis technique seems not directly applicable to problems with…
Applying parallel-in-time algorithms to multiscale Hamiltonian systems to obtain stable long time simulations is very challenging. In this paper, we present novel data-driven methods aimed at improving the standard parareal algorithm…