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Simulation of complex dynamical systems arising in many applications is computationally challenging due to their size and complexity. Model order reduction, machine learning, and other types of surrogate modeling techniques offer cheaper and simpler ways to describe the dynamics of these systems but are inexact and introduce additional approximation errors. In order to overcome the computational difficulties of the full complex models, on one hand, and the limitations of surrogate models, on the other, this work proposes a new accelerated time-stepping strategy that combines information from both. This approach is based on the multirate infinitesimal general-structure additive Runge–Kutta framework. The inexpensive surrogate model is integrated with a small time step to guide the solution trajectory, and the full model is treated with a large time step to occasionally correct for the surrogate model error and ensure convergence. We provide a theoretical error analysis, and several numerical experiments, to show that this approach can be significantly more efficient than using only the full or only the surrogate model for the integration. Accepted version

Multifidelity methods aim to leverage the availability of models at different levels of fidelity describing the same physical phenomena and are receiving growing attention in computational science. One field that can considerably benefits from statistical multifidelity approaches is data assimilation. This chapter presents a broad overview of multifidelity methods in data assimilation for hierarchies of models and hierarchies of observations. We introduce the theoretical multifidelity Kalman filter, and discuss its practical implementation using an ensemble-based framework as the multifidelity ensemble Kalman filter (MFEnKF). The discussion builds upon the theory of linear and nonlinear control variates. Numerical examples compare the multifidelity and the traditional EnKF.

As a result of the economic crisis of 2009-2010, the road traffic on the national road network, for the period 2011-2014, decreased considerably. Thus, the evolution coefficients, for the period 2020-2025, registered a trend of decrease in road traffic. Based on the analysis of the results of the automatic traffic records, it was found that the average daily average traffic increased by about 4.7% in 2016 compared to 2015 (the year of the last general circulation census) and is in continuous growth, one of the reasons being removal of car registration tax. In 2015, for the development of evolution coefficients and the rates of evolution of traffic on the national road network, the linear regression method was used which took into account both the evolution of road traffic reported in 1995, 2000, 2005 and 2010, as well as the evolution of road traffic on the traffic counters network for the period 2010-2015. The paper analyzes aspects of the efficiency of the method used until the present and the need to develop coefficients and rates of evolution based on more complex methods, based on several economic and social indicators, including the projected evolution of GDP.

Sensitivity analysis is one of the most prominent gradient based optimization techniques for mechanical systems. Model sensitivities are the derivatives of the generalized coordinates defining the motion of the system in time with respect to the system design parameters. These sensitivities can be calculated using finite differences, but the accuracy and computational inefficiency of this method limits its use. Hence, the methodologies of direct and adjoint sensitivity analysis have gained prominence. Recent research has presented computationally efficient methodologies for both direct and adjoint sensitivity analysis of complex multibody dynamic systems. The contribution of this article is in the development of the mathematical framework for conducting the direct sensitivity analysis of multibody dynamic systems with joint friction using the index-1 formulation. For modeling friction in multibody systems, the Brown and McPhee friction model has been used. This model incorporates the effects of both static and dynamic friction on the model dynamics. A case study has been conducted on a spatial slider-crank mechanism to illustrate the application of this methodology to real-world systems. Using computer models, with and without joint friction, effect of friction on the dynamics and model sensitivities has been demonstrated. The sensitivities of slider velocity have been computed with respect to the design parameters of crank length, rod length, and the parameters defining the friction model. Due to the highly non-linear nature of friction, the model dynamics are more sensitive during the transition phases, where the friction coefficient changes from static to dynamic and vice versa.