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Particle smoothing methods are used for inference of stochastic processes based on noisy observations. Typically, the estimation of the marginal posterior distribution given all observations is cumbersome and computational intensive. In…
Iterative refinement (IR) is a popular scheme for solving a linear system of equations based on gradually improving the accuracy of an initial approximation. Originally developed to improve upon the accuracy of Gaussian elimination,…
Modelling the sudden depressurisation of superheated liquids through nozzles is a challenge because the pressure drop causes rapid flash boiling of the liquid. The resulting jet usually demonstrates a wide range of structures, including…
In this paper, we present splitting methods that are based on iterative schemes and applied to plasma simulations. The motivation arose of solving the Coulomb collisions, which are modeled by nonlinear stochastic differential equations. We…
Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process and…
Computational fluid dynamics (CFD) is a powerful tool for modeling turbulent flow and is commonly used for urban microclimate simulations. However, traditional CFD methods are computationally intensive, requiring substantial hardware…
A study is conducted to evaluate four derivative estimation methods when solving a large sparse nonlinear programming problem that arises from the approximation of an optimal control problem using a direct collocation method. In particular,…
Markov chain Monte Carlo methods are primarily used for sampling from a given probability distribution and estimating multi-dimensional integrals based on the information contained in the generated samples. Whenever it is possible, more…
A set of programs for the numerical simulation of the diffusion decomposition processes was developed by using simulation methods, kinetic and particle method. The complex has been validated on the model system Ni-Al by the growth of -phase…
Diffusion and flow matching models generate high-fidelity data by simulating paths defined by Ordinary or Stochastic Differential Equations (ODEs/SDEs), starting from a tractable prior distribution. The probability flow ODE formulation…
High-intensity laser plasma interactions create complex computational problems because they involve both fluid and kinetic regimes, which need models that maintain physical precision while keeping computational speed. The research…
Simulation-based optimization using agent-based models is typically carried out under the assumption that the gradient describing the sensitivity of the simulation output to the input cannot be evaluated directly. To still apply…
Without question regarding its pivotal significance, the computation of function derivatives carries substantial weight within a multitude of engineering and applied mathematical fields. These encompass optimization, the development of…
This paper proposes a new class of real-time optimization schemes to overcome system-model mismatch of uncertain processes. This work's novelty lies in integrating derivative-free optimization schemes and multi-fidelity Gaussian processes…
Computing solutions to partial differential equations using the fast Fourier transform can lead to unwanted oscillatory behavior. Due to the periodic nature of the discrete Fourier transform, waves that leave the computational domain on one…
Inverse design of large-area metasurfaces can potentially exploit the full parameter space that such devices offer and achieve highly efficient multifunctional flat optical elements. However, since practically useful flat optics elements…
It is a long-standing challenge to accurately and efficiently compute thermodynamic quantities of many-body systems at thermal equilibrium. The conventional methods, e.g., Markov chain Monte Carlo, require many steps to equilibrate. The…
On the example of the Poynting-Thomson-Zener rheological model for solids, which exhibits both dissipation and wave propagation - with nonlinear dispersion relation -, we introduce and investigate a finite difference numerical scheme. Our…
Fractional derivative relaxation type equations (FREs) including fractional diffusion equation and fractional relaxation equation, have been widely used to describe anomalous phenomena in physics. To utilize the characteristics of…
Traditionally, neural networks are parameterized using optimization procedures such as stochastic gradient descent, RMSProp and ADAM. These procedures tend to drive the parameters of the network toward a local minimum. In this article, we…