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We propose a method for multi-scale hybrid simulations of molecular dynamics (MD) and computational fluid dynamics (CFD). In the method, usual lattice-mesh based simulations are applied for CFD level, but each lattice is associated with a…
Accurately predicting turbulent flows remains a central challenge in fluid dynamics due to their high dimensionality and intrinsic nonlinearity. Recent developments in quantum algorithms and machine learning offer new opportunities for…
The never-ending computational demand from simulations of turbulence makes computational fluid dynamics (CFD) a prime application use case for current and future exascale systems. High-order finite element methods, such as the spectral…
For quantum algorithms for problems in which the task is to compute an entire field of values, like e.g. computational fluid dynamics (CFD), it is often proposed amplitude encoding w.r.t. multiple qubits; however, the efforts implied by it…
Flow models are a cornerstone of modern machine learning. They are generative models that progressively transform probability distributions according to learned dynamics. Specifically, they learn a continuous-time Markov process that…
This paper explores the use of quantum computing, specifically the use of HHL and VQLS algorithms, to solve optimal power flow problem in electrical grids. We investigate the effectiveness of these quantum algorithms in comparison to…
An efficient algorithm for computing the terms appearing in the Generalised Kolmogorov Equation (GKE) written for the indefinite plane channel flow is presented. The algorithm, which features three distinct strategies for parallel…
These notes are an introduction to fluctuating hydrodynamics (FHD) and the formulation of numerical schemes for the resulting stochastic partial differential equations (PDEs). Fluctuating hydrodynamics was originally introduced by Landau…
We propose quantum methods for solving differential equations that are based on a gradual improvement of the solution via an iterative process, and are targeted at applications in fluid dynamics. First, we implement the Jacobi iteration on…
A computational method for numeric resolution of a PDEs system, based on a Finite Differences schema integrated by interpolations of partial results, and an estimate of the error of its solution respect to the normal FD solution.
The past years have seen a surge in quantum algorithms for computational fluid dynamics (CFD). These algorithms have in common that whilst promising a speed-up in the performance of the algorithm, no specific method of measurement has been…
For computational fluid dynamics (CFD) applications with a large number of grid points/cells, parallel computing is a common efficient strategy to reduce the computational time. How to achieve the best performance in the modern…
This paper explores the feasibility of quantum simulation for partial differential equations (PDEs) with physical boundary or interface conditions. Semi-discretisation of such problems does not necessarily yield Hamiltonian dynamics and…
We examine nonlinear Kolmogorov partial differential equations (PDEs). Here the nonlinear part of the PDE comes from its Hamiltonian where one maximizes over all possible drift and diffusion coefficients which fall within a…
Computational Fluid Dynamics (CFD) is a hugely important subject with applications in almost every engineering field, however, fluid simulations are extremely computationally and memory demanding. Towards this end, we present Lat-Net, a…
Despite the progress in high performance computing, Computational Fluid Dynamics (CFD) simulations are still computationally expensive for many practical engineering applications such as simulating large computational domains and highly…
We present a novel variational quantum framework for nonlinear partial differential equation (PDE) constrained optimization problems. The proposed work extends the recently introduced bi-level variational quantum PDE constrained…
Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…
Motivated by the modeling of the spatial structure of the velocity field of three-dimensional turbulent flows, and the phenomenology of cascade phenomena, a linear dynamics has been recently proposed able to generate high velocity gradients…
Extracting the latent underlying structures of complex nonlinear local and nonlocal flows is essential for their analysis and modeling. In this work, we attempt to provide a consistent framework through Koopman theory and its related…