arXiv subjects

Igor Shevchenko

Publications and source records attributed to Igor Shevchenko.

13 recordsLinked to original sources

arXiv2025

Data assimilation for energy-aware hybrid models

This work integrates ensemble-based data assimilation (DA) with the energy-aware hybrid modeling approach, applied to a three-layer quasi-geostrophic (QG) model of the Gulf Stream flow. Building on prior DA success in the QG channel regime, where stochastic corrections based on EOFs were effective, we show that this method fails to address persistent errors in the more complex, dynamically richer Gulf Stream setting.To overcome this, we employ a hybrid model that controls energy at selected scales, maintaining dynamic consistency and physical realism. We evaluate the combined effect of hybrid modeling and DA, using a particle filter which combines model reduction, tempering, jittering, and nudging. Numerical experiments show that the hybrid model reproduces both the large-scale jet and small-scale vortices seen in high-resolution reference simulations, but missing in the standard (non-hybrid) QG model. When DA is incorporated, the hybrid model further reduces tracking error and ensemble divergence. Moreover, targeted assimilation from the most energetic region matches tracking error and uncertainty reduction of full-domain networks, highlighting the critical importance of observation network design. These findings demonstrate that combining energy-aware hybrid modeling with ensemble-based DA enables high-fidelity, computationally efficient tracking of the reference solution even under sparse, noisy, localized observations.

physics.flu-dyn↗

arXiv2024

Advection of the image point in probabilistically-reconstructed phase spaces

Insufficient reference data is ubiquitous in data-driven computational fluid dynamics, as it is usually too expensive to compute or impossible to observe over long enough times needed for data-driven methods. The lack of data can significantly compromise the fidelity of results computed with data-driven methods or render them inapplicable. To challenge this problem, we propose a probabilistic reconstruction method that enhances the hyper-parameterisation (HP) approach with ideas underlying the probabilistic-evolutionary approach. We offer to use the HP method ``Advection of the image point'' on data sampled from the joint probability distribution of the reference dataset. The HP method has been tested regionally on the sea surface temperature and surface relative vorticity computed with the global 1/4-deg and 1/12-deg resolution NEMO model. Our results show that the HP solution (the solution computed with the HP method) in the probabilistically-reconstructed and reduced (in terms of dimensionality) phase space at 1/4-deg resolution is more accurate than the 1/4-deg-solution computed with NEMO. Additionally, the HP solution is several orders of magnitude faster to compute than the 1/4-deg NEMO solution. The proposed method shows encouraging results for the NEMO model and the potential for the use in other operational ocean and ocean-atmospheric models for both deterministic and probabilistic predictions. Furthermore, the method can be used as a fast reanalysis tool allowing the complex dynamics of a comprehensive ocean model to be approximated by the HP solution. It can also function as a dynamic interpolation method to fill gaps in observational data.

physics.flu-dyn↗

arXiv2024

On energy-aware hybrid models

This study proposes deterministic and stochastic energy-aware hybrid models that should enable simulations of idealized and primitive-equations Geophysical Fluid Dynamics (GFD) models at low resolutions without compromising on quality compared with high-resolution runs. Such hybrid models bridge the data-driven and physics-driven modelling paradigms by combining regional stability and classical GFD models at low resolution that cannot reproduce high-resolution reference flow features (large-scale flows and small-scale vortices) which are, however, resolved. Hybrid models use an energy-aware correction of advection velocity and extra forcing compensating for the drift of the low-resolution model away from the reference phase space. The main advantages of hybrid models are that they allow for physics-driven flow recombination within the reference energy band, reproduce resolved reference flow features, and produce more accurate ensemble forecasts than their classical GFD counterparts. Hybrid models offer appealing benefits and flexibility to the modelling and forecasting communities, as they are computationally cheap and can use both numerically-computed flows and observations from different sources. All these suggest that the hybrid approach has the potential to exploit low-resolution models for long-term weather forecasts and climate projections thus offering a new cost effective way of GFD modelling. The proposed hybrid approach has been tested on a three-layer quasi-geostrophic model for a beta-plane Gulf Stream flow configuration. The results show that the low-resolution hybrid model reproduces the reference flow features that are resolved on the coarse grid and also gives a more accurate ensemble forecast than the physics-driven model.

physics.flu-dyn↗

arXiv2023

On a probabilistic evolutionary approach to ocean modelling: From Lorenz-63 to idealized ocean models

In this study we develop an alternative way to model the ocean reflecting the chaotic nature of ocean flows and uncertainty of ocean models -- instead of making use of classical deterministic or stochastic differential equations we offer a probabilistic evolutionary approach (PEA) that capitalizes on the use of probabilistic dynamics in phase space. The main feature of the data-driven version of PEA proposed in this work is that it does not require to know the physics behind the flow dynamics to model it. Within the PEA framework we develop two probabilistic evolutionary methods, which are based on probabilistic evolutionary models using quasi time-invariant structures in phase space. The methods have been tested on complete and incomplete reference data sets generated by the Lorenz 63 system and by an idealized multi-layer quasi-geostrophic model. The results show that both methods reproduce large- and small-scale features of the reference flow by keeping the probabilistic dynamics within the reference phase space (the phase space of the reference flow). The proposed approach offers appealing benefits and a great flexibility to ocean modellers working with mathematical models and measurements. The most remarkable one is that it provides an alternative to the mainstream ocean parameterizations, requires no modification of existing ocean models, and easy to implement. Moreover, it does not depend on the nature of input data, and therefore can work with both numerically-computed flows and real measurements from different sources (drifters, weather stations, etc.).

physics.flu-dyn↗

arXiv2022

A hyper-parameterization method for comprehensive ocean models: Advection of the image point

Idealized and comprehensive ocean models at low resolutions cannot reproduce nominally-resolved flow structures similar to those presented in the high-resolution solution. Although there are various underlying physical reasons for this, from the dynamical system point of view all these reasons manifest themselves as a low-resolution trajectory avoiding the phase space occupied by the reference solution (the high-resolution solution projected onto the coarse grid). In order to solve this problem, a set of hyper-parameterization methods has recently been proposed and successfully tested on idealized ocean models. In this work, for the first time we apply one of hyper-parameterization methods (Advection of the image point) to a comprehensive, rather than idealized, general circulation model of the North Atlantic. The results show that the hyper-parameterization method significantly improves a non-eddy-resolving solution towards the reference eddy-resolving solution by reproducing both the large- and small-scale features of the Gulf Stream flow. The proposed method is much faster than even a single run of the coarse-grid ocean model, requires no modification of the model, and is easy to implement. Moreover, the method can take not only the reference solution as input data but also real measurements from different sources (drifters, weather stations, etc.), or combination of both. All this offers a great flexibility to ocean modellers working with mathematical models and/or measurements.

physics.flu-dyn↗

arXiv2021

A method for preserving nominally-resolved flow patterns in low-resolution ocean simulations: Constrained dynamics

Inability of low-resolution ocean models to simulate many important aspects of the large-scale general circulation is a common problem. In the view of physics, the main reason for this failure are the missed dynamical effects of the unresolved small scales of motion on the explicitly resolved large scale motions. Complimentary to this mainstream physics-based perspective, we propose to address this failure from the dynamical systems point of view, namely, as the persistent tendency of phase space trajectories representing the low-resolution solution to escape the right region of the corresponding phase space, which is occupied by the reference eddy-resolving solution. Based on this concept, we propose to use methods of constrained optimization to confine the low-resolution solution to remain within the correct phase space region, without attempting to amend the eddy physics by introducing a process-based parameterisation. This approach is advocated as a novel framework for data-driven hyper-parameterisation of mesoscale oceanic eddies in non-eddy-resolving models. We tested the idea in the context of classical, baroclinic beta-plane turbulence model and showed that non-eddy-resolving solution can be substantially improved towards the reference eddy-resolving benchmark.

physics.ao-ph↗

arXiv2021

On a minimum set of equations for parameterisations in comprehensive ocean circulation models

The complexity of comprehensive ocean models poses an important question for parameterisations: is there a minimum set of equations that should be parameterised, on the one hand, to reduce the development to a minimum, and, on the other hand, to ensure an accurate representation of large-scale flow patterns? This work seeks to answer this to assist modern parameterisations be more selective in their targets. For this, we considered a North Atlantic configuration of the MIT general circulation model and studied contributions of different model equations to the accuracy of representation of the Gulf Stream at low resolution. Our results suggest that it is enough to parameterise only the tracer equations for temperature and salinity and leave the other equations in the hydrodynamic part, as well as the atmospheric model unmodified.

physics.ao-ph↗

arXiv2021

A method for preserving nominally-resolved flow patterns in low-resolution ocean simulations

Accurate representation of large-scale flow patterns in low-resolution ocean simulations is one of the most challenging problems in ocean modelling. The main difficulty is to correctly reproduce effects of unresolved small scales on the resolved large scales. For this purpose, most of current research is focused on development of parameterisations accounting for the small scales. In this work we propose an alternative to the mainstream ideas by showing how to reconstruct a dynamical system from the available reference solution data (our proxy for observations) and, then, how to use this system for modelling not only large-scale but also nominally-resolved flow patterns at low resolutions. The proposed methodology robustly allows to retrieve a system of equations underlying reduced dynamics of the observed data. Remarkably, its solutions simulate not only large-scale but also small-scale flow features, which can be nominally resolved by the low-resolution grid.

math.DS↗

arXiv2019

Data assimilation for a quasi-geostrophic model with circulation-preserving stochastic transport noise

This paper contains the latest installment of the authors' project on developing ensemble based data assimilation methodology for high dimensional fluid dynamics models. The algorithm presented here is a particle filter that combines model reduction, tempering, jittering, and nudging. The methodology is tested on a two-layer quasi-geostrophic model for a $\beta$-plane channel flow with $O(10^6)$ degrees of freedom out of which only a minute fraction are noisily observed. The model is reduced by following the stochastic variational approach for geophysical fluid dynamics introduced in Holm (Proc Roy Soc A, 2015) as a framework for deriving stochastic parametrisations for unresolved scales. The reduction is substantial: the computations are done only for $O(10^4)$ degrees of freedom. We introduce a stochastic time-stepping scheme for the two-layer model and prove its consistency in time. Then, we analyze the effect of the different procedures (tempering combined with jittering and nudging) on the performance of the data assimilation procedure using the reduced model, as well as how the dimension of the observational data (the number of "weather stations") and the data assimilation step affect the accuracy and uncertainty of the results.

math.NA↗

arXiv2019

A Particle Filter for Stochastic Advection by Lie Transport (SALT): A case study for the damped and forced incompressible 2D Euler equation

In this work, we combine a stochastic model reduction with a particle filter augmented with tempering and jittering, and apply the combined algorithm to a damped and forced incompressible 2D Euler dynamics defined on a simply connected bounded domain. We show that using the combined algorithm, we are able to assimilate data from a reference system state (the ``truth") modelled by a highly resolved numerical solution of the flow that has roughly $3.1\times10^6$ degrees of freedom, into a stochastic system having two orders of magnitude less degrees of freedom, which is able to approximate the true state reasonably accurately for $5$ large scale eddy turnover times, using modest computational hardware. The model reduction is performed through the introduction of a stochastic advection by Lie transport (SALT) model as the signal on a coarser resolution. The SALT approach was introduced as a general theory using a geometric mechanics framework from Holm, Proc. Roy. Soc. A (2015). This work follows on the numerical implementation for SALT presented by Cotter et al, SIAM Multiscale Model. Sim. (2019) for the flow in consideration. The model reduction is substantial: The reduced SALT model has $4.9\times 10^4$ degrees of freedom. Results from reliability tests on the assimilated system are also presented.

stat.AP↗

arXiv2018

Modelling uncertainty using stochastic transport noise in a 2-layer quasi-geostrophic model

The stochastic variational approach for geophysical fluid dynamics was introduced by Holm (Proc Roy Soc A, 2015) as a framework for deriving stochastic parameterisations for unresolved scales. This paper applies the variational stochastic parameterisation in a two-layer quasi-geostrophic model for a beta-plane channel flow configuration. We present a new method for estimating the stochastic forcing (used in the parameterisation) to approximate unresolved components using data from the high resolution deterministic simulation, and describe a procedure for computing physically-consistent initial conditions for the stochastic model. We also quantify uncertainty of coarse grid simulations relative to the fine grid ones in homogeneous (teamed with small-scale vortices) and heterogeneous (featuring horizontally elongated large-scale jets) flows, and analyse how the spread of stochastic solutions depends on different parameters of the model. The parameterisation is tested by comparing it with the true eddy-resolving solution that has reached some statistical equilibrium and the deterministic solution modelled on a low-resolution grid. The results show that the proposed parameterisation significantly depends on the resolution of the stochastic model and gives good ensemble performance for both homogeneous and heterogeneous flows, and the parameterisation lays solid foundations for data assimilation.

physics.flu-dyn↗

arXiv2018

Numerically Modelling Stochastic Lie Transport in Fluid Dynamics

We present a numerical investigation of stochastic transport in ideal fluids. According to Holm (Proc Roy Soc, 2015) and Cotter et al. (2017), the principles of transformation theory and multi-time homogenisation, respectively, imply a physically meaningful, data-driven approach for decomposing the fluid transport velocity into its drift and stochastic parts, for a certain class of fluid flows. In the current paper, we develop new methodology to implement this velocity decomposition and then numerically integrate the resulting stochastic partial differential equation using a finite element discretisation for incompressible 2D Euler fluid flows. The new methodology tested here is found to be suitable for coarse graining in this case. Specifically, we perform uncertainty quantification tests of the velocity decomposition of Cotter et al. (2017), by comparing ensembles of coarse-grid realisations of solutions of the resulting stochastic partial differential equation with the "true solutions" of the deterministic fluid partial differential equation, computed on a refined grid. The time discretization used for approximating the solution of the stochastic partial differential equation is shown to be consistent. We include comprehensive numerical tests that confirm the non-Gaussianity of the stream function, velocity and vorticity fields in the case of incompressible 2D Euler fluid flows.

physics.flu-dyn↗

arXiv2014

Absorbing boundary conditions for the Westervelt equation

The focus of this work is on the construction of a family of nonlinear absorbing boundary conditions for the Westervelt equation in one and two space dimensions. The principal ingredient used in the design of such conditions is pseudo-differential calculus. This approach enables to develop high order boundary conditions in a consistent way which are typically more accurate than their low order analogs. Under the hypothesis of small initial data, we establish local well-posedness for the Westervelt equation with the absorbing boundary conditions. The performed numerical experiments illustrate the efficiency of the proposed boundary conditions for different regimes of wave propagation.

math.NA↗