arXiv subjects

Daniel R. Gurevich

Publications and source records attributed to Daniel R. Gurevich.

7 recordsLinked to original sources

arXiv2026

Data-driven modeling of multiscale phenomena with applications to fluid turbulence

This paper introduces a novel data driven framework for constructing accurate and general equivariant models of multiscale phenomena which does not rely on specific assumptions about the underlying physics. This framework is illustrated using incompressible fluid turbulence as an example that is representative, practically important, reasonably simple, and exceedingly well studied. We use direct numerical simulations of freely decaying turbulence in two spatial dimensions to infer an effective field theory comprising explicit, interpretable evolution equations for both the large (resolved) and small (modeled) scales. The resulting closed system of equations is capable of accurately describing the effect of small scales, including backscatter -- the flow of energy from small to large scales, which is particularly pronounced in two dimensions -- which is an outstanding challenge that, to our knowledge, no existing alternative successfully tackles.

physics.flu-dyn↗

arXiv2026

Physics-informed data-driven inference of an interpretable equivariant LES model of incompressible fluid turbulence

Restrictive phenomenological assumptions represent a major roadblock for the development of accurate subgrid-scale models of fluid turbulence. Specifically, these assumptions limit a model's ability to describe key quantities of interest, such as local fluxes of energy and enstrophy, in the presence of diverse coherent structures. This paper introduces a symbolic data-driven subgrid-scale model that requires no phenomenological assumptions and has no adjustable parameters, yet it outperforms leading LES models. A combination of a priori and a posteriori benchmarks shows that the model produces accurate predictions of various quantities including local fluxes across a broad range of two-dimensional turbulent flows. While the model is inferred using LES-style spatial coarse-graining, its structure is more similar to RANS models, as it employs an additional field to describe subgrid scales. We find that this field must have a rank-two tensor structure in order to correctly represent both the components of the subgrid-scale stress tensor and the various fluxes.

physics.flu-dyn↗

arXiv2023

Learning fluid physics from highly turbulent data using sparse physics-informed discovery of empirical relations (SPIDER)

We show how a complete mathematical description of a complicated physical phenomenon can be learned from observational data via a hybrid approach combining three simple and general ingredients: physical assumptions of smoothness, locality, and symmetry, a weak formulation of differential equations, and sparse regression. To illustrate this, we extract a system of governing equations describing flows of incompressible Newtonian fluids -- the Navier-Stokes equation, the continuity equation, and the boundary conditions -- from numerical data describing a highly turbulent channel flow in three dimensions. These relations have the familiar form of partial differential equations, which are easily interpretable and readily provide information about the relative importance of different physical effects as well as insight into the quality of the data, serving as a useful diagnostic tool. The approach described here is remarkably robust, yielding accurate results for very high noise levels, and should thus be well-suited to experimental data.

physics.flu-dyn↗

arXiv2019

Using Noisy or Incomplete Data to Discover Models of Spatiotemporal Dynamics

Sparse regression has recently emerged as an attractive approach for discovering models of spatiotemporally complex dynamics directly from data. In many instances, such models are in the form of nonlinear partial differential equations (PDEs); hence sparse regression typically requires evaluation of various partial derivatives. However, accurate evaluation of derivatives, especially of high order, is infeasible when the data are noisy, which has a dramatic negative effect on the result of regression. We present a novel and rather general approach that addresses this difficulty by using a weak formulation of the problem. For instance, it allows accurate reconstruction of PDEs involving high-order derivatives, such as the Kuramoto-Sivashinsky equation, from data with a considerable amount of noise. The flexibility of our approach also allows reconstruction of PDE models that involve latent variables which cannot be measured directly with acceptable accuracy. This is illustrated by reconstructing a model for a weakly turbulent flow in a thin fluid layer, where neither the forcing nor the pressure field is known.

math.DS↗

arXiv2019

Robust Approach for Rotor Mapping in Cardiac Tissue

The motion of and interaction between phase singularities that anchor spiral waves captures many qualitative and, in some cases, quantitative features of complex dynamics in excitable systems. Being able to accurately reconstruct their position is thus quite important, even if the data are noisy and sparse, as in electrophysiology studies of cardiac arrhythmias, for instance. A recently proposed global topological approach [Marcotte & Grigoriev, Chaos 27, 093936 (2017)] promises to dramatically improve the quality of the reconstruction compared with traditional, local approaches. Indeed, we found that this approach is capable of handling noise levels exceeding the range of the signal with minimal loss of accuracy. Moreover, it also works successfully with data sampled on sparse grids with spacing comparable to the mean separation between the phase singularities for complex patterns featuring multiple interacting spiral waves.

nlin.CD↗

arXiv2019

Robust and optimal sparse regression for nonlinear PDE models

This paper investigates how models of spatiotemporal dynamics in the form of nonlinear partial differential equations can be identified directly from noisy data using a combination of sparse regression and weak formulation. Using the 4th-order Kuramoto-Sivashinsky equation for illustration, we show how this approach can be optimized in the limits of low and high noise, achieving accuracy that is orders of magnitude better than what existing techniques allow. In particular, we derive the scaling relation between the accuracy of the model, the parameters of the weak formulation, and the properties of the data, such as its spatial and temporal resolution and the level of noise.

math.DS↗

arXiv2016

Streamwise localization of traveling wave solutions in channel flow

Channel flow of an incompressible fluid at Reynolds numbers above 2400 possesses a number of different spatially localized solutions that approach laminar flow far upstream and downstream. We use one such relative time-periodic solution, which corresponds to a spatially localized version of a Tollmien-Schlichting wave, to illustrate how the upstream and downstream asymptotics can be computed analytically. In particular, we show that for these spanwise uniform states the asymptotics predict the exponential localization that has been observed for numerically computed solutions of several canonical shear flows but never properly understood theoretically.

nlin.PS↗