Physics-informed machine learning of the Lagrangian dynamics of velocity gradient tensor

Tian, Yifeng; Livescu, Daniel; Chertkov, Michael

doi:10.1103/physrevfluids.6.094607

Cited by 17 publications

(44 citation statements)

References 46 publications

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“…In the PIML framework, which aims to leverage the capabilities of NNs in advancing scientific applications, the mathematical and physical laws and constraints are either built into the architectures of NN or integrated into the loss functions. Various studies have shown that the PIML framework is advantageous in improving robustness, efficiency, interpretability over a physics-blind one [37,63]. In this Section, we describe how the physics constraints are included in (otherwise generic) pair-wise function f in Eq.…”

Section: Physics-informed Choice Of the Pair-wise Interactionmentioning

confidence: 99%

“…Then rotational invariance of the scalar component of the force requires that, T f s = f s . Respective constraint which needs to be imposed on the transformed vector component of f v , T f v , is that it becomes a linear combination of the rotation-aware vector bases and scalar functions of rotational invariant scalars (we follow here the so-called Tensor Basis (TB) approach of [27,63]).…”

Section: Physics-informed Choice Of the Pair-wise Interactionmentioning

confidence: 99%

“…Here in Eq. ( 3) I and b denote, respectively, the scalar invariants and vector bases of the bases expansion approach of [27,63] and are defined using pair-particle information:…”

Section: Physics-informed Choice Of the Pair-wise Interactionmentioning

confidence: 99%

“…velocity and acceleration statistics at the resolved scale. Let us now turn to a more advanced diagnostics and test the so-called Q-R plane statistics of the coarse-grained velocity gradient [7,63]. Statistics in the Q − R plane, where Q and R are second and third order invariants of the velocity gradient tensor coarse-grained at the resolved scale, d, is known to determine a variety of important characteristics of turbulence, such as the flow topology, deformation of material volume, energy cascade, and intermittency.…”

Section: Ultimate Test Of the L-lesmentioning

confidence: 99%

“…A continuous convolution network was constructed to learn SPH-inspired Lagrangian simulation in [64]. Three of us (YT,DL and MC) have reported in [63] development of a PIML approach to design a closure model for the Lagrangian (single particle) dynamics of the Velocity Gradient Tensor (VGT).…”

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confidence: 99%

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Lagrangian Large Eddy Simulations via Physics Informed Machine Learning

Tian¹,

Woodward²,

Stepanov³

et al. 2022

Preprint

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High Reynolds Homogeneous Isotropic Turbulence (HIT) is fully described within the Navier-Stocks (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at reduced but sufficiently large range of resolved scales, have designed heuristics, known under the name of Large Eddy Simulation (LES). In the usual picture, LES is described in terms of the evolving in time Eulerian velocity field defined over the points of a spatial grid with the meanspacing correspondent to the resolved scale. This classic Eulerian LES depends on assumptions about effects of sub-grid scales on the resolved scales.In this manuscript, we take an alternative approach and design novel LES heuristics stated in terms of Lagrangian particles moving with the turbulent flow. Our Lagrangian LES, thus L-LES, is described by equations that generalize the weakly compressible Smooth Particle Hydrodynamics (SPH) formulation with extended parametric and functional freedom which is then resolved/fixed via Machine Learning (ML) training on Lagrangian data from a Direct Numerical Simulation (DNS) of the NS equations. The L-LES framework includes parameters which are explainable in clear physical terms, e.g. parameters describing effects of eddy-diffusivity and smoothing kernels, and Neural Networks (NN) to represent effects of smaller (unresolved) scales and relations between

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Section: Physics-informed Choice Of the Pair-wise Interactionmentioning

confidence: 99%

Section: Physics-informed Choice Of the Pair-wise Interactionmentioning

confidence: 99%

“…Here in Eq. ( 3) I and b denote, respectively, the scalar invariants and vector bases of the bases expansion approach of [27,63] and are defined using pair-particle information:…”

Section: Physics-informed Choice Of the Pair-wise Interactionmentioning

confidence: 99%

Section: Ultimate Test Of the L-lesmentioning

confidence: 99%

mentioning

confidence: 99%

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Lagrangian Large Eddy Simulations via Physics Informed Machine Learning

Tian¹,

Woodward²,

Stepanov³

et al. 2022

Preprint

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Physics‐Informed Machine Learning for Inverse Design of Optical Metamaterials

Sarkar,

Ji,

Jermain

et al. 2023

Advanced Photonics Research

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Optical metamaterials manipulate light through various confinement and scattering processes, offering unique advantages like high performance, small form factor and easy integration with semiconductor devices. However, designing metasurfaces with suitable optical responses for complex metamaterial systems remains challenging due to the exponentially growing computation cost and the ill‐posed nature of inverse problems. To expedite the computation for the inverse design of metasurfaces, a physics‐informed deep learning (DL) framework is used. A tandem DL architecture with physics‐based learning is used to select designs that are scientifically consistent, have low error in design prediction, and accurate reconstruction of optical responses. The authors focus on the inverse design of a representative plasmonic device and consider the prediction of design for the optical response of a single wavelength incident or a spectrum of wavelength in the visible light range. The physics‐based constraint is derived from solving the electromagnetic wave equations for a simplified homogenized model. The model converges with an accuracy up to 97% for inverse design prediction with the optical response for the visible light spectrum as input, and up to 96% for optical response of single wavelength of light as input, with optical response reconstruction accuracy of 99%.

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