Deep learning compares turbulence models in plasma physics.
problem Predicting edge plasma turbulence in magnetic fusion reactors.
method Physics-informed deep learning framework for comparing two-fluid and gyrokinetic models.
result Good overall agreement between two-fluid theory and gyrokinetic models in turbulent field fluctuations.
Transfer learning improves chaotic dynamics predictions with less data.
problem Efficiently predicting chaotic dynamics with limited data.
method Transfer learning for nonlinear dynamics, optimizing transfer rate and leveraging small-scale turbulence universality.
result Significantly more accurate inference of chaotic dynamics achieved.
Researchers use quantum chaos and RMT to analyze turbulence, revealing unique scaling laws.
problem Understanding the statistical structure and scaling laws of turbulence.
method Applied tools from quantum chaos and Random Matrix Theory to analyze turbulence datasets.
result Turbulence Gram matrices exhibit power-law scalings distinct from classical chaos and random data.
Physics-informed ML models improve turbulence understanding in fusion plasmas.
problem Improving turbulence modeling in fusion plasma devices.
method Physics-informed deep learning framework constrained by PDEs.
result Direct quantitative comparisons of turbulent fields between theory and gyrokinetic models.
Physics-informed model reduces RBC simulation costs.
problem Computational infeasibility of direct numerical simulations for turbulent systems.
method Combines CNN and recurrent architecture, penalized with PDEs, uses conformal prediction.
result Significant reduction in computational cost for long-term simulations.
New neural operators model turbulence with memory and randomness.
problem Modeling turbulence in complex fluid dynamics with memory and randomness.
method Symmetrized activation functions, fractional derivatives, and stochastic noise.
result Theoretical guarantees for approximation quality in turbulent phenomena.
Physics-informed neural networks improve surrogate modeling of turbulent Rayleigh-Bénard convection.
problem Modeling turbulent Rayleigh-Bénard convection with high accuracy and efficiency.
method Physics-informed neural networks (PINNs) with novel padding and regularization techniques.
result Significantly improved predictive accuracy of surrogate models at high Rayleigh numbers Ra = 2 × 10^9.
This article is a short nontechnical survey of recent progresses in fluid dynamics and differential geometry, relating a conjecture of Lars Onsager to the work of Nash on isometric embeddings.
HFNO enhances interpretability of turbulent flows through parallel wavenumber bin processing.
problem Opaque inner workings of Fourier Neural Operators (FNOs) hinder physical interpretability.
method Introduces HFNO, a novel FNO-based architecture that processes wavenumber bins in parallel, enhancing interpretability.
result HFNO decomposes turbulent flows across various scales, enabling increased interpretability and multiscale modeling.
While deep learning has shown tremendous success in a wide range of domains, it remains a grand challenge to incorporate physical principles in a systematic manner to the design, training, and inference of such models. In this paper, we aim to predict turbulent flow by learning its highly nonlinear dynamics from spatio…
We develop an adversarial-reinforcement learning scheme for microswimmers in statistically homogeneous and isotropic turbulent fluid flows, in both two (2D) and three dimensions (3D). We show that this scheme allows microswimmers to find non-trivial paths, which enable them to reach a target on average in less time tha…
Data-driven methods for improving turbulence modeling in Reynolds-Averaged Navier-Stokes (RANS) simulations have gained significant interest in the computational fluid dynamics community. Modern machine learning algorithms have opened up a new area of black-box turbulence models allowing for the tuning of RANS simulati…
Neural networks predict flow and elastic stresses in viscoelastic turbulence.
problem Predicting flow and elastic stresses in viscoelastic turbulent flows using limited experimental data.
method Convolutional neural networks trained on wall-normal velocity and pressure data.
result Neural networks accurately predict flow and elastic stresses, especially during low-drag events.
A theory for the evolution of a metric g driven by the equations of three-dimensional continuum mechanics is developed. This metric in turn allows for the local existence of an evolving three-dimensional Riemannian manifold immersed in the six-dimensional Euclidean space. The Nash-Kuiper theorem is then applied to th…
The financial market and turbulence have been broadly compared on account of the same quantitative methods and several common stylized facts they shared. In this paper, the She-Leveque (SL) hierarchy, proposed to explain the anomalous scaling exponents deviated from Kolmogorov monofractal scaling of the velocity fluctu…
Generative models tackle incompressible fluid flows by enforcing divergence-free constraints.
problem Simulating incompressible fluid flows with generative models.
method Score-based diffusion models with divergence-free constraint.
result Models can reproduce Kolmogorov turbulence characteristics.
New probabilistic constructions for Kähler-Einstein metrics.
problem Finding Kähler-Einstein metrics on complex algebraic varieties.
method Microcanonical measures and maximum entropy principles.
result Novel characterizations and evolution equations.
The understanding of the dynamics of the velocity gradients in turbulent flows is critical to understanding various non-linear turbulent processes. The pressure-Hessian and the viscous-Laplacian govern the evolution of the velocity-gradients and are known to be non-local in nature. Over the years, several simplified dy…
New framework uses dynamics to justify Gaussian process for turbulent flows.
problem Lack of rigorous justification for Gaussian process priors in turbulent flows.
method Introduces a dynamics-informed Gaussian process framework based on quasi-Gaussianity.
result Provides a principled, long-time dynamical justified GP prior for turbulent flows.
Turbulence is still one of the main challenges for accurately predicting reactive flows. Therefore, the development of new turbulence closures which can be applied to combustion problems is essential. Data-driven modeling has become very popular in many fields over the last years as large, often extensively labeled, da…
Paper applies fluid dynamics to stock market behavior.
problem Understanding stock market dynamics using physical principles.
method Uses Stokes law to model stock market as fluid system.
result Stock market dynamics can be explained by physical properties.
Gaussian Process Hydrodynamics approximates fluid flow equations using probabilistic kernels.
problem Approximating fluid flow equations with fewer particles and uncertainty estimates.
method Lagrangian particle-based approach with Gaussian Process (GP) prior and physics-informed kernels.
result GPH requires fewer particles and provides uncertainty estimates.
Jointly estimates flow fields and particle properties from Lagrangian data.
problem Estimating flow fields and particle properties from sparse, noisy Lagrangian data.
method Data assimilation framework coupling Eulerian and Lagrangian models.
result Joint estimation of flow fields and particle properties in various flow regimes.
We describe tests validating progress made toward acceleration and automation of hydrodynamic codes in the regime of developed turbulence by three Deep Learning (DL) Neural Network (NN) schemes trained on Direct Numerical Simulations of turbulence. Even the bare DL solutions, which do not take into account any physics …
Study assesses data-driven and physics-based SGS models for transcritical combustion.
problem Challenges in simulating high-pressure combustion systems due to complex fluid behaviors.
method Comparison of physics-based and random forest machine learning models in turbulent transcritical non-premixed flames.
result Random forest models can effectively model subgrid stresses, providing insight into their formation.
Mandelbrot unified diverse fields with scaling concept.
problem Understanding Mandelbrot's intellectual approach.
method Tracing Mandelbrot's contributions across math, physics, and economics.
result Scaling concept unified Mandelbrot's diverse work.
GyroSwin models plasma turbulence with neural nets, reducing costs and capturing neglected nonlinearities.
problem Understanding plasma turbulence in fusion reactors, which impairs confinement and limits reactor design.
method Introduces GyroSwin, a scalable 5D neural surrogate that approximates 5D nonlinear gyrokinetic simulations.
result GyroSwin outperforms reduced models in heat flux prediction and captures turbulent energy cascade.
Study on complex tori foliations and flat geometries.
problem Understanding turbulent foliations on compact complex tori.
method Defined and analyzed smooth turbulent foliations on compact complex tori.
result All transversely holomorphic Cartan geometries are flat.
Neural surrogates speed up 5D gyrokinetic simulations of plasma turbulence.
problem Expensive numerical simulations of plasma turbulence hinder fusion reactor design.
method Trained a hierarchical vision transformer in 5D to predict plasma quantities faster.
result Neural surrogates predict plasma quantities two orders of magnitude faster than numerical codes.
Derives a Hamiltonian model for 3D axially symmetric magnetohydrodynamics.
problem Modeling of 3D axially symmetric magnetohydrodynamics.
method Hamiltonian formulation and matrix discretization.
result First discrete model for 3D magnetohydrodynamics compatible with underlying Lie-Poisson structure.
NN-Turb generates turbulent velocity statistics using neural networks.
problem Creating a 1D field with turbulent velocity statistics.
method Fully-convolutional neural network (NN-Turb) to generate the field.
result NN-Turb generates a 1D field that satisfies Kolmogorov's 2/3 and 4/5 laws, exhibiting intermittency.
xVAE models extreme turbulence events in turbulent flows.
problem Capturing extreme events in turbulent flows.
method Max-infinitely divisible process with heavy-tailed distributions embedded into a standard VAE framework.
result xVAE more robust in capturing extreme values compared to POD modes.
Study predicts turbulent electric fields in fusion plasmas using deep learning.
problem Predicting turbulent electric fields in fusion plasmas.
method Physics-informed deep learning, drift-reduced Braginskii theory, experimental data.
result Neutrals broaden turbulent field amplitudes and increase shearing rates.
We consider the kinematics of specific fluid spacetimes admitting timelike congruences of Ricci Solitons. These fluids includes string cloud, string fluid, perfect fluid, radially symmetric fluid, anisotropic fluid and relativistic magneto-fluid. Results are obtained and important physical aspects are discussed.
Prices in financial markets exhibit extreme jumps far more often than can be accounted for by external news. Further, magnitudes of price changes are correlated over long times. These so called stylized facts are quantified by scaling laws similar to, for example, turbulent fluids. They are believed to reflect the comp…
Neural network predicts turbulence near-wall regions efficiently.
problem Reducing computational cost in turbulent flow simulations.
method Fully-convolutional neural network trained on DNS data.
result FCN predicts velocity fluctuations at y+=50 with less than 20% error. There are three equivalent ways of representing two jointly observed real-valued signals: as a bivariate vector signal, as a single complex-valued signal, or as two analytic signals known as the rotary components. Each representation has unique advantages depending on the system of interest and the application goals. I…
Paper proves a rigidity result for static perfect fluids.
problem Proving a rigidity result for static perfect fluids.
method Robinson's divergence formula and boundary conditions.
result Rigidity result for static perfect fluids.
Three physics-constrained regression exercises for image velocimetry and turbulence modeling.
problem Image velocimetry and turbulence modeling challenges.
method Physics-constrained regression exercises implemented as toy problems.
result Python codes provided for all exercises.
Novel deep learning approach for fast, differentiable fluid simulations.
problem Challenges in solving incompressible fluid dynamics equations efficiently.
method Physics-constrained training approach for convolutional neural networks.
result Trained models can handle various fluid phenomena and offer fast simulations.
FLUID-LLM uses LLMs to predict fluid dynamics with improved accuracy.
problem Leveraging LLMs for CFD due to their pattern recognition abilities but struggles with fluid dynamics complexities.
method Combines pre-trained LLMs with spatiotemporal-aware encoding to predict unsteady fluid dynamics.
result Significant performance improvements in CFD predictions across various datasets.
No projective structure found on foliations of elliptic curves.
problem Existence of transversely projective structures on foliations.
method Analyzing foliations on the product of two elliptic curves.
result Generic nonsingular turbulent foliations do not have transversely projective structures.
New turbulence index using TDA detects financial market transitions.
problem Detecting critical transitions in financial markets.
method Persistent homology for identifying topological features.
result Persistent homology-based index captures financial data transitions.
The paper analyzes financial market turbulence using mathematical physics.
problem Understanding price fluctuations caused by information asymmetry.
method Spectrum analysis to decompose pricing patterns.
result Identifies phase correlations in financial stock market turbulence.
Convolutional networks predict turbulence from wall quantities.
problem Predicting turbulence fields from wall-shear-stress components and wall pressure.
method Two CNN models: FCN and FCN-POD, trained on DNS data.
result FCN and FCN-POD models outperform EPOD in predicting turbulence fields.
Physics-guided reinforcement learning optimizes swimming in turbulent flows.
problem Optimizing swimming efforts to maintain proximity in turbulent environments.
method Physics-informed actor-physicist reinforcement learning algorithm.
result Physics-informed reinforcement learning outperforms standard methods in turbulent flow control.
This paper examines cryptocurrency integration with traditional markets, showing how network structure and turbulence influence cross-asset spillovers.
problem Understanding how cryptocurrencies integrate with traditional financial markets and the impact of market stress on cross-asset spillovers.
method Combining rolling correlation networks, community structure, market-specific and system-wide Turbulence Indices, and VAR-based connectedness analysis.
result Cross-asset integration is episodic, with network structure and turbulence playing a role in transmission during stress periods.
The study examines perfect fluid spacetimes and their properties.
problem Characterizing properties of perfect fluid spacetimes with concircular vector fields.
method Analyzing the conformal curvature tensor, state equation, and solitons in perfect fluid spacetimes.
result Perfect fluid spacetimes with concircular vector fields have specific properties related to the state equation and solitons.