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.
New method for fluid approximation of CTMCs without population structure.
problem Approximating the macro-scale behavior of large CTMCs.
method Spectral analysis of CTMC transition matrix, diffusion maps, Gaussian process regression.
result Construct an ODE approximating CTMC mean in continuous space.
Machine learning enhances fluid mechanics by analyzing complex data.
problem Analyzing large volumes of fluid mechanics data.
method Machine learning techniques to extract information from data.
result Machine learning enriches and transforms fluid mechanics research.
Paper develops physics-informed, boundary-constrained Gaussian process for fluid flow field reconstruction.
problem Reconstructing fluid flow fields from limited data.
method Physics-informed, boundary-constrained Gaussian process regression.
result Derives physics-informed kernels for simulating incompressible flows.
Rolling Diffusion improves video prediction by progressively corrupting frames based on their temporal position.
problem Improving video prediction accuracy by accounting for temporal dynamics.
method A sliding window denoising process that assigns more noise to frames that appear later in a sequence.
result Rolling Diffusion outperforms standard diffusion models in tasks with complex temporal dynamics.
Machine learning optimizes polymer fiber synthesis.
problem Complex material synthesis requires impractical experimentation.
method Bayesian optimisation using machine learning.
result Efficiently directs synthesis to achieve material and process objectives.
We introduce a novel description of the dynamics of the order book of financial markets as that of an effective colloidal Brownian particle embedded in fluid particles. The analysis of a comprehensive market data enables us to identify all motions of the fluid particles. Correlations between the motions of the Brownian…
In this paper, we establish a fluid limit for a two--sided Markov order book model. Our main result states that in a certain asymptotic regime, a pair of measure-valued processes representing the "sell-side shape" and "buy-side shape" of an order book converges to a pair of deterministic measure-valued processes in a c…
Hybrid model combines neural networks and fluid dynamics for efficient, generalized simulations.
problem Inefficient and poor generalization of deep learning approximations of fluid dynamics.
method Combines graph neural networks with a differentiable PDE solver inside a neural network.
result Hybrid model generalizes well to new scenarios and outperforms both neural network and traditional methods.
Study kinematics of Ricci Solitons in various fluid spacetimes.
problem Understanding the motion of Ricci Solitons in different fluid spacetimes.
method Examined specific fluid spacetimes including string cloud, string fluid, etc., and analyzed kinematics.
result Obtained results and discussed physical aspects of these spacetimes.
Identifies most probable flows for Kunita SDEs in fluid dynamics.
problem Modeling stochastic processes with Eulerian noise and deterministic drifts.
method Equipping the domain with a Riemannian metric from the noise, solving the resulting PDEs.
result Most probable flows differ from deterministic flows, especially under noise.
Machine learning infers fluid dynamics from data without prior knowledge.
problem Inferring complex fluid behavior from limited data.
method Reservoir computing for partial and full inference of fluid variables and energy functions.
result Reservoir systems can infer long-term fluid dynamics and energy spectra from past data.
Order positions are key variables in algorithmic trading. This paper studies the limiting behavior of order positions and related queues in a limit order book. In addition to the fluid and diffusion limits for the processes, fluctuations of order positions and related queues around their fluid limits are analyzed. As a…
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.
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.
The paper models CBF dynamics using queueing theory and insurance risk models.
problem Understanding and optimizing the operation of community bail funds.
method Combining queueing theory with classic insurance risk models.
result A fluid limit for the blocking model of CBF operations.
Paper finds exact solutions for static fluids with symmetries.
problem Finding exact solutions for static fluids with symmetries.
method Utilized symmetries to solve Einstein's equation for a perfect fluid on a static manifold.
result Exact solutions found for static fluids with symmetries.
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.
The paper finds conditions for pseudosymmetric spacetimes to be perfect fluids.
problem Characterizing pseudosymmetric spacetimes as perfect fluids.
method Analyzes generalized Robertson-Walker spacetimes, conformally flat spacetimes, and dust fluids.
result Conditions for pseudosymmetric spacetimes to be perfect fluids are established.
Study fluid spacetimes, proving shear-free implies vanishing expansion or vorticity.
problem Understanding shear and vorticity in perfect-fluid spacetimes.
method Analyzing perfect-fluid spacetimes using Weyl tensor and divergence.
result Proves shear-free implies vanishing expansion or vorticity for perfect fluids.
Generative model creates fluid simulations from parameters.
problem Creating fast and accurate fluid simulations from parameters.
method Convolutional neural network trained on parameterized fluid data with a novel loss function.
result Generative model accurately approximates fluid simulations and handles complex parameterizations.
New method efficiently simulates fluid flows across various conditions.
problem High computational cost in simulating fluid flows.
method Parameter-conditioned sequential generative modeling of neural networks.
result Trained models simulate fluid flows at orders of magnitude faster than traditional methods.
The study examines properties of perfect fluid spacetimes in Einstein's theory.
problem Analyzing curvature properties of perfect fluid spacetimes.
method Assuming perfect fluid as the source, the paper investigates solutions to Einstein's field equations.
result Properties of perfect fluid spacetimes are explored in the context of Einstein's theory.
The paper studies Ricci solitons in perfect fluid spacetimes with specific vector fields.
problem Analyzing Ricci solitons in perfect fluid spacetimes with torse-forming vector fields.
method Examined perfect fluid spacetimes with torse-forming vector fields ξ, determined Ricci solitons, and classified their behavior as expanding, steady, or shrinking.
result Conditions for the behavior of Ricci solitons in these spacetimes were identified.
Study proves fluid limits of fragmented limit-order markets.
problem Modeling fragmented limit-order markets with small and frequent orders.
method Proved convergence of discrete system to fluid limit characterized by coupled nonlinear ODEs.
result Fluid system converges to stationary equilibrium state over time.
The study identifies unique fluid flow patterns.
problem Understanding incompressible fluid flows with straight streamlines.
method Local differential geometry of line congruences to integrate Euler equations.
result Only specific fluid flows are possible with straight streamlines.
PhyDNN uses physics knowledge to improve drag force prediction models.
problem Complex physical processes in fluid dynamics are hard to model accurately.
method Physics-guided structural priors and aggregate supervision for deep learning.
result PhyDNN achieves a significant 8.46% improvement in drag force prediction.
New conditions for GRW space-times to be perfect-fluid space-times.
problem Conditions for GRW space-times to be perfect-fluid.
method Gray's decomposition of the gradient of the Ricci tensor, determining Ricci tensor forms in invariant subspaces.
result For most GRW space-times, the Ricci tensor is Einstein or perfect fluid.
Proposes a new binary classification model inspired by fluid phase separation.
problem Binary classification challenges.
method Discretization of nonlinear reaction-diffusion equation coupled with ODE, inspired by fluid dynamics.
result PSBC model achieves comparable performance to traditional methods on MNIST.
Study on static perfect fluid space-time geometry and boundary estimates.
problem Investigate the geometry and boundary properties of static perfect fluid space-time.
method Used generalized Reilly's formula to establish geometric inequalities and boundary estimates.
result Obtained new boundary estimates involving the Brown-York mass and first eigenvalue of the Jacobi operator.
Certain solutions of a sextic sigma-model Lagrangian reminiscent of Skyrme model correspond to perfect fluids with stiff matter equation of state. We analyse from a differential geometric perspective this correspondence extended to general barotropic fluids.
Paper develops a new fluid flow model with energy exchange through boundaries.
problem Modeling ideal fluid flow with energy exchange through boundaries.
method Port-Hamiltonian model based on Stokes-Dirac structures.
result Wide range of fluid dynamical systems can be achieved with this model.
Using a simple and well-motivated modification of the stress-energy tensor for a viscous fluid proposed by Lichnerowicz, we prove that Einstein's equations coupled to a relativistic version of the Navier-Stokes equations are well-posed in a suitable Gevrey class if the fluid is incompressible and irrotational. These la…
Survey on matrix hydrodynamics, a 2D fluid model.
problem Modeling 2D incompressible fluids.
method Spatial discretization via quantization theory.
result Basic demonstration of matrix hydrodynamics.
RotEqNet preserves rotation symmetry in fluid systems using high-order tensors.
problem Lack of rotational symmetry in machine learning models for fluid systems.
method Introduces RotEqNet, a network that guarantees rotation-equivariance for high-order tensors.
result RotEqNet reduces errors and maintains rotation-equivariance in fluid systems.
Study of k-almost Yamabe solitons in perfect fluid spacetimes.
problem Analyzing k-almost Yamabe solitons in perfect fluid spacetimes. method Examined perfect fluid spacetimes and k-almost Yamabe solitons using Einstein field equations. result Characterized properties of k-almost Yamabe solitons in perfect fluid spacetimes. Smartfluidnet accelerates Eulerian fluid simulation with neural networks.
problem Current neural network methods for Eulerian fluid simulation lack flexibility and generalization.
method Smartfluidnet automates model generation and dynamic switching to meet user requirements.
result Smartfluidnet achieves 1.46x and 590x speedup compared to state-of-the-art models, with better simulation quality.
This paper resolves the stiff fluid case for orthogonal Bianchi B fluids near the singularity.
problem The asymptotic behavior of orthogonal Bianchi class B stiff fluids near the initial singularity.
method Expansion-normalised variables and convergence analysis of the Jacobs set.
result All solutions converge to a specific subset of the Jacobs set, differing from non-stiff cases.
Survey links fluid dynamics conjecture to geometry.
problem Understanding turbulence and its relation to geometry.
method Relates Lars Onsager's conjecture to Nash's isometric embeddings.
result Recent progress in fluid dynamics and differential geometry.
Geometric Hydrodynamics tackles open problems in fluid dynamics.
problem Open problems in fluid dynamics and invariant metrics.
method Variational settings, models for invariant metrics, Cauchy and boundary value problems.
result New constructions and recent developments in fluid dynamics.
Paper presents a brain tumor segmentation method using NGMM and 3D FVF.
problem Automatic brain tumor segmentation from MRIs is challenging.
method Normalized Gaussian Bayesian classifier and 3D Fluid Vector Flow algorithm.
result The method successfully segments brain tumors from MRI images.
Proves well-posedness for hard phase model in general relativity.
problem Modeling fluid dynamics in curved spacetime.
method A priori estimates and well-posedness in Sobolev spaces, coupled interior-boundary system of wave equations.
result Proves existence and uniqueness of solutions in Sobolev spaces.
Incompressible fluid dynamics on special manifolds.
problem Fluid dynamics on specific geometric manifolds.
method Analyzes G-invariant vector fields on compact manifolds. result Shows existence of smooth solutions to Euler equations.
Faster neural network predictions for aerodynamics simulations.
problem Challenges in simulating complex systems like jets and spacecraft due to computational resources and time.
method A novel model-free approach using a cluster network architecture to reformulate and expand pre-computed datasets.
result Nearly as accurate as state-of-the-art model-based approximations, an order of magnitude faster, and easier to apply.
Investigates fluid flow perturbations using geometric theory.
problem Analyzing linear perturbations in non-equilibrium fluid flows.
method Uses second order variations of the action and Jacobi fields.
result Demonstrates numerical simulations of perturbation dynamics.
The paper explores the geometric properties of fluid flows and their symmetries.
problem Understanding the geometric properties of fluid flows and their symmetries.
method Analyzing the Euler equation and its relation to geodesic flows on groupoids of multiphase diffeomorphisms.
result Generalized flows, multiphase fluids, and vortex sheets are all geodesics on certain groupoids of multiphase diffeomorphisms.
The paper studies geometric structures in perfect fluid spacetimes with specific metrics.
problem Analyzing the geometric properties of perfect fluid spacetimes with specific metrics.
method Investigates conditions for conformal Ricci-Yamabe soliton and derives Laplace equations.
result Conditions for expanding, steady, or shrinking conformal Ricci-Yamabe solitons are identified.
There is a remarkable and canonical problem in 3D geometry and topology: To understand existing models of 3D fluid motion or to create new ones that may be useful. We discuss from an algebraic viewpoint the PDE called Euler's equation for incompressible frictionless fluid motion. In part I we define a "finite dimension…