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.
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 shows instability of naked singularities in perfect fluid models.
problem Instability of naked singularities in Einstein equations coupled with isothermal perfect fluid.
method Investigated spherically symmetric self-similar naked singularities under C1,α perturbations of an external massless scalar field. result Spherically symmetric self-similar naked singularities are unstable to trapped surface formation.
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.
We prove short-time existence for the Einstein-Euler-Entropy system for non-isentropic fluids with data in uniformly local Sobolev spaces. The cases of compact as well as non-compact Cauchy surfaces are covered. The method employed uses a Lagrangian description of the fluid flow which is based on techniques developed b…
The paper studies steady motions of fibre-reinforced fluids on curved surfaces.
problem Analyzing steady motions of fibre-reinforced fluids on curved surfaces.
method Expressing kinematic equations in terms of the intrinsic Gauss equation and identifying integrable cases.
result Derives a variant of the integrable Tzitzéica equation encoding orthogonal coordinate systems on pseudospherical surfaces.
Paper shows geometric frequency and Lagrange derivative equivalence for electric and fluid systems.
problem Understanding and classifying system operating conditions based on electric quantity waveform distortions.
method Demonstrates equivalence between geometric frequency and Lagrange derivative through numerical examples.
result Identifies components of Lagrange derivative that relate to geometric frequency and waveform distortions.
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…
Paper extends port-Hamiltonian model to include internal energy for compressible and incompressible flow.
problem Modeling fluid flow dynamics with internal energy and constraints.
method Derived port-Hamiltonian model using interconnection maps and added internal energy and constraint forces.
result Model accurately represents both compressible and incompressible fluid flow.
Recent developments in machine-learning algorithms have led to impressive performance increases in many traditional application scenarios of artificial intelligence research. In the area of deep reinforcement learning, deep learning functional architectures are combined with incremental learning schemes for sequential …
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.
FLUID uses flows to unify filtering and smoothing for complex systems.
problem Bayesian filtering and smoothing for high-dimensional nonlinear systems.
method FLUID encodes observation histories into a fixed summary statistic, using flows for filtering and smoothing.
result FLUID provides accurate approximations of filtering and smoothing distributions.
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.
SPH-ParVI uses fluid dynamics to sample unknown densities efficiently.
problem Sampling partially known densities or using gradients in probabilistic models.
method Smoothed Particle Hydrodynamics (SPH) for modeling fluid dynamics to approximate target densities.
result SPH-ParVI provides fast, flexible, scalable, and deterministic sampling for Bayesian inference and generative models.
We infer both microscopic and macroscopic behaviors of a three-dimensional chaotic fluid flow using reservoir computing. In our procedure of the inference, we assume no prior knowledge of a physical process of a fluid flow except that its behavior is complex but deterministic. We present two ways of inference of the co…
Geometric framework for Newton's equations on diffeomorphism groups.
problem Modeling fluid dynamics and related systems on geometric spaces.
method Geodesic approach and infinite-dimensional information geometry.
result Unified framework for various fluid dynamics equations.
In this paper an approach is proposed to represent a class of dissipative mechanical systems by corresponding infinite-dimensional Hamiltonian systems. This approach is based upon the following structure: for any non-conservative classical mechanical system and arbitrary initial conditions, there exists a conservative …
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.
The control of complex systems is of critical importance in many branches of science, engineering, and industry. Controlling an unsteady fluid flow is particularly important, as flow control is a key enabler for technologies in energy (e.g., wind, tidal, and combustion), transportation (e.g., planes, trains, and automo…
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.
The paper corrects bias in fluid approximation for better decision-making in stochastic optimization.
problem Bias introduced by using mean values in fluid approximation leads to suboptimal decisions.
method Identifying a decision-corrected point estimate that yields optimal decisions.
result A corrected point estimate exists under certain conditions and can be computed algorithmically.
Survey on computational models in dynamical systems, including new universality concepts.
problem Understanding the relationship between computational models and dynamical systems.
method Review of recent works on Turing universality, Topological Kleene Field Theories, and dynamical bordisms.
result Introduction of new perspectives on computability through dynamical systems.
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.
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.
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.
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.
Derives a fluid model for fish swarming in arbitrary dimensions.
problem Modeling fish swarming behavior in various dimensions.
method Develops a novel n-dimensional model using bundle geometry and variational formulation. result Derives the self-organized hydrodynamic model from the interacting particle system.
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.
We present a geometric analysis of the incompressible averaged Euler equations for an ideal inviscid fluid. We show that solutions of these equations are geodesics on the volume-preserving diffeomorphism group of a new weak right invariant pseudo metric. We prove that for precompact open subsets of Rn, thi…
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.
On curved spaces, viscous fluids reach equilibrium quickly.
problem Thermalization of viscous fluids on negatively curved manifolds.
method Stochastic Navier-Stokes equations with kinematically selected deformation Laplacian.
result Exponential thermalization rate of $2νλ_\Def$.
Fluid approximations have seen great success in approximating the macro-scale behaviour of Markov systems with a large number of discrete states. However, these methods rely on the continuous-time Markov chain (CTMC) having a particular population structure which suggests a natural continuous state-space endowed with a…
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.
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 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.
Paper presents a new approach to continuum mechanics using port-Hamiltonian framework.
problem Geometric formulation of solid and fluid mechanics.
method Port-Hamiltonian framework, Dirac structures, Hamiltonian reduction theory.
result Systematic derivation of port-Hamiltonian models for solid and fluid mechanics.
This paper presents a novel generative model to synthesize fluid simulations from a set of reduced parameters. A convolutional neural network is trained on a collection of discrete, parameterizable fluid simulation velocity fields. Due to the capability of deep learning architectures to learn representative features of…
The paper optimizes LLM inference systems through queueing theory.
problem Efficient LLM inference for AI agents under various routing topologies.
method Developed a fluid-limit framework for multi-class batched processing networks under K-FCFS scheduling.
result Proved that work-conserving scheduling algorithms maximize throughput for LLM inference.
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.
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.
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.
A new method uses neural networks to improve POD-Galerkin models for complex systems.
problem Improving computational efficiency and accuracy in solving non-linear high-dimensional systems.
method Deep learning-based closure modeling using neural networks to approximate POD-Galerkin operators.
result The CD-ROM approach produces more accurate and stable models for complex 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.
The field of fluid mechanics is rapidly advancing, driven by unprecedented volumes of data from field measurements, experiments and large-scale simulations at multiple spatiotemporal scales. Machine learning offers a wealth of techniques to extract information from data that could be translated into knowledge about the…