A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Paper extends port-Hamiltonian model to include internal energy for compressible and incompressible flow.
Paper develops a new fluid flow model with energy exchange through boundaries.
We study the problem of inviscid slightly compressible fluids in a bounded domain. We find a unique solution to the initial-boundary value problem and show that it is near the analogous solution for an incompressible fluid provided the initial conditions for the two problems are close. In particular, the divergence of …
Computational Fluid Dynamics (CFD) is a hugely important subject with applications in almost every engineering field, however, fluid simulations are extremely computationally and memory demanding. Towards this end, we present Lat-Net, a method for compressing both the computation time and memory usage of Lattice Boltzm…
Stable long-term predictions for fluid flows using neural networks.
We present a deep generative model, named Monge-Ampère flow, which builds on continuous-time gradient flow arising from the Monge-Ampère equation in optimal transport theory. The generative map from the latent space to the data space follows a dynamical system, where a learnable potential function guides a compressible…
Analysis of Vlasov plasma dynamics using matched pair Lie-Poisson formulation.
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 computational cost associated with simulating fluid flows can make it infeasible to run many simulations across multiple flow conditions. Building upon concepts from generative modeling, we introduce a new method for learning neural network models capable of performing efficient parameterized simulations of fluid f…
Over the past few years, we developed a mathematically rigorous method to study the dynamical processes associated to nonlinear Forchheimer flows for slightly compressible fluids. We have proved the existence of a geometric transformation which relates constant mean curvature surfaces and time-invariant pressure distri…
Researchers use quantum chaos and RMT to analyze turbulence, revealing unique scaling laws.
The study identifies unique fluid flow patterns.
The paper explores the geometric properties of fluid flows and their symmetries.
In this note we survey some recent results for the Euler equations in compressible and incompressible fluid dynamics. The main point of all these theorems is the surprising fact that a suitable variant of Gromov's -principle holds in several cases.
Investigates fluid flow perturbations using geometric theory.
Researchers identify surfaces with special fluid flow fields.
Identifies most probable flows for Kunita SDEs in fluid dynamics.
FLUID uses flows to unify filtering and smoothing for complex systems.
The study identifies conjugate and cut points in ideal fluid motion configurations.
Jointly estimates flow fields and particle properties from Lagrangian data.
In this article we write the equations of barotropic compressible fluid mechanics as a geodesic equation on an infinite-dimensional manifold. The equations are given by \begin{align} u_t + \nabla_uu = -\frac{1}ρ \grad p \\ ρ_t + \diver{(ρu)} = 0, \end{align} where the fluid fills up a compact manifold , is a tim…
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…
Study Godbillon-Vey invariants in non-Lorentzian spacetimes and fluid dynamics.
We revisit the geodesic approach to ideal hydrodynamics and present a related geometric framework for Newton's equations on groups of diffeomorphisms and spaces of probability densities. The latter setting is sufficiently general to include equations of compressible and incompressible fluid dynamics, magnetohydrodynami…
Deep learning predicts fluid flow in porous media, accelerating simulations by orders of magnitude.
Existence of a conjugate point in the incompressible Euler flow on a sphere and an ellipsoid is considered. Misiolek (1996) formulated a differential-geometric criterion (we call M-criterion) for the existence of a conjugate point in a fluid flow. In this paper, it is shown that no zonal flow (stationary Euler flow) sa…
The sectional curvature of the volume preserving diffeomorphism group of a Riemannian manifold can give information about the stability of inviscid, incompressible fluid flows on . We demonstrate that the submanifold of the volumorphism group of the solid flat torus generated by axisymmetric fluid flows with swi…
Paper finds new criteria for conjugate points in fluid flows.
Paper develops physics-informed, boundary-constrained Gaussian process for fluid flow field reconstruction.
LFlows model fluid densities and velocities using invertible maps that satisfy the continuity equation.
In this work, we analyze the flow filtration process of slightly compressible fluids in porous media containing man made fractures with complex geometries. We model the coupled fracture-porous media system where the linear Darcy flow is considered in porous media and the nonlinear Forchheimer equation is used inside th…
Neural networks are increasingly used in complex (data-driven) simulations as surrogates or for accelerating the computation of classical surrogates. In many applications physical constraints, such as mass or energy conservation, must be satisfied to obtain reliable results. However, standard machine learning algorithm…
Generative models tackle incompressible fluid flows by enforcing divergence-free constraints.
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…
SPH-ParVI uses fluid dynamics to sample unknown densities efficiently.
Study reveals how to determine area and curvature from fluid flow resonances.
We consider the regularity of an interface between two incompressible and inviscid fluids flows in the presence of surface tension. We obtain local in time estimates on the interface in and the velocity fields in . These estimates are obtained using geometric considerations which show th…
IDF++ improves integer discrete flows for lossless compression.
We present a frame-invariant method for detecting coherent structures from Lagrangian flow trajectories that can be sparse in number, as is the case in many fluid mechanics applications of practical interest. The method, based on principles used in graph coloring and spectral graph drawing algorithms, examines a measur…
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…
The Skew Mean Curvature Flow(SMCF) is a Schrödinger-type geometric flow canonically defined on a co-dimension two submanifold, which generalizes the famous vortex filament equation in fluid dynamics. In this paper, we prove the local existence and uniqueness of general dimensional SMCF in Euclidean spaces.
This research smooths out fluid equations to avoid sudden shocks.
Hybrid model combines neural networks and fluid dynamics for efficient, generalized simulations.
Lossless compression methods shorten the expected representation size of data without loss of information, using a statistical model. Flow-based models are attractive in this setting because they admit exact likelihood optimization, which is equivalent to minimizing the expected number of bits per message. However, con…
Generative Adversarial Networks have been shown to be powerful in generating content. To this end, they have been studied intensively in the last few years. Nonetheless, training these networks requires solving a saddle point problem that is difficult to solve and slowly converging. Motivated from techniques in the reg…
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.
We consider the Hele-Shaw flow that arises from injection of two-dimensional fluid into a point of a curved surface. The resulting fluid domains have and are more or less determined implicitly by a mean value property for harmonic functions. We improve on the results of Hedenmalm and Shimorin \cite{HS} and obtain essen…