arXiv research

Smartfluidnet accelerates Eulerian fluid simulation with neural networks.

Identifies most probable flows for Kunita SDEs in fluid dynamics.

The Immersed Boundary (IB) method is a widely-used numerical methodology for the simulation of fluid-structure interaction problems. The IB method utilizes an Eulerian discretization for the fluid equations of motion while maintaining a Lagrangian representation of structural objects. Operators are defined for transmit…

Study on stability in discretized hydrodynamics model.

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…

This paper provides a precise sense in which the time t map for the Euler equations of an ideal fluid in a region in R^n (or a smooth compact n-manifold with boundary) is a Poisson map relative to the Lie-Poisson bracket associated with the group of volume preserving diffeomorphism group. This is interesting and nontri…

This work presents a partitioned solution procedure to compute shape gradients in fluid-structure interaction (FSI) using black-box adjoint solvers. Special attention is paid to project the gradients onto the undeformed configuration. This is due to the mixed Lagrangian-Eulerian formulation of large-displacement FSI in…

Novel deep learning approach for fast, differentiable fluid simulations.

New method uses dynamic sampling to improve PINNs efficiency.

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…

Spatial graphs of non-Eulerian or proper Eulerian planar graphs are unknottable by region crossing changes.

Hybrid model combines neural networks and fluid dynamics for efficient, generalized simulations.

New $3$-manifolds created from $4$-regular graphs with unique Eulerian cycles.

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…

FLUID-LLM uses LLMs to predict fluid dynamics with improved accuracy.

SPH-ParVI uses fluid dynamics to sample unknown densities efficiently.

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…

Investigates fluid flow perturbations using geometric theory.

Convolutional neural networks were recently employed to fully reconstruct fluid simulation data from a set of reduced parameters. However, since (de-)convolutions traditionally trained with supervised L1-loss functions do not discriminate between low and high frequencies in the data, the error is not minimized efficien…

Deep learning predicts fluid flow in porous media, accelerating simulations by orders of magnitude.

A graph (digraph) $G=(V,E)$ with a set $T\subseteq V$ of terminals is called inner Eulerian if each nonterminal node $v$ has even degree (resp. the numbers of edges entering and leaving $v$ are equal). Cherkassky and Lovász showed that the maximum number of pairwise edge-disjoint $T$-paths in an inner Eulerian graph $G…

A new method solves high-dimensional MFGs using particle-based flow matching.

RotEqNet preserves rotation symmetry in fluid systems using high-order tensors.

We proposed a novel graph convolutional neural network that could construct a coarse, sparse latent point cloud from a dense, raw point cloud. With a novel non-isotropic convolution operation defined on irregular geometries, the model then can reconstruct the original point cloud from this latent cloud with fine detail…

We consider generalized linear transient convection-diffusion problems for differential forms on bounded domains in $\mathbb{R}^{n}$. These involve Lie derivatives with respect to a prescribed smooth vector field. We construct both new Eulerian and semi-Lagrangian approaches to the discretization of the Lie derivatives…

New method preserves topology in Hodge decomposition for scalar and vector fields.

In this paper we give a new proof of the (strong) displacement convexity of a class of integral functionals defined on a compact Riemannian manifold satisfying a lower Ricci curvature bound. Our approach does not rely on existence and regularity results for optimal transport maps on Riemannian manifolds, but it is base…

We prove a number of new restrictions on the enumerative properties of homology manifolds and semi-Eulerian complexes and posets. These include a determination of the affine span of the fine $h$-vector of balanced semi-Eulerian complexes and the toric $h$-vector of semi-Eulerian posets. The lower bounds on simplicial h…

Jointly estimates flow fields and particle properties from Lagrangian data.

Deep learning compares turbulence models in plasma physics.

Paper develops physics-informed, boundary-constrained Gaussian process for fluid flow field reconstruction.

The action principle by Low [Proc. R. Soc. Lond. A 248, 282--287] for the classic Vlasov-Maxwell system contains a mix of Eulerian and Lagrangian variables. This renders the Noether analysis of reparametrization symmetries inconvenient, especially since the well-known energy- and momentum-conservation laws for the syst…

Physics-informed model reduces RBC simulation costs.

Many models in mathematical physics are given as non-linear partial differential equation of hydrodynamic type; the incompressible Euler, KdV, and Camassa--Holm equations are well-studied examples.A beautiful approach to well-posedness is to go from the Eulerian to a Lagrangian description.Geometrically it corresponds …

Incorporating computational fluid dynamics in the design process of jets, spacecraft, or gas turbine engines is often challenged by the required computational resources and simulation time, which depend on the chosen physics-based computational models and grid resolutions. An ongoing problem in the field is how to simu…

Real-life control tasks involve matters of various substances---rigid or soft bodies, liquid, gas---each with distinct physical behaviors. This poses challenges to traditional rigid-body physics engines. Particle-based simulators have been developed to model the dynamics of these complex scenes; however, relying on app…

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 study constructs links from polytope subgraphs and proves their hyperbolic properties.

This paper speeds up simulations of hypersonic reentry by combining traditional and neural methods.

Theory of point vortices extended to closed surfaces.

Paper applies fluid dynamics to stock market behavior.

Physics-based simulations are often used to model and understand complex physical systems and processes in domains like fluid dynamics. Such simulations, although used frequently, have many limitations which could arise either due to the inability to accurately model a physical process owing to incomplete knowledge abo…

Rolling Diffusion improves video prediction by progressively corrupting frames based on their temporal position.

New algorithms improve vascular flow simulations in aortic aneurysms.

Mean field games (MFG) and mean field control (MFC) are critical classes of multi-agent models for efficient analysis of massive populations of interacting agents. Their areas of application span topics in economics, finance, game theory, industrial engineering, crowd motion, and more. In this paper, we provide a flexi…

The paper models CBF dynamics using queueing theory and insurance risk models.

Simulates financial market orders using anomalous diffusion models.