Related papers: Lagrangian basis method for dimensionality reducti…
This paper introduces a novel Lagrangian fluid solver based on covector flow maps. We aim to address the challenges of establishing a robust flow-map solver for incompressible fluids under complex boundary conditions. Our key idea is to use…
Lagrangian-based methods are classical methods for solving convex optimization problems with equality constraints. We present novel prediction-correction frameworks for such methods and their variants, which can achieve $O(1/k)$ non-ergodic…
A Lagrangian numerical scheme for solving nonlinear degenerate Fokker-Planck equations in space dimensions $d\ge2$ is presented. It applies to a large class of nonlinear diffusion equations, whose dynamics are driven by internal energies…
Reconstructing 3D fluid velocity fields from sparse 2D video observations is a highly ill-posed inverse problem, demanding both transport consistency with observed motion and physical validity under fluid laws. Existing methods typically…
Advective transport of scalar quantities through surfaces is of fundamental importance in many scientific applications. From the Eulerian perspective of the surface it can be quantified by the well-known integral of the flux density. The…
Non-convex functional constrained optimization problems have gained substantial attention in machine learning and data science, addressing broad requirements that typically go beyond the often performance-centric objectives. An influential…
This work proposes a model-reduction methodology that preserves Lagrangian structure (equivalently Hamiltonian structure) and achieves computational efficiency in the presence of high-order nonlinearities and arbitrary parameter dependence.…
Numerical simulations are a valuable research and layout tool for fluid flow problems, yet repeated evaluations of parametrized problems, necessary to solve optimization problems, can be very costly. One option to speed up this process is…
Optimization problems with convex quadratic cost and polyhedral constraints are ubiquitous in signal processing, automatic control and decision-making. We consider here an enlarged problem class that allows to encode logical conditions and…
For a class of nonsmooth composite optimization problems with linear equality constraints, we utilize a Lyapunov-based approach to establish the global exponential stability of the primal-dual gradient flow dynamics based on the proximal…
A new simple Lagrangian method with favorable stability and efficiency properties for computing general plane curve evolutions is presented. The method is based on the flowing finite volume discretization of the intrinsic partial…
Transport and mixing of scalar quantities in fluid flows is ubiquitous in industry and Nature. Turbulent flows promote efficient transport and mixing by their inherent randomness. Laminar flows lack such a natural mixing mechanism and…
The optimal control of a globally unstable two-dimensional separated boundary layer over a bump is considered using augmented Lagrangian optimization procedures. The present strategy allows of controlling the flow from a fully developed…
A closure theory is developed for inhomogeneous turbulent flow, which enables a systematic derivation of the turbulence constitutive relations without relying on any empirical parameters. Renormalized-perturbation approximation is performed…
This paper addresses a class of general nonsmooth and nonconvex composite optimization problems subject to nonlinear equality constraints. We assume that a part of the objective function and the functional constraints exhibit local…
We introduce Lagrangian Flow Networks (LFlows) for modeling fluid densities and velocities continuously in space and time. By construction, the proposed LFlows satisfy the continuity equation, a PDE describing mass conservation in its…
In this paper, a projected primal-dual gradient flow of augmented Lagrangian is presented to solve convex optimization problems that are not necessarily strictly convex. The optimization variables are restricted by a convex set with…
The aim of this paper is to prove that a three dimensional Lagrangian flow which defines equatorially trapped water waves is dynamically possible. This is achieved by applying a mixture of analytical and topological methods to prove that…
As most mathematically justifiable Lagrangian coherent structure detection methods rely on spatial derivatives, their applicability to sparse trajectory data has been limited. For experimental fluid dynamicists and natural scientists…
In this paper, we consider a nonconvex optimization problem with nonlinear equality constraints. We assume that both, the objective function and the functional constraints are locally smooth. For solving this problem, we propose a…