Related papers: The gradient flow in simple field theories
Two primary scalar auxiliary variable (SAV) approaches are widely applied for simulating gradient flow systems, i.e., the nonlinear energy-based approach and the Lagrange multiplier approach. The former guarantees unconditional energy…
Minute amount of long chain flexible polymer dissolved in a turbulent flow can drastically change flow properties, such as reducing the drag and enhancing mixing. One fundamental riddle is how these polymer additives interact with the…
We study enhancement of diffusive mixing on a compact Riemannian manifold by a fast incompressible flow. Our main result is a sharp description of the class of flows that make the deviation of the solution from its average arbitrarily small…
Incompressible flows can be effective mixers by appropriately advecting a passive tracer to produce small filamentation length scales. In addition, diffusion is generally perceived as beneficial to mixing due to its ability to homogenise a…
Normalizing flows can be used to construct unbiased, reduced-variance estimators for lattice field theory observables that are defined by a derivative with respect to action parameters. This work implements the approach for observables…
We study enhancement of diffusive mixing by fast incompressible time-periodic flows. The class of relaxation-enhancing flows that are especially efficient in speeding up mixing has been introduced in [2]. The relaxation-enhancing property…
It is well-known that many diffusion equations can be recast as Wasserstein gradient flows. Moreover, in recent years, by modifying the Wasserstein distance appropriately, this technique has been transferred to further evolution equations…
Liquid droplet dynamics are widely used in biological and engineering applications, which contain complex interfacial instabilities and pattern formation such as droplet merging, splitting, and transport. This paper studies a class of mean…
Finding latent structures in data is drawing increasing attention in diverse fields such as image and signal processing, fluid dynamics, and machine learning. In this work we examine the problem of finding the main modes of gradient flows.…
This work provides a comprehensive exploration of various methods in solving incompressible flows using a projection method, and their relation to the occurrence and management of checkerboard oscillations. It employs an algebraic…
Gradient-driven diffusion in crowded, multicomponent mixtures is a topic of high interest because of its role in biological processes such as transport in cell membranes. In partially phase-separated solutions, gradient-driven diffusion…
We analyze the gradient flow of a potential energy in the space of probability measures when we substitute the optimal transport geometry with a geometry based on Sinkhorn divergences, a debiased version of entropic optimal transport. This…
The Yang--Mills gradient flow has many interesting applications in lattice QCD. In this talk, some recent and possible future uses of the flow are discussed, emphasizing the underlying theoretical concepts rather than any computational…
The charging and dissolution of mineral surfaces in contact with flowing liquids are ubiquitous in nature, as most minerals in water spontaneously acquire charge and dissolve. Mineral dissolution has been studied extensively under…
In perturbative consideration of the Yang--Mills gradient flow, it is useful to introduce a gauge non-covariant term ("gauge-fixing term") to the flow equation that gives rise to a Gaussian damping factor also for gauge degrees of freedom.…
We report on salient features of a mixed lattice QCD action using valence M\"{o}bius domain-wall fermions solved on the dynamical $N_f=2+1+1$ HISQ ensembles generated by the MILC Collaboration. The approximate chiral symmetry properties of…
This paper contributes to the exploration of a recently introduced computational paradigm known as second-order flows, which are characterized by novel dissipative hyperbolic partial differential equations extending accelerated gradient…
While methods exist for aligning flow matching models--a popular and effective class of generative models--with human preferences, existing approaches fail to achieve both adaptation efficiency and probabilistically sound prior…
Existing analyses of optimization in deep learning are either continuous, focusing on (variants of) gradient flow, or discrete, directly treating (variants of) gradient descent. Gradient flow is amenable to theoretical analysis, but is…
The $L^2$ gradient flow of the Ginzburg-Landau free energy functional leads to the Allen Cahn equation that is widely used for modeling phase separation. Machine learning methods for solving the Allen-Cahn equation in its strong form suffer…