arXiv research

Smooth orbit equivalence proves metric equivalence for geodesic flows.

Guillarmou extends X-ray transform to magnetic and thermostat flows.

In this paper, we will recover Hamilton's Harnack inequality for the Ricci flow from the view point of Hyperbolic thermostat.

Alternative construction of quasi-Fuchsian flows using vortex equations.

Researchers study injectivity of magnetic and thermostatic nonabelian ray transforms on compact surfaces.

We introduce a new family of thermostat flows on the unit tangent bundle of an oriented Riemannian $2$-manifold. Suitably reparametrised, these flows include the geodesic flow of metrics of negative Gauss curvature and the geodesic flow induced by the Hilbert metric on the quotient surface of divisible convex sets. We …

The study shows conditions for thermostats to have no conjugate points.

The paper studies ray transforms on surfaces with negative curvature, proving injectivity and determining connections and Higgs fields.

In this paper we consider the Gaussian thermostat ray transform on both closed Riemannian surfaces and compact Riemannian surfaces with boundary. We establish certain results on the injectivity of the thermostat ray transform and the surjectivity of its adjoint.

We show a Hopf type rigidity for thermostats without conjugate points on a 2-torus

Improved stability for large-scale Bayesian sampling.

Study resonant forms for dissipative Anosov flows on 3-manifolds.

RL applied to TCLs for power consumption control.

Study proves uniqueness for ray transform on surfaces with obstacles.

Learning in deep models using Bayesian methods has generated significant attention recently. This is largely because of the feasibility of modern Bayesian methods to yield scalable learning and inference, while maintaining a measure of uncertainty in the model parameters. Stochastic gradient MCMC algorithms (SG-MCMC) a…

We propose a new sampling method, the thermostat-assisted continuously-tempered Hamiltonian Monte Carlo, for Bayesian learning on large datasets and multimodal distributions. It simulates the Nosé-Hoover dynamics of a continuously-tempered Hamiltonian system built on the distribution of interest. A significant advantag…

Monte Carlo sampling for Bayesian posterior inference is a common approach used in machine learning. The Markov Chain Monte Carlo procedures that are used are often discrete-time analogues of associated stochastic differential equations (SDEs). These SDEs are guaranteed to leave invariant the required posterior distrib…

We consider a general family of curves $Γ$ on a compact oriented Finsler surface $(M,F)$ with boundary $\partial M$. Let $\varphi\in C^{\infty}(M)$ and $ω$ a smooth 1-form on $M$. We show that $\int_{γ(t)}\{\varphi(γ(t))+ω_{γ(t)}(\dotγ(t))\}\,dt=0$ holds for every $γ\inΓ$ whose endpoints belong to $\partial M$, $γ(a)…

Recent studies have shown that the aggregated dynamic flexibility of an ensemble of thermostatic loads can be modeled in the form of a virtual battery. The existing methods for computing the virtual battery parameters require the knowledge of the first-principle models and parameter values of the loads in the ensemble.…

We use online convex optimization (OCO) for setpoint tracking with uncertain, flexible loads. We consider full feedback from the loads, bandit feedback, and two intermediate types of feedback: partial bandit where a subset of the loads are individually observed and the rest are observed in aggregate, and Bernoulli feed…

Bayesian max-margin models have shown superiority in various practical applications, such as text categorization, collaborative prediction, social network link prediction and crowdsourcing, and they conjoin the flexibility of Bayesian modeling and predictive strengths of max-margin learning. However, Monte Carlo sampli…

Hamiltonian Monte Carlo (HMC) is an efficient Bayesian sampling method that can make distant proposals in the parameter space by simulating a Hamiltonian dynamical system. Despite its popularity in machine learning and data science, HMC is inefficient to sample from spiky and multimodal distributions. Motivated by the …

A new hierarchy quantifies agency in systems based on information processing.

Recent advances in Bayesian learning with large-scale data have witnessed emergence of stochastic gradient MCMC algorithms (SG-MCMC), such as stochastic gradient Langevin dynamics (SGLD), stochastic gradient Hamiltonian MCMC (SGHMC), and the stochastic gradient thermostat. While finite-time convergence properties of th…

Proposes a method to handle missing inputs in Bayesian optimization.

New flows introduced for symplectic geometry.

The paper examines Ricci flows with closed and smooth tangent flows, proving uniqueness and characterizing ancient flows.

Proves uniqueness of geometric flow in various Riemannian manifolds.

Study of twisted Calabi flow connecting J-flow and Calabi flow on Kähler manifolds.

Investigate scalar curvature under geometric flows

Streets and Tian introduced pluriclosed flow and symplectic curvature flow in recent years. Here we construct a curvature flow to unify these two flows. We show the short time existence of our flow and exhibit an obstruction to long time existence.

We consider four extended Ricci flow systems---that is, Ricci flow coupled with other geometric flows---and prove dynamical stability of certain classes of stationary solutions of these flows. The systems include Ricci flow coupled with harmonic map flow (studied abstractly and in the context of Ricci flow on warped pr…

The article calculates the $\mathbb{F}$-convergence rate for Ricci flows with closed and smooth tangent flows.

Paper introduces Tensor Gauge Flow Models for better data encoding.

Study K-R flow on Hirzebruch surfaces, showing tangent flows are K-R flows with orbifold singularities.

Ancient curve shortening flows have entropy and curvature bounds equivalent.

The study disproves rotating ancient flows in 4D space.

Simplifies residual flows to make flow-based modeling more practical.

Existence of translating solutions shown for curve diffusion flow.

Modeling bone microarchitecture adaptation using geometric flows.

Variational inference relies on flexible approximate posterior distributions. Normalizing flows provide a general recipe to construct flexible variational posteriors. We introduce Sylvester normalizing flows, which can be seen as a generalization of planar flows. Sylvester normalizing flows remove the well-known single…

The Hodge star mean curvature flow on a 3-dimension Riemannian or pseudo-Riemannian manifold, the geometric Airy flow on a Riemannian manifold, the Schrodingier flow on Hermitian manifolds, and the shape operator curve flow on submanifolds are natural non-linear dispersive curve flows in geometric analysis. A curve flo…

In many fields of science, high-dimensional integration is required. Numerical methods have been developed to evaluate these complex integrals. We introduce the code i-flow, a python package that performs high-dimensional numerical integration utilizing normalizing flows. Normalizing flows are machine-learned, bijectiv…

The study examines mass drop and multiplicity in mean curvature flow.

We explore the harmonic-Ricci flow---that is, Ricci flow coupled with harmonic map flow---both as it arises naturally in certain principal bundle constructions related to Ricci flow and as a geometric flow in its own right. We demonstrate that one natural geometric context for the flow is a special case of the locally …

Using the conformally invariant Cotton tensor, we define a geometric flow, the "Cotton flow", which is exclusive to three dimensions. This flow tends to evolve the initial metrics into conformally flat ones, and is somewhat orthogonal to the Yamabe flow, the latter being a flow within a conformal class. We define an en…

The paper studies mean curvature flow in a Ricci flow background with extended Ricci flow.

Mean curvature flow is not a gradient flow on two nondegenerate metric spaces.