arXiv research

Efficiently predicts long-time dynamics of quantum spin models using MLP regression.

A new ML method predicts long-time-step molecular dynamics, preserving symplectic and time-reversible properties.

MD-GAN learns long-time molecular behavior from short-time data with multi-particle input.

We propose a deep generative Markov State Model (DeepGenMSM) learning framework for inference of metastable dynamical systems and prediction of trajectories. After unsupervised training on time series data, the model contains (i) a probabilistic encoder that maps from high-dimensional configuration space to a small-siz…

We study the use of feedforward neural networks (FNN) to develop models of nonlinear dynamical systems from data. Emphasis is placed on predictions at long times, with limited data availability. Inspired by global stability analysis, and the observation of the strong correlation between the local error and the maximum …

We propose coalescent mechanism of economic grow because of redistribution of external resources. It leads to Zipf distribution of firms over their sizes, turning to stretched exponent because of size-dependent effects, and predicts exponential distribution of income between individuals. We also present new approach to…

This is the first of a series of papers on the long-time behavior of 3 dimensional Ricci flows with surgery. In this paper we first fix a notion of Ricci flows with surgery, which will be used in this and the following three papers. Then we review Perelman's long-time estimates and generalize them to the case in which …

Generative models for complex stochastic dynamics using adversarial learning.

The Kähler-Ricci flow yields bounded diameter and Ricci curvature for minimal models.

This paper proves long-time accuracy of ensemble Kalman filters for chaotic and machine-learned systems.

Prove long-time existence of pluriclosed flow on certain fibrations

New criteria for long-time existence of parabolic flow from 11D supergravity.

The study provides a criterion for diffeomorphism via long-time Ricci flow.

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

The anomaly flow on a complex 3-fold is studied with integral Shi-type estimates and long-time existence conditions.

A new RNN model tackles long-time dependencies with fast, invertible, and memory-efficient hidden states.

Develops a new parabolic equation for surfaces, proving long-time existence and convergence.

Proves long-time Ricci flow existence and topological rigidity for pinched integral curvature manifolds.

Researchers prove long-time existence for two landmark Brownian motion.

Flow preserves volume on flat torus, converging to stable set.

Study long-term asset liquidation behavior with external flows.

Physics-informed neural networks (PINNs) encode physical conservation laws and prior physical knowledge into the neural networks, ensuring the correct physics is represented accurately while alleviating the need for supervised learning to a great degree. While effective for relatively short-term time integration, when …

Introduces generalized Yamabe flows with long-time existence and convergence results.

Solves long-time solutions for a specific equation on hyperkähler manifolds.

We show that three-dimensional homogeneous Ricci flow solutions that admit finite-volume quotients have long-time limits given by expanding solitons. We show that the same is true for a large class of four-dimensional homogeneous solutions. We give an extension of Hamilton's compactness theorem that does not assume a l…

Study shows uniform bounds on torsion and curvature for Chern-Ricci flow solutions.

In this paper we study Inverse Mean Curvature Flow (IMCF) on manifolds that are conformal to a warped product manifold. To this end, we show how the gradient conformal vector field in warped product manifolds is related to the conformal vector field on the conformal metric and use this to gain control of the flow in or…

Study models Ricci flow on complex surfaces, showing mixed behavior.

Long term investment is one of the major investment strategies. However, calculating intrinsic value of some company and evaluating shares for long term investment is not easy, since analyst have to care about a large number of financial indicators and evaluate them in a right manner. So far, little help in predicting …

In this paper we present a rather general phenomenological theory of tick-by-tick dynamics in financial markets. Many well-known aspects, such as the Lévy scaling form, follow as particular cases of the theory. The theory fully takes into account the non-Markovian and non-local character of financial time series. Predi…

Study shows long-term flow on special manifolds with positive Yamabe constant.

We recast the Calabi flow in DeGiorgi's language of minimizing movements. We establish the long time existence of minimizing movements for K-energy with arbitrary initial condition. Furthermore we establish some a priori regularity of these solutions, and that sufficiently regular minimizing movements are smooth soluti…

Study the long-time behavior of Hermitian-Yang-Mills flow on non-Kähler manifolds.

Paper proves curvature estimates for a specific flow on Kähler manifolds.

Kahler-Ricci flow long-time behavior and initial data

Existence of balanced embedding proved for complex manifold into infinite-dimensional space.

We prove long-time existence and convergence results for spacelike solutions to mean curvature flow in the pseudo-Euclidean space $\mathbb{R}^{n,m}$, which are entire or defined on bounded domains and satisfying Neumann or Dirichlet boundary conditions. As an application, we prove long-time existence and convergence of…

Study shows Ricci flow's convergence and harmonic map heat flow's long-time existence.

We prove that at a finite singular time for the Harmonic Ricci Flow on a surface of positive genus both the energy density of the map component and the curvature of the domain manifold have to blow up simultaneously. As an immediate consequence, we obtain smooth long-time existence for the Harmonic Ricci Flow with larg…

We study the long time behaviour of Ricci flow with bubbling-off on a possibly noncompact $3$-manifold of finite volume whose universal cover has bounded geometry. As an application, we give a Ricci flow proof of Thurston's hyperbolisation theorem for $3$-manifolds with toral boundary that generalizes Perelman's proof …

In this paper we study the long time existence of the Ricci-harmonic flow in terms of scalar curvature and Weyl tensor which extends Cao's result \cite{Cao2011} in the Ricci flow. In dimension four, we also study the integral bound of the "Riemann curvature" for the Ricci-harmonic flow generalizing a recently result of…

Clinical outcome prediction based on the Electronic Health Record (EHR) plays a crucial role in improving the quality of healthcare. Conventional deep sequential models fail to capture the rich temporal patterns encoded in the longand irregular clinical event sequences. We make the observation that clinical events at a…

Proves long-term smoothness of curved surfaces evolving under specific curvature rules.

For autonomous agents to successfully operate in the real world, anticipation of future events and states of their environment is a key competence. This problem has been formalized as a sequence extrapolation problem, where a number of observations are used to predict the sequence into the future. Real-world scenarios …

We describe some relations between the long-time asymptotic behavior of the vacuum Einstein evolution equations and the geometrization of 3-manifolds. These relations are expressed in terms of evolution of CMC hypersurfaces in the vacuum space-time.Some results are also obtained on the singularity avoidance of CMC foli…

Adaptive method for prediction sets under changing data distributions.

Learning to predict future images from a video sequence involves the construction of an internal representation that models the image evolution accurately, and therefore, to some degree, its content and dynamics. This is why pixel-space video prediction may be viewed as a promising avenue for unsupervised feature learn…

Given a closed 3-manifold with an initial Riemannian metric of negative sec- tional curvature, we consider the cross curvature flow an evolution equation of metric on M3. We prove long-time existence of a solution to the cross curvature flow via the maximum principle theorem. Besides, we demonstrate the solution exists…