相关论文: Calabi-Yau Metrics, Energy Functionals and Machine…

We study certain polarized degenerations of Calabi-Yau manifolds near an intermediate complex structure limit, and improve the potential $C^0$-convergence to a metric convergence result on the generic region for the corresponding collapsing…

In this paper, we introduce discrete Calabi flow to the graphics research community and present a novel conformal mesh parameterization algorithm. Calabi energy has a succinct and explicit format. Its corresponding flow is conformal and…

We introduce \texttt{cymyc}, a high-performance Python library for numerical investigation of the geometry of a large class of string compactification manifolds and their associated moduli spaces. We develop a well-defined geometric ansatz…

We show how machine learning techniques based on Bayesian inference can be used to reach new levels of realism in the computer simulation of molecular materials, focusing here on water. We train our machine-learning algorithm using…

Materials discovery is often compared to the challenge of finding a needle in a haystack. While much work has focused on accurately predicting the properties of candidate materials with machine learning (ML), which amounts to evaluating…

Let (M, \omega) be a compact symplectic 4-manifold with a compatible almost complex structure J. The problem of finding a J-compatible symplectic form with prescribed volume form is an almost-K\"ahler analogue of Yau's theorem and is…

We show that K-energy minimizing movements agree with smooth solutions to Calabi flow as long as the latter exist. As corollaries we conclude that in a general Kahler class long time solutions of Calabi flow minimize both K-energy and…

Machine Learning tools are nowadays widely applied extensively to the prediction of the properties of molecular materials, using datasets extracted from high-throughput computational models. In several cases of scientific and technological…

The B-model approach of topological string theory leads to difference equations by quantizing algebraic mirror curves. It is known that these quantum mechanical systems are solved by the refined topological strings. Recently, it was pointed…

The development by machine learning of models predicting materials' properties usually requires the use of a large number of consistent data for training. However, quality experimental datasets are not always available or self-consistent.…

Many large scale problems in computational fluid dynamics such as uncertainty quantification, Bayesian inversion, data assimilation and PDE constrained optimization are considered very challenging computationally as they require a large…

We develop tools of Bayesian inference on the moduli space of Calabi--Yau (CY) manifolds. We sample from the invariant Weil--Petersson (WP) measure using Markov Chain Monte Carlo and normalising flows on \Kahler moduli space with dimension…

This paper reviews the most notable works applying machine learning techniques (ML) in the context of geophysics and corresponding subbranches. We showcase both the progress achieved to date as well as the important future directions for…

Many complex multi-target prediction problems that concern large target spaces are characterised by a need for efficient prediction strategies that avoid the computation of predictions for all targets explicitly. Examples of such problems…

We prove that the deformation theory of compactifiable asymptotically cylindrical Calabi-Yau manifolds is unobstructed. This relies on a detailed study of the Dolbeault-Hodge theory and its description in terms of the cohomology of the…

In order to make accurate predictions of material properties, current machine-learning approaches generally require large amounts of data, which are often not available in practice. In this work, an all-round framework is presented which…

We present an algorithm for learning parametric constraints from locally-optimal demonstrations, where the cost function being optimized is uncertain to the learner. Our method uses the Karush-Kuhn-Tucker (KKT) optimality conditions of the…

In this note we use the Calabi ansatz, in the context of metrics with conical singularities along a divisor, to produce regular Calabi-Yau cones and K\"ahler-Einstein metrics of negative Ricci with a cuspidal point. As an application, we…

This is a short expository note about Calabi-Yau manifolds and degenerations of their Ricci-flat metrics.

Recent work has shown a variety of ways in which machine learning can be used to accelerate the solution of constrained optimization problems. Increasing demand for real-time decision-making capabilities in applications such as artificial…