Non-crossing Quantile Regression Neural Network as a Calibration Tool for Ensemble Weather Forecasts

Despite the maturity of ensemble numerical weather prediction(NWP),the resulting forecasts are still,more often than not,under-dispersed.As such,forecast calibration tools have become popular.Among those tools,quantile regression(QR)is highly competitive in terms of both flexibility and predictive performance.Nevertheless,a long-standing problem of QR is quantile crossing,which greatly limits the interpretability of QR-calibrated forecasts.On this point,this study proposes a non-crossing quantile regression neural network(NCQRNN),for calibrating ensemble NWP forecasts into a set of reliable quantile forecasts without crossing.The overarching design principle of NCQRNN is to add on top of the conventional QRNN structure another hidden layer,which imposes a non-decreasing mapping between the combined output from nodes of the last hidden layer to the nodes of the output layer,through a triangular weight matrix with positive entries.The empirical part of the work considers a solar irradiance case study,in which four years of ensemble irradiance forecasts at seven locations,issued by the European Centre for Medium-Range Weather Forecasts,are calibrated via NCQRNN,as well as via an eclectic mix of benchmarking models,ranging from the naïve climatology to the state-of-the-art deep-learning and other non-crossing models.Formal and stringent forecast verification suggests that the forecasts post-processed via NCQRNN attain the maximum sharpness subject to calibration,amongst all competitors.Furthermore,the proposed conception to resolve quantile crossing is remarkably simple yet general,and thus has broad applicability as it can be integrated with many shallow-and deep-learning-based neural networks.

Seattering Diagrams,Sheaves,and Curves

We review the recent proof of the N.Takahashi's conjecture on genus 0 Gromov Witten invariants of(P^(2),E),where E is a smooth cubic curve in the complex projective plane P^(2).The main idea is the use of the algebraic notion of scattering diagram as a bridge between the world of Gromov-Witten invariants of(P^(2),E)and the world of moduli spaces of coherent sheaves on P^(2).Using this bridge,the N.Takahashi's conjecture can be translated into a manageable question about moduli spaces of coherent sheaves onP^(2)This survey is based on a three hours lecture series given as part of the Beijing-Zurich moduli workshop in Beijing,9-12 September 2019.

Doubly coupled matter fields in massive bigravity

In the context of massive （bi-）gravity, non-minimal matter couplings have been proposed. These couplings are special in the sense that they are free of the Boulware-Deser ghost below the strong coupling scale and can be used consistently as an effective field theory. Furthermore, they enrich the phenomenology of massive gravity. We consider these couplings in the framework of bimetric gravity and study the cosmological implications for background and linear tensor, vector, and scalar Previous works have investigated special branches of solutions. Here we perform a complete perturbation analysis for the general background equations of motion, completing previous analyses.

Dark energy in the Swampland Ⅱ

We have recently pointed out [1] that the string swampland conjectures [2], if true, provide important constraints on dark energy models. The constraints apply to the field range of a scalar field Φ described by an effective field theory, and to the slope of the potential Ⅴ of such fields.

Mechanical characterization and induced crystallization in nanocomposites of thermoplastics and carbon nanotubes

Nanocomposites built from polymers and carbon nanotubes(CNTs)are a promising class of materials.Computer modeling can provide nanoscale views of the polymer–CNT interface,which are much needed to foster the manufacturing and development of such materials.However,setting up periodic nanocomposite models is a challenging task.Here we propose a computational workflow based on Molecular Dynamics simulations.