Probabilistic weather forecasting is critical for decision-making in
high-impact domains such as flood forecasting, energy system planning or
transportation routing, where quantifying the uncertainty of a forecast --
including probabilities of extreme events -- is essential to guide important
cost-benefit trade-offs and mitigation measures. Traditional probabilistic
approaches rely on producing ensembles from physics-based models, which sample
from a joint distribution over spatio-temporally coherent weather trajectories,
but are expensive to run. An efficient alternative is to use a machine learning
(ML) forecast model to generate the ensemble, however state-of-the-art ML
forecast models for medium-range weather are largely trained to produce
deterministic forecasts which minimise mean-squared-error. Despite improving
skills scores, they lack physical consistency, a limitation that grows at
longer lead times and impacts their ability to characterize the joint
distribution. We introduce GenCast, a ML-based generative model for ensemble
weather forecasting, trained from reanalysis data. It forecasts ensembles of
trajectories for 84 weather variables, for up to 15 days at 1 degree resolution
globally, taking around a minute per ensemble member on a single Cloud TPU v4
device. We show that GenCast is more skillful than ENS, a top operational
ensemble forecast, for more than 96\% of all 1320 verification targets on CRPS
and Ensemble-Mean RMSE, while maintaining good reliability and physically
consistent power spectra. Together our results demonstrate that ML-based
probabilistic weather forecasting can now outperform traditional ensemble
systems at 1 degree, opening new doors to skillful, fast weather forecasts that
are useful in key applications.

基于机器学习的概率天气预测模型 GenCast 在 1 度分辨率下可以比传统的集合系统更准确地预测天气，并展示了良好的可靠性和物理一致性。

GenCast：基于扩散的中期天气集成预测

GenCast: Diffusion-based ensemble forecasting for medium-range weather

Deep operator networks (DeepONets) are receiving increased attention thanks
to their demonstrated capability to approximate nonlinear operators between
infinite-dimensional Banach spaces. However, despite their remarkable early
promise, they typically require large training data-sets consisting of paired
input-output observations which may be expensive to obtain, while their
predictions may not be consistent with the underlying physical principles that
generated the observed data. In this work, we propose a novel model class
coined as physics-informed DeepONets, which introduces an effective
regularization mechanism for biasing the outputs of DeepOnet models towards
ensuring physical consistency. This is accomplished by leveraging automatic
differentiation to impose the underlying physical laws via soft penalty
constraints during model training. We demonstrate that this simple, yet
remarkably effective extension can not only yield a significant improvement in
the predictive accuracy of DeepOnets, but also greatly reduce the need for
large training data-sets. To this end, a remarkable observation is that
physics-informed DeepONets are capable of solving parametric partial
differential equations (PDEs) without any paired input-output observations,
except for a set of given initial or boundary conditions. We illustrate the
effectiveness of the proposed framework through a series of comprehensive
numerical studies across various types of PDEs. Strikingly, a trained physics
informed DeepOnet model can predict the solution of $\mathcal{O}(10^3)$
time-dependent PDEs in a fraction of a second -- up to three orders of
magnitude faster compared a conventional PDE solver. The data and code
accompanying this manuscript are publicly available at
https://github.com/PredictiveIntelligenceLab/Physics-informed-DeepONets.

本文提出了一种被称为物理学知识不同 DeepONets 的新模型类，通过使用自动差分在模型训练期间施加软惩罚约束来实现重力定律，其将 DeepONet 模型输出偏向于确保物理一致性，进而显著提高 DeepONets 的预测准确性，并大大减少了大型训练数据集的需求。

利用物理信息的深度神经网络学习参数偏微分方程的解算子

Learning the solution operator of parametric partial differential  equations with physics-informed DeepOnets

This paper presents a new condition, the fully physical consistency for a set
of inertial parameters to determine if they can be generated by a physical
rigid body. The proposed condition ensure both the positive definiteness and
the triangular inequality of 3D inertia matrices as opposed to existing
techniques in which the triangular inequality constraint is ignored. This paper
presents also a new parametrization that naturally ensures that the inertial
parameters are fully physical consistency. The proposed parametrization is
exploited to reformulate the inertial identification problem as a manifold
optimization problem, that ensures that the identified parameters can always be
generated by a physical body. The proposed optimization problem has been
validated with a set of experiments on the iCub humanoid robot.

本文提出了一种新的条件，即完全物理一致性，用于确定一组惯性参数是否可由物理刚体生成；提出的条件保证三维惯性矩阵的正定性和三角不等式。本文还提出了一种新的参数化方法，自然保证惯性参数完全符合物理一致性。利用该参数化方法，将惯性识别问题重新表示为流形优化问题，从而保证识别出的参数始终可以被物理刚体所生成。在 iCub 人形机器人上进行了一系列实验，验证了所提出的优化问题。