In various applications, probabilistic forecasts are required to quantify the inherent uncertainty associated with the forecast. However, numerous modern forecasting methods are still designed to create deterministic forecasts. Transforming these deterministic forecasts into probabilistic forecasts is often challenging and based on numerous assumptions that may not hold in real-world situations. Therefore, the present article proposes a novel approach for creating probabilistic forecasts from arbitrary deterministic forecasts. In order to implement this approach, we use a conditional Invertible Neural Network (cINN). More specifically, we apply a cINN to learn the underlying distribution of the data and then combine the uncertainty from this distribution with an arbitrary deterministic forecast to generate accurate probabilistic forecasts. Our approach enables the simple creation of probabilistic forecasts without complicated statistical loss functions or further assumptions. Besides showing the mathematical validity of our approach, we empirically show that our approach noticeably outperforms traditional methods for including uncertainty in deterministic forecasts and generally outperforms state-of-the-art probabilistic forecasting benchmarks.

翻译：在各类应用中，概率预测被用于量化预测固有的不确定性。然而，当前众多现代预测方法仍以产生确定性预测为目标。将这类确定性预测转化为概率预测往往充满挑战，且需依赖诸多在现实情境中难以成立的假设。为此，本文提出了一种从任意确定性预测生成概率预测的全新方法。为实现该方法，我们采用了条件可逆神经网络（cINN）。具体而言，通过cINN学习数据的潜在分布，随后将该分布的不确定性与任意确定性预测相结合，从而生成精确的概率预测。该方法无需复杂的统计损失函数或额外假设，即可便捷地创建概率预测。除验证方法的数学有效性外，实验结果表明，本方法在纳入确定性预测的不确定性方面显著优于传统方法，且整体上超越当前最先进的概率预测基准模型。