Predicting the spatiotemporal variation in streamflow along with uncertainty
quantification enables decision-making for sustainable management of scarce
water resources. Process-based hydrological models (aka physics-based models)
are based on physical laws, but using simplifying assumptions which can lead to
poor accuracy. Data-driven approaches offer a powerful alternative, but they
require large amount of training data and tend to produce predictions that are
inconsistent with physical laws. This paper studies a constrained reasoning and
learning (CRL) approach where physical laws represented as logical constraints
are integrated as a layer in the deep neural network. To address small data
setting, we develop a theoretically-grounded training approach to improve the
generalization accuracy of deep models. For uncertainty quantification, we
combine the synergistic strengths of Gaussian processes (GPs) and deep temporal
models (i.e., deep models for time-series forecasting) by passing the learned
latent representation as input to a standard distance-based kernel. Experiments
on multiple real-world datasets demonstrate the effectiveness of both CRL and
GP with deep kernel approaches over strong baseline methods.

预测流域水量的时空变化及不确定性量化有助于可持续管理宝贵的水资源，本文研究了约束推理和学习方法，在深度神经网络中将物理定律作为逻辑约束层进行集成，并结合高斯过程和深度时间模型进行不确定性量化。实验证明，这些方法在多个真实数据集上比基线方法具有更好的效果。

水资源管理的带不确定性量化的径流预测：一种约束推理与学习方法

Streamflow Prediction with Uncertainty Quantification for Water  Management: A Constrained Reasoning and Learning Approach

In the hydrology field, time series forecasting is crucial for efficient
water resource management, improving flood and drought control and increasing
the safety and quality of life for the general population. However, predicting
long-term streamflow is a complex task due to the presence of extreme events.
It requires the capture of long-range dependencies and the modeling of rare but
important extreme values. Existing approaches often struggle to tackle these
dual challenges simultaneously. In this paper, we specifically delve into these
issues and propose Distance-weighted Auto-regularized Neural network (DAN), a
novel extreme-adaptive model for long-range forecasting of stremflow enhanced
by polar representation learning. DAN utilizes a distance-weighted multi-loss
mechanism and stackable blocks to dynamically refine indicator sequences from
exogenous data, while also being able to handle uni-variate time-series by
employing Gaussian Mixture probability modeling to improve robustness to severe
events. We also introduce Kruskal-Wallis sampling and gate control vectors to
handle imbalanced extreme data. On four real-life hydrologic streamflow
datasets, we demonstrate that DAN significantly outperforms both
state-of-the-art hydrologic time series prediction methods and general methods
designed for long-term time series prediction.

本文提出了距离加权自正则化神经网络（DAN）模型，用于改进极端天气事件的长期水文流量预测。在四个真实水文流量数据集上验证，DAN 模型在超过其他水文时间序列预测方法和长期时间序列预测方法方面表现出显著的优越性。

极端适应模型之极坐标表示学习的长期时间序列预测

Learning from Polar Representation: An Extreme-Adaptive Model for  Long-Term Time Series Forecasting

Streamflow observation data is vital for flood monitoring, agricultural, and
settlement planning. However, such streamflow data are commonly plagued with
missing observations due to various causes such as harsh environmental
conditions and constrained operational resources. This problem is often more
pervasive in under-resourced areas such as Sub-Saharan Africa. In this work, we
reconstruct streamflow time series data through bias correction of the GEOGloWS
ECMWF streamflow service (GESS) forecasts at ten river gauging stations in
Benin Republic. We perform bias correction by fitting Quantile Mapping,
Gaussian Process, and Elastic Net regression in a constrained training period.
We show by simulating missingness in a testing period that GESS forecasts have
a significant bias that results in low predictive skill over the ten Beninese
stations. Our findings suggest that overall bias correction by Elastic Net and
Gaussian Process regression achieves superior skill relative to traditional
imputation by Random Forest, k-Nearest Neighbour, and GESS lookup. The findings
of this work provide a basis for integrating global GESS streamflow data into
operational early-warning decision-making systems (e.g., flood alert) in
countries vulnerable to drought and flooding due to extreme weather events.

本研究通过对贝宁共和国的十个河流测量站进行偏差校正，研究发现弹性网络回归和高斯过程回归的整体偏差校正相对于传统的随机森林、k 近邻和 GESS 记录的插补方法具有更强的技能。这一发现为将全球 GESS 流量数据整合到对极端天气事件脆弱的国家的操作性预警决策系统（例如洪水警报）中提供了基础。