Due largely to challenges associated with physical interpretability of machine learning (ML) methods, and because model interpretability is key to credibility in management applications, many scientists and practitioners are hesitant to discard traditional physical-conceptual (PC) modeling approaches despite their poorer predictive performance. Here, we examine how to develop parsimonious minimally-optimal representations that can facilitate better insight regarding system functioning. The term minimally-optimal indicates that the desired outcome can be achieved with the smallest possible effort and resources, while parsimony is widely held to support understanding. Accordingly, we suggest that ML-based modeling should use computational units that are inherently physically-interpretable, and explore how generic network architectures comprised of Mass-Conserving-Perceptron can be used to model dynamical systems in a physically-interpretable manner.
In the context of spatially-lumped catchment-scale modeling, we find that both physical interpretability and good predictive performance can be achieved using a distributed-state network with context-dependent gating and information sharing across nodes. The distributed-state mechanism ensures a sufficient number of temporally-evolving properties of system storage while information-sharing ensures proper synchronization of such properties. The results indicate that MCP-based ML models with only a few layers (up to two) and relativity few physical flow pathways (up to three) can play a significant role in ML-based streamflow modelling.
A Gated Catchment Hydrology Model (GCHM) for Physically-Interpretable Rainfall-Evapotranspiration-Runoff Simulation Across Diverse Hydroclimatic Regimes
QDeepGR4J: Quantile-based ensemble of deep learning and GR4J hybrid rainfall-runoff models for extreme flow prediction with uncertainty quantification
School of Mathematics and Statistics, University of New South Wales, Sydney, NSW 2052, Australia（数学与统计学学院，新南威尔士大学，悉尼，新南威尔士州，2052，澳大利亚）；Data Analytics for Resources and Environments, Australian Research Council—Industrial Transformation Training Centre, Sydney, NSW, Australia（资源与环境数据分析，澳大利亚研究理事会—工业转型培训中心，悉尼，新南威尔士州，澳大利亚）
Towards CONUS-Wide ML-Augmented Conceptually-Interpretable Modeling of Catchment-Scale Precipitation-Storage-Runoff Dynamics
Earth and Environmental Science Area, Lawrence Berkeley National Lab（伯克利国家实验室地球与环境科学部）；Department of Hydrology and Atmospheric Science, University of Arizona（亚利桑那大学水文学与大气科学系）；School for the Environment, University of Massachusetts Boston（马萨诸塞大学波士顿分校环境学院）；Department of Civil Engineering, The University of Hong Kong（香港大学土木工程系）
Use of 1D-CNN for input data size reduction of LSTM in Hourly Rainfall-Runoff modeling
International Research Organization for Advanced Science and Technology, Kumamoto University（熊本大学先进科学技术国际研究机构）；Center for Water Cycle, Marine Environment, and Disaster Management, Kumamoto University（熊本大学水循环、海洋环境与灾害管理研究中心）；Department of Civil and Environmental Engineering, University of California, Davis（加州大学戴维斯分校土木与环境工程系）；Graduated School of Science and Technology, Kumamoto University（熊本大学科学与技术研究生院）；Faculty of Advanced Science and Technology, Kumamoto University（熊本大学先进科学技术学部）
Leveraging Exogenous Signals for Hydrology Time Series Forecasting
College of Computing（计算学院）；Georgia Institute of Technology（佐治亚理工学院）；University of Virginia（弗吉尼亚大学）；School of Data Science（数据科学学院）；Computer Science（计算机科学）；Biocomplexity Institute（生物复杂性研究所）
HydroNets: Leveraging River Structure for Hydrologic Modeling
Google Research（谷歌研究院）；The Hebrew University of Jerusalem（耶路撒冷希伯来大学）；Johannes Kepler University Linz（林茨约翰内斯·开普勒大学）；Technion - Israel Institute of Technology（以色列理工学院）
Differentiable, learnable, regionalized process-based models with physical outputs can approach state-of-the-art hydrologic prediction accuracy
The Pennsylvania State University（宾夕法尼亚州立大学）
整个水循环中水文变量的预测对于水资源管理以及下游应用（如生态系统和水质建模）具有重要价值。最近，纯数据驱动的深度学习模型（如长短期记忆（LSTM））在降雨径流和其他地球科学变量建模方面表现出似乎难以克服的性能，但它们无法预测未经训练的物理变量，并且仍然具有挑战性解释。在这里，我们展示了可微分、可学习、基于过程的模型（这里称为δ模型）可以接近LSTM的性能水平，用于区域化参数化的密集观测变量（流量）。我们使用一个简单的水文模型HBV作为骨干，并使用嵌入式神经网络，它只能在一个可微的编程框架中进行训练，以参数化，增强或替换基于过程的模型模块。在不使用集合或后处理器的情况下，δ模型可以为Daymet强迫数据集获得美国671个流域的中值Nash Sutcliffe效率为0.732，而具有相同设置的最先进的LSTM模型为0.748。对于另一个强迫数据集，差异甚至更小：0.715 vs. 0.722。同时，所得到的可学习的基于过程的模型可以输出一整套未经训练的变量，例如，土壤和地下水储存，积雪，蒸散和基流，后来受到他们的观察。模拟的蒸散量和基流排放量与其他估计值一致。通用框架可以处理具有各种过程复杂性的模型，并为从大数据中学习物理开辟了道路。
Operator-based machine learning framework for generalizable prediction of unsteady treatment dynamics in stormwater infrastructure
Water Infrastructure Laboratory, Department of Civil and Environmental Engineering, University of Tennessee, Knoxville, Tennessee 37996, USA（水基础设施实验室，土木与环境工程系，田纳西大学， Knoxville，田纳西州 37996，美国）
