Bayesian LSTM With Stochastic Variational Inference for Estimating Model Uncertainty in Process‐Based Hydrological Models

Significant attention has recently been paid to deep learning as a method for improved catchment modeling. Compared with process‐based models, deep learning is often criticized for its lack of interpretability. One solution is to combine a process‐based hydrological model with a residual error model...

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Vydané v:	Water resources research Ročník 57; číslo 9
Hlavní autori:	Li, Dayang, Marshall, Lucy, Liang, Zhongmin, Sharma, Ashish, Zhou, Yan
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Washington John Wiley & Sons, Inc 01.09.2021
Predmet:	Artificial neural networks Bayesian analysis Bayesian inference Bayesian theory Catchment models Catchments Deep learning Errors Groundwater Groundwater models Hydrologic models Hydrologic processes hydrological model Hydrology Intervals LSTM Machine learning Markov chain Markov chains Mathematical models MIKE SHE model uncertainty Modelling Natural language processing Neural networks Parameters probabilistic prediction Probability theory regression analysis Regression models Reliability Sharpness Statistical analysis Statistical inference Statistical methods stochastic variational inference Uncertainty Watersheds
ISSN:	0043-1397, 1944-7973
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Abstract	Significant attention has recently been paid to deep learning as a method for improved catchment modeling. Compared with process‐based models, deep learning is often criticized for its lack of interpretability. One solution is to combine a process‐based hydrological model with a residual error model based on deep learning to give full scope to their respective advantages. In classical residual error models, Bayesian inference via Markov chain Monte Carlo (MCMC) is commonly used to provide an estimation of the uncertainty. However, deep neural networks tend to have excessively large numbers of parameters, making MCMC an unsuitable approach. Here, we introduce an alternative to Bayesian MCMC sampling called stochastic variational inference (SVI) which has recently been developed for Bayesian deep learning in Natural Language Processing. We implement SVI in a Long Short‐Term Memory (LSTM) network and construct residual error models in process‐based hydrological models. This approach is examined in the contrasting geographical and climatic characteristics of two catchments from China, the Tangnaihai catchment and the Shiquan catchment. Compared with the Bayesian linear regression model, the Bayesian LSTM provides better uncertainty estimates. Specifically, the proposed method improves the Continuous Ranked Probability Score (CRPS) by over 10% in both two catchments. In the Tangnaihai catchment, it provides more than 10% narrower uncertainty intervals in terms of Sharpness with slightly superior Reliability. In the Shiquan catchment, it provides comparable uncertainty intervals with better Reliability. Further, our study highlights the scalability of SVI to high‐dimensional parameter spaces in hydrological applications (e.g., distributed hydrological models, groundwater models). Key Points Residual error models are constructed to take advantages of process‐based hydrological models and Bayesian deep learning Bayesian Long Short‐Term Memory provides better streamflow uncertainty estimates than a Bayesian linear regression model Stochastic variational inference as an alternative to Markov chain Monte Carlo is viable to estimate tens of thousands of parameters
AbstractList	Significant attention has recently been paid to deep learning as a method for improved catchment modeling. Compared with process‐based models, deep learning is often criticized for its lack of interpretability. One solution is to combine a process‐based hydrological model with a residual error model based on deep learning to give full scope to their respective advantages. In classical residual error models, Bayesian inference via Markov chain Monte Carlo (MCMC) is commonly used to provide an estimation of the uncertainty. However, deep neural networks tend to have excessively large numbers of parameters, making MCMC an unsuitable approach. Here, we introduce an alternative to Bayesian MCMC sampling called stochastic variational inference (SVI) which has recently been developed for Bayesian deep learning in Natural Language Processing. We implement SVI in a Long Short‐Term Memory (LSTM) network and construct residual error models in process‐based hydrological models. This approach is examined in the contrasting geographical and climatic characteristics of two catchments from China, the Tangnaihai catchment and the Shiquan catchment. Compared with the Bayesian linear regression model, the Bayesian LSTM provides better uncertainty estimates. Specifically, the proposed method improves the Continuous Ranked Probability Score (CRPS) by over 10% in both two catchments. In the Tangnaihai catchment, it provides more than 10% narrower uncertainty intervals in terms of Sharpness with slightly superior Reliability. In the Shiquan catchment, it provides comparable uncertainty intervals with better Reliability. Further, our study highlights the scalability of SVI to high‐dimensional parameter spaces in hydrological applications (e.g., distributed hydrological models, groundwater models). Significant attention has recently been paid to deep learning as a method for improved catchment modeling. Compared with process‐based models, deep learning is often criticized for its lack of interpretability. One solution is to combine a process‐based hydrological model with a residual error model based on deep learning to give full scope to their respective advantages. In classical residual error models, Bayesian inference via Markov chain Monte Carlo (MCMC) is commonly used to provide an estimation of the uncertainty. However, deep neural networks tend to have excessively large numbers of parameters, making MCMC an unsuitable approach. Here, we introduce an alternative to Bayesian MCMC sampling called stochastic variational inference (SVI) which has recently been developed for Bayesian deep learning in Natural Language Processing. We implement SVI in a Long Short‐Term Memory (LSTM) network and construct residual error models in process‐based hydrological models. This approach is examined in the contrasting geographical and climatic characteristics of two catchments from China, the Tangnaihai catchment and the Shiquan catchment. Compared with the Bayesian linear regression model, the Bayesian LSTM provides better uncertainty estimates. Specifically, the proposed method improves the Continuous Ranked Probability Score (CRPS) by over 10% in both two catchments. In the Tangnaihai catchment, it provides more than 10% narrower uncertainty intervals in terms of Sharpness with slightly superior Reliability. In the Shiquan catchment, it provides comparable uncertainty intervals with better Reliability. Further, our study highlights the scalability of SVI to high‐dimensional parameter spaces in hydrological applications (e.g., distributed hydrological models, groundwater models). Key Points Residual error models are constructed to take advantages of process‐based hydrological models and Bayesian deep learning Bayesian Long Short‐Term Memory provides better streamflow uncertainty estimates than a Bayesian linear regression model Stochastic variational inference as an alternative to Markov chain Monte Carlo is viable to estimate tens of thousands of parameters Significant attention has recently been paid to deep learning as a method for improved catchment modeling. Compared with process‐based models, deep learning is often criticized for its lack of interpretability. One solution is to combine a process‐based hydrological model with a residual error model based on deep learning to give full scope to their respective advantages. In classical residual error models, Bayesian inference via Markov chain Monte Carlo (MCMC) is commonly used to provide an estimation of the uncertainty. However, deep neural networks tend to have excessively large numbers of parameters, making MCMC an unsuitable approach. Here, we introduce an alternative to Bayesian MCMC sampling called stochastic variational inference (SVI) which has recently been developed for Bayesian deep learning in Natural Language Processing. We implement SVI in a Long Short‐Term Memory (LSTM) network and construct residual error models in process‐based hydrological models. This approach is examined in the contrasting geographical and climatic characteristics of two catchments from China, the Tangnaihai catchment and the Shiquan catchment. Compared with the Bayesian linear regression model, the Bayesian LSTM provides better uncertainty estimates. Specifically, the proposed method improves the Continuous Ranked Probability Score (CRPS) by over 10% in both two catchments. In the Tangnaihai catchment, it provides more than 10% narrower uncertainty intervals in terms of Sharpness with slightly superior Reliability. In the Shiquan catchment, it provides comparable uncertainty intervals with better Reliability. Further, our study highlights the scalability of SVI to high‐dimensional parameter spaces in hydrological applications (e.g., distributed hydrological models, groundwater models). Residual error models are constructed to take advantages of process‐based hydrological models and Bayesian deep learning Bayesian Long Short‐Term Memory provides better streamflow uncertainty estimates than a Bayesian linear regression model Stochastic variational inference as an alternative to Markov chain Monte Carlo is viable to estimate tens of thousands of parameters
Author	Liang, Zhongmin Zhou, Yan Marshall, Lucy Li, Dayang Sharma, Ashish
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Snippet	Significant attention has recently been paid to deep learning as a method for improved catchment modeling. Compared with process‐based models, deep learning is...
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SubjectTerms	Artificial neural networks Bayesian analysis Bayesian inference Bayesian theory Catchment models Catchments Deep learning Errors Groundwater Groundwater models Hydrologic models Hydrologic processes hydrological model Hydrology Intervals LSTM Machine learning Markov chain Markov chains Mathematical models MIKE SHE model uncertainty Modelling Natural language processing Neural networks Parameters probabilistic prediction Probability theory regression analysis Regression models Reliability Sharpness Statistical analysis Statistical inference Statistical methods stochastic variational inference Uncertainty Watersheds
Title	Bayesian LSTM With Stochastic Variational Inference for Estimating Model Uncertainty in Process‐Based Hydrological Models
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