From calibration to parameter learning: Harnessing the scaling effects of big data in geoscientific modeling
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Abstract (arXiv)
The behaviors and skills of models in many geosciences (e.g., hydrology and ecosystem sciences) strongly depend on spatially-varying parameters that need calibration. A well-calibrated model can reasonably propagate information from observations to unobserved variables via model physics, but traditional calibration is highly inefficient and results in non-unique solutions. Here we propose a novel differentiable parameter learning (dPL) framework that efficiently learns a global mapping between inputs (and optionally responses) and parameters. Crucially, dPL exhibits beneficial scaling curves not previously demonstrated to geoscientists: as training data increases, dPL achieves better performance, more physical coherence, and better generalizability (across space and uncalibrated variables), all with orders-of-magnitude lower computational cost. We demonstrate examples that learned from soil moisture and streamflow, where dPL drastically outperformed existing evolutionary and regionalization methods, or required only ~12.5% of the training data to achieve similar performance. The generic scheme promotes the integration of deep learning and process-based models, without mandating reimplementation.
Key facts. Cited by 26 papers in the map (data through 7 Oct 2026). First posted on arXiv 30 Jul 2020.
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Citing papers per year: 2021: 2; 2022: 3; 2023: 9; 2024: 3; 2025: 5; 2026: 4.
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- 2022Differentiable, learnable, regionalized process-based models with physical outputs can approach state-of-the-art hydrologic prediction accuracycited by 21
- 2022Differentiable Programming for Earth System Modelingcited by 21
- 2025Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equationscited by 14
- 2023When Geoscience Meets Foundation Models: Towards General Geoscience Artificial Intelligence Systemcited by 13
- 2024Knowledge-guided Machine Learning: Current Trends and Future Prospectscited by 13
- 2023Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrologycited by 11
- 2021The data synergy effects of time-series deep learning models in hydrologycited by 10
- 2023Probing the limit of hydrologic predictability with the Transformer networkcited by 9
- 2022Bathymetry Inversion using a Deep-Learning-Based Surrogate for Shallow Water Equations Solverscited by 6
- 2023A Mass-Conserving-Perceptron for Machine Learning-Based Modeling of Geoscientific Systemscited by 6
- 2024Towards Interpretable Physical-Conceptual Catchment-Scale Hydrological Modeling using the Mass-Conserving-Perceptroncited by 4
- 2025Foundation Models for Environmental Science: A Survey of Emerging Frontierscited by 4
14 more
- 2023Differentiable modeling to unify machine learning and physical models and advance Geosciencescited by 3
- 2024Using Machine Learning to Discover Parsimonious and Physically-Interpretable Representations of Catchment-Scale Rainfall-Runoff Dynamicscited by 3
- 2025A Deep State Space Model for Rainfall-Runoff Simulationscited by 3
- 2021Surrogate Model for Shallow Water Equations Solvers with Deep Learningcited by 2
- 2025Deep Learning Meets Process-Based Models: A Hybrid Approach to Agricultural Challengescited by 1
- 2023Fully Convolutional Networks for Dense Water Flow Intensity Prediction in Swedish Catchment Areascited by 0
- 2023Perspectives on AI Architectures and Co-design for Earth System Predictabilitycited by 0
- 2023Learning Regionalization using Accurate Spatial Cost Gradients within a Differentiable High-Resolution Hydrological Model: Application to the French Mediterranean Regioncited by 0
- 2023Differentiable DG with Neural Operator Source Term Correctioncited by 0
- 2025Scientifically-Interpretable Reasoning Network (ScIReN): Discovering Hidden Relationships in the Carbon Cycle and Beyondcited by 0
- 2026Process-Aware AI for Rainfall-Runoff Modeling: A Mass-Conserving Neural Framework with Hydrological Process Constraintscited by 0
- 2026Pure and physics-guided deep learning approaches for spatio-temporal groundwater level predictioncited by 0
- 2026A Differentiable Framework for Global Circulation Model Precipitation Bias Correctioncited by 0
- 2026Constrained hybrid modelling to predict microbial dynamics and organic matter turnover in soil systemscited by 0
- 2026Constrained hybrid modelling to predict microbial dynamics and organic matter turnover in soil systems18 Jun 2026
- 2026A Differentiable Framework for Global Circulation Model Precipitation Bias Correction24 Apr 2026
- 2026Pure and physics-guided deep learning approaches for spatio-temporal groundwater level prediction26 Mar 2026
- 2026Process-Aware AI for Rainfall-Runoff Modeling: A Mass-Conserving Neural Framework with Hydrological Process Constraints26 Mar 2026
- 2025Scientifically-Interpretable Reasoning Network (ScIReN): Discovering Hidden Relationships in the Carbon Cycle and Beyond16 Jun 2025
- 2025Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations13 May 2025
- 2025Deep Learning Meets Process-Based Models: A Hybrid Approach to Agricultural Challenges22 Apr 2025
- 2025Foundation Models for Environmental Science: A Survey of Emerging Frontiers5 Apr 2025
- 2025A Deep State Space Model for Rainfall-Runoff Simulations24 Jan 2025
- 2024Using Machine Learning to Discover Parsimonious and Physically-Interpretable Representations of Catchment-Scale Rainfall-Runoff Dynamics6 Dec 2024
- 2024Knowledge-guided Machine Learning: Current Trends and Future Prospects24 Mar 2024
- 2024Towards Interpretable Physical-Conceptual Catchment-Scale Hydrological Modeling using the Mass-Conserving-Perceptron25 Jan 2024
14 more
- 2023Differentiable DG with Neural Operator Source Term Correction29 Oct 2023
- 2023A Mass-Conserving-Perceptron for Machine Learning-Based Modeling of Geoscientific Systems12 Oct 2023
- 2023Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrology8 Oct 2023
- 2023When Geoscience Meets Foundation Models: Towards General Geoscience Artificial Intelligence System13 Sep 2023
- 2023Learning Regionalization using Accurate Spatial Cost Gradients within a Differentiable High-Resolution Hydrological Model: Application to the French Mediterranean Region2 Aug 2023
- 2023Probing the limit of hydrologic predictability with the Transformer network21 Jun 2023
- 2023Perspectives on AI Architectures and Co-design for Earth System Predictability7 Apr 2023
- 2023Fully Convolutional Networks for Dense Water Flow Intensity Prediction in Swedish Catchment Areas4 Apr 2023
- 2023Differentiable modeling to unify machine learning and physical models and advance Geosciences10 Jan 2023
- 2022Differentiable Programming for Earth System Modeling29 Aug 2022
- 2022Differentiable, learnable, regionalized process-based models with physical outputs can approach state-of-the-art hydrologic prediction accuracy28 Mar 2022
- 2022Bathymetry Inversion using a Deep-Learning-Based Surrogate for Shallow Water Equations Solvers5 Mar 2022
- 2021Surrogate Model for Shallow Water Equations Solvers with Deep Learning20 Dec 2021
- 2021The data synergy effects of time-series deep learning models in hydrology6 Jan 2021
- 2022Differentiable, learnable, regionalized process-based models with physical outputs can approach state-of-the-art hydrologic prediction accuracycited by 21
- 2022Differentiable Programming for Earth System Modelingcited by 21
- 2025Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equationscited by 14
- 2023When Geoscience Meets Foundation Models: Towards General Geoscience Artificial Intelligence Systemcited by 13
- 2024Knowledge-guided Machine Learning: Current Trends and Future Prospectscited by 13
- 2023Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrologycited by 11
- 2021The data synergy effects of time-series deep learning models in hydrologycited by 10
- 2023Probing the limit of hydrologic predictability with the Transformer networkcited by 9
- 2022Bathymetry Inversion using a Deep-Learning-Based Surrogate for Shallow Water Equations Solverscited by 6
- 2023A Mass-Conserving-Perceptron for Machine Learning-Based Modeling of Geoscientific Systemscited by 6
- 2024Towards Interpretable Physical-Conceptual Catchment-Scale Hydrological Modeling using the Mass-Conserving-Perceptroncited by 4
- 2025Foundation Models for Environmental Science: A Survey of Emerging Frontierscited by 4
12 most cited of 26 All 26 (JSON)
- 2026Constrained hybrid modelling to predict microbial dynamics and organic matter turnover in soil systems18 Jun 2026
- 2026A Differentiable Framework for Global Circulation Model Precipitation Bias Correction24 Apr 2026
- 2026Pure and physics-guided deep learning approaches for spatio-temporal groundwater level prediction26 Mar 2026
- 2026Process-Aware AI for Rainfall-Runoff Modeling: A Mass-Conserving Neural Framework with Hydrological Process Constraints26 Mar 2026
- 2025Scientifically-Interpretable Reasoning Network (ScIReN): Discovering Hidden Relationships in the Carbon Cycle and Beyond16 Jun 2025
- 2025Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations13 May 2025
- 2025Deep Learning Meets Process-Based Models: A Hybrid Approach to Agricultural Challenges22 Apr 2025
- 2025Foundation Models for Environmental Science: A Survey of Emerging Frontiers5 Apr 2025
- 2025A Deep State Space Model for Rainfall-Runoff Simulations24 Jan 2025
- 2024Using Machine Learning to Discover Parsimonious and Physically-Interpretable Representations of Catchment-Scale Rainfall-Runoff Dynamics6 Dec 2024
- 2024Knowledge-guided Machine Learning: Current Trends and Future Prospects24 Mar 2024
- 2024Towards Interpretable Physical-Conceptual Catchment-Scale Hydrological Modeling using the Mass-Conserving-Perceptron25 Jan 2024
12 newest of 26 All 26 (JSON)