# From calibration to parameter learning: Harnessing the scaling effects of big data in geoscientific modeling

arXiv: https://arxiv.org/abs/2007.15751 · HTML: https://mlsanity.com/paper/2007.15751/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jul 2020.

## Built on by (most cited first, 26 of 26)

- [Differentiable Programming for Earth System Modeling](https://mlsanity.com/paper/2208.13825/) (2022)
- [Differentiable, learnable, regionalized process-based models with physical outputs can approach state-of-the-art hydrologic prediction accuracy](https://mlsanity.com/paper/2203.14827/) (2022)
- [Knowledge-guided Machine Learning: Current Trends and Future Prospects](https://mlsanity.com/paper/2403.15989/) (2024)
- [Sensitivity-Constrained Fourier Neural Operators for Forward and Inverse Problems in Parametric Differential Equations](https://mlsanity.com/paper/2505.08740/) (2025)
- [When Geoscience Meets Foundation Models: Towards General Geoscience Artificial Intelligence System](https://mlsanity.com/paper/2309.06799/) (2023)
- [Physics-aware Machine Learning Revolutionizes Scientific Paradigm for Machine Learning and Process-based Hydrology](https://mlsanity.com/paper/2310.05227/) (2023)
- [The data synergy effects of time-series deep learning models in hydrology](https://mlsanity.com/paper/2101.01876/) (2021)
- [Probing the limit of hydrologic predictability with the Transformer network](https://mlsanity.com/paper/2306.12384/) (2023)
- [A Mass-Conserving-Perceptron for Machine Learning-Based Modeling of Geoscientific Systems](https://mlsanity.com/paper/2310.08644/) (2023)
- [Bathymetry Inversion using a Deep-Learning-Based Surrogate for Shallow Water Equations Solvers](https://mlsanity.com/paper/2203.02821/) (2022)
- [Towards Interpretable Physical-Conceptual Catchment-Scale Hydrological Modeling using the Mass-Conserving-Perceptron](https://mlsanity.com/paper/2401.14521/) (2024)
- [Differentiable modeling to unify machine learning and physical models and advance Geosciences](https://mlsanity.com/paper/2301.04027/) (2023)
- [Using Machine Learning to Discover Parsimonious and Physically-Interpretable Representations of Catchment-Scale Rainfall-Runoff Dynamics](https://mlsanity.com/paper/2412.04845/) (2024)
- [Foundation Models for Environmental Science: A Survey of Emerging Frontiers](https://mlsanity.com/paper/2504.04280/) (2025)
- [A Deep State Space Model for Rainfall-Runoff Simulations](https://mlsanity.com/paper/2501.14980/) (2025)
- [Surrogate Model for Shallow Water Equations Solvers with Deep Learning](https://mlsanity.com/paper/2112.10889/) (2021)
- [Deep Learning Meets Process-Based Models: A Hybrid Approach to Agricultural Challenges](https://mlsanity.com/paper/2504.16141/) (2025)
- [Fully Convolutional Networks for Dense Water Flow Intensity Prediction in Swedish Catchment Areas](https://mlsanity.com/paper/2304.01658/) (2023)
- [Perspectives on AI Architectures and Co-design for Earth System Predictability](https://mlsanity.com/paper/2304.03748/) (2023)
- [Learning Regionalization using Accurate Spatial Cost Gradients within a Differentiable High-Resolution Hydrological Model: Application to the French Mediterranean Region](https://mlsanity.com/paper/2308.02040/) (2023)
- [Differentiable DG with Neural Operator Source Term Correction](https://mlsanity.com/paper/2310.18897/) (2023)
- [Scientifically-Interpretable Reasoning Network (ScIReN): Discovering Hidden Relationships in the Carbon Cycle and Beyond](https://mlsanity.com/paper/2506.14054/) (2025)
- [Process-Aware AI for Rainfall-Runoff Modeling: A Mass-Conserving Neural Framework with Hydrological Process Constraints](https://mlsanity.com/paper/2603.25093/) (2026)
- [Pure and physics-guided deep learning approaches for spatio-temporal groundwater level prediction](https://mlsanity.com/paper/2603.25779/) (2026)
- [A Differentiable Framework for Global Circulation Model Precipitation Bias Correction](https://mlsanity.com/paper/2604.23045/) (2026)
- [Constrained hybrid modelling to predict microbial dynamics and organic matter turnover in soil systems](https://mlsanity.com/paper/2606.20329/) (2026)

## 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.