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- Nature Reviews Earth & Environment
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Abstract. As a genre of physics-informed machine learning, differentiable process-based hydrologic models (abbreviated as δ or delta models) with regionalized deep-network-based parameterization pipelines were recently shown to provide daily streamflow prediction performance closely approaching that of state-of-the-art long short-term memory (LSTM) deep networks. Meanwhile, δ models provide a full suite of diagnostic physical variables and guaranteed mass conservation. Here, we ran experiments to test (1) their ability to extrapolate to regions far from streamflow gauges and (2) their ability to make credible predictions of long-term (decadal-scale) change trends. We evaluated the models based on daily hydrograph metrics (Nash–Sutcliffe model efficiency coefficient, etc.) and predicted decadal streamflow trends. For prediction in ungauged basins (PUB; randomly sampled ungauged basins representing spatial interpolation), δ models either approached or surpassed the performance of LSTM in daily hydrograph metrics, depending on the meteorological forcing data used. They presented a comparable trend performance to LSTM for annual mean flow and high flow but worse trends for low flow. For prediction in ungauged regions (PUR; regional holdout test representing spatial extrapolation in a highly data-sparse scenario), δ models surpassed LSTM in daily hydrograph metrics, and their advantages in mean and high flow trends became prominent. In addition, an untrained variable, evapotranspiration, retained good seasonality even for extrapolated cases. The δ models' deep-network-based parameterization pipeline produced parameter fields that maintain remarkably stable spatial patterns even in highly data-scarce scenarios, which explains their robustness. Combined with their interpretability and ability to assimilate multi-source observations, the δ models are strong candidates for regional and global-scale hydrologic simulations and climate change impact assessment.more » « less
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.
Abstract. Geoscientific models are facing increasing challenges to exploit growing datasets coming from remote sensing. Universal differential equations (UDEs), aided by differentiable programming, provide a new scientific modelling paradigm enabling both complex functional inversions to potentially discover new physical laws and data assimilation from heterogeneous and sparse observations. We demonstrate an application of UDEs as a proof of concept to learn the creep component of ice flow, i.e. a nonlinear diffusivity differential equation, of a glacier evolution model. By combining a mechanistic model based on a two-dimensional shallow-ice approximation partial differential equation with an embedded neural network, i.e. a UDE, we can learn parts of an equation as nonlinear functions that then can be translated into mathematical expressions. We implemented this modelling framework as ODINN.jl, a package in the Julia programming language, providing high performance, source-to-source automatic differentiation (AD) and seamless integration with tools and global datasets from the Open Global Glacier Model in Python. We demonstrate this concept for 17 different glaciers around the world, for which we successfully recover a prescribed artificial law describing ice creep variability by solving ∼ 500 000 ordinary differential equations in parallel. Furthermore, we investigate which are the best tools in the scientific machine learning ecosystem in Julia to differentiate and optimize large nonlinear diffusivity UDEs. This study represents a proof of concept for a new modelling framework aiming at discovering empirical laws for large-scale glacier processes, such as the variability in ice creep and basal sliding for ice flow, and new hybrid surface mass balance models.
null (Ed.)Conventionally, neural network constitutive laws for path-dependent elasto-plastic solids are trained via supervised learning performed on recurrent neural network, with the time history of strain as input and the stress as input. However, training neural network to replicate path-dependent constitutive responses require significant more amount of data due to the path dependence. This demand on diverse and abundance of accurate data, as well as the lack of interpretability to guide the data generation process, could become major roadblocks for engineering applications. In this work, we attempt to simplify these training processes and improve the interpretability of the trained models by breaking down the training of material models into multiple supervised machine learning programs for elasticity, initial yielding and hardening laws that can be conducted sequentially. To predict pressure-sensitivity and rate dependence of the plastic responses, we reformulate the Hamliton-Jacobi equation such that the yield function is parametrized in the product space spanned by the principle stress, the accumulated plastic strain and time. To test the versatility of the neural network meta-modeling framework, we conduct multiple numerical experiments where neural networks are trained and validated against (1) data generated from known benchmark models, (2) data obtained from physical experiments and (3) data inferred from homogenizing sub-scale direct numerical simulations of microstructures. The neural network model is also incorporated into an offline FFT-FEM model to improve the efficiency of the multiscale calculations.more » « less
Machine learning (ML) provides a powerful framework for the analysis of high‐dimensional datasets by modelling complex relationships, often encountered in modern data with many variables, cases and potentially non‐linear effects. The impact of ML methods on research and practical applications in the educational sciences is still limited, but continuously grows, as larger and more complex datasets become available through massive open online courses (MOOCs) and large‐scale investigations. The educational sciences are at a crucial pivot point, because of the anticipated impact ML methods hold for the field. To provide educational researchers with an elaborate introduction to the topic, we provide an instructional summary of the opportunities and challenges of ML for the educational sciences, show how a look at related disciplines can help learning from their experiences, and argue for a philosophical shift in model evaluation. We demonstrate how the overall quality of data analysis in educational research can benefit from these methods and show how ML can play a decisive role in the validation of empirical models. Specifically, we (1) provide an overview of the types of data suitable for ML and (2) give practical advice for the application of ML methods. In each section, we provide analytical examples and reproducible R code. Also, we provide an extensive Appendix on ML‐based applications for education. This instructional summary will help educational scientists and practitioners to prepare for the promises and threats that come with the shift towards digitisation and large‐scale assessment in education.
Context and implications Rationale for this study
In 2020, the worldwide SARS‐COV‐2 pandemic forced the educational sciences to perform a rapid paradigm shift with classrooms going online around the world—a hardly novel but now strongly catalysed development. In the context of data‐driven education, this paper demonstrates that the widespread adoption of machine learning techniques is central for the educational sciences and shows how these methods will become crucial tools in the collection and analysis of data and in concrete educational applications. Helping to leverage the opportunities and to avoid the common pitfalls of machine learning, this paper provides educators with the theoretical, conceptual and practical essentials.
Why the new findings matter
The process of teaching and learning is complex, multifaceted and dynamic. This paper contributes a seminal resource to highlight the digitisation of the educational sciences by demonstrating how new machine learning methods can be effectively and reliably used in research, education and practical application.
Implications for educational researchers and policy makers
The progressing digitisation of societies around the globe and the impact of the SARS‐COV‐2 pandemic have highlighted the vulnerabilities and shortcomings of educational systems. These developments have shown the necessity to provide effective educational processes that can support sometimes overwhelmed teachers to digitally impart knowledge on the plan of many governments and policy makers. Educational scientists, corporate partners and stakeholders can make use of machine learning techniques to develop advanced, scalable educational processes that account for individual needs of learners and that can complement and support existing learning infrastructure. The proper use of machine learning methods can contribute essential applications to the educational sciences, such as (semi‐)automated assessments, algorithmic‐grading, personalised feedback and adaptive learning approaches. However, these promises are strongly tied to an at least basic understanding of the concepts of machine learning and a degree of data literacy, which has to become the standard in education and the educational sciences.
Demonstrating both the promises and the challenges that are inherent to the collection and the analysis of large educational data with machine learning, this paper covers the essential topics that their application requires and provides easy‐to‐follow resources and code to facilitate the process of adoption.