Publications

Projected Neural Differential Equations for Learning Constrained Dynamics

Alistair White, Anna Büttner, Maximilian Gelbrecht, Valentin Duruisseaux, Niki Kilbertus, Frank Hellmann, Niklas Boers

Preprint, 2024

Neural differential equations offer a powerful approach for learning dynamics from data. However, they do not impose known constraints that should be obeyed by the learned model. It is well-known that enforcing constraints in surrogate models can enhance their generalizability and numerical stability. In this paper, we introduce projected neural differential equations (PNDEs), a new method for constraining neural differential equations based on projection of the learned vector field to the tangent space of the constraint manifold… Read more

Machine Learning for Predicting Chaotic Systems

Christof Schötz, Alistair White, Maximilian Gelbrecht, Niklas Boers

Preprint, 2024

Predicting chaotic dynamical systems is critical in many scientific fields such as weather prediction, but challenging due to the characterizing sensitive dependence on initial conditions. Traditional modeling approaches require extensive domain knowledge, often leading to a shift towards data-driven methods using machine learning. However, existing research provides inconclusive results on which machine learning methods are best suited for predicting chaotic systems. In this paper, we compare different lightweight and heavyweight machine learning architectures… Read more

ClimSim-Online: A Large Multi-Scale Dataset and Framework for Hybrid ML-Physics Climate Emulation

Sungduk Yu, Zeyuan Hu, Akshay Subramaniam, Walter Hannah, Liran Peng, Jerry Lin, Mohamed Aziz Bhouri, Ritwik Gupta, Björn Lütjens, Justus C. Will, Gunnar Behrens, Julius J. M. Busecke, Nora Loose, Charles I. Stern, Tom Beucler, Bryce Harrop, Helge Heuer, Benjamin R. Hillman, Andrea Jenney, Nana Liu, Alistair White, Tian Zheng, Zhiming Kuang, Fiaz Ahmed, Elizabeth Barnes, Noah D. Brenowitz, Christopher Bretherton, Veronika Eyring, Savannah Ferretti, Nicholas Lutsko, Pierre Gentine, Stephan Mandt, J. David Neelin, Rose Yu, Laure Zanna, Nathan Urban, Janni Yuval, Ryan Abernathey, Pierre Baldi, Wayne Chuang, Yu Huang, Fernando Iglesias-Suarez, Sanket Jantre, Po-Lun Ma, Sara Shamekh, Guang Zhang, Michael Pritchard

Preprint, 2024

Modern climate projections lack adequate spatial and temporal resolution due to computational constraints, leading to inaccuracies in representing critical processes like thunderstorms that occur on the sub-resolution scale. Hybrid methods combining physics with machine learning (ML) offer faster, higher fidelity climate simulations by outsourcing compute-hungry, high-resolution simulations to ML emulators. However, these hybrid ML-physics simulations require domain-specific data and workflows that have been inaccessible to many ML experts. As an extension of the ClimSim dataset (Yu et al., 2024), we present ClimSim-Online, which also includes an end-to-end workflow for developing hybrid ML-physics simulators…. Read more

Stabilized Neural Differential Equations for Learning Dynamics with Explicit Constraints

Alistair White, Niki Kilbertus, Maximilian Gelbrecht, Niklas Boers

Published in Advances in Neural Information Processing Systems, 2023

Many successful methods to learn dynamical systems from data have recently been introduced. However, ensuring that the inferred dynamics preserve known constraints, such as conservation laws or restrictions on the allowed system states, remains challenging. We propose stabilized neural differential equations (SNDEs), a method to enforce arbitrary manifold constraints for neural differential equations… Read more

Differentiable Programming for Earth System Modeling

Maximilian Gelbrecht, Alistair White, Sebastian Bathiany, Niklas Boers

Published in Geoscientific Model Development, 2023

Earth system models (ESMs) are the primary tools for investigating future Earth system states at timescales from decades to centuries, especially in response to anthropogenic greenhouse gas release. State-of-the-art ESMs can reproduce the observational global mean temperature anomalies of the last 150 years. Nevertheless, ESMs need further improvements, most importantly regarding (i) the large spread in their estimates of climate sensitivity, i.e., the temperature response to increases in atmospheric greenhouse gases; (ii) the modeled spatial patterns of key variables such as temperature and precipitation; (iii) their representation of extreme weather events; and (iv) their representation of multistable Earth system components and the ability to predict associated abrupt transitions. Here, we argue that making ESMs automatically differentiable has a huge potential to advance ESMs… Read more