# Helmholtz AI FFT seminar series #5: </br> Marcel Nonnenmacher
###### tags: `HelmholtzAI`,`FFT`
## :memo: Seminar details
**02 September 2021, 11:00 - 12:00**
- Speaker: **Marcel Nonnenmacher**, postdoc, Helmholtz AI young investigator group (YIG) @ Helmholtz-Zentrum hereon GmbH (Hereon)
- Title: **Learning Earth system model dynamics with implicit schemes**
- Chair: **David Greenberg**, Head of Helmholtz AI YIG @ Hereon
> Models of atmosphere and ocean rest on the accurate formulation and numerical solution of dynamical systems. Aside from deriving the dynamics equations from first principles, Machine Learning (ML) has developed methods for inferring dynamics in a bottom-up fashion from data, be it simulation data or real-world observations. These ML-based dynamical systems promise fast, parallelizable models with readily available model derivatives for downstream applications such as data assimilation. By training directly on simulation data without analyzing source code or equations, this approach supports simulators in any programming language on any hardware without specialized routines for each case.
> In our first demonstration, we train ML models on complete or partial system states of the chaotic Lorenz-96 simulator and evaluated the accuracy of their dynamics and derivatives. We found that derivatives of the ML models enable accurate 4D-Var data assimilation and closed-loop tuning of parametrizations.
> But where dynamical models in practice can rely on a range of possible numerical solvers – including explicit, implicit and semi-implicit schemes – work in ML so far focused on explicit forward solvers, where the future system state is an explicit function of the current state. This poses limitations when applied to stiff systems, when dealing with long-range spatial interactions within the system updates, or when trying to learn fast and accurate ML emulators for existing atmosphere and ocean models solved with (semi-)implicit schemes.
> In ongoing work, we address these limitations with implicit neural layers, by defining ML-based dynamical systems trained and solved with (semi-)implicit schemes. We show on the shallow water equations that these ML-based systems trained and solved with an implicit scheme can closely capture stable dynamics from simulation data, with fewer parameters than when solved with explicit schemes.
### VC details
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## :memo: Notes
:bulb: Write down notes and/or interesting information of the seminar. For example, observations auxiliar to the content which is not contained in the slidedeck.
- Emulator examples:
- S. Wiewel, M. Becher, N. Thuerey: "*Latent Space Physics: Towards Learning the Temporal Evolution of Fluid Flow*". Computer Graphics Forum, Volume 38 (2019). https://doi.org/10.1111/cgf.13620
- A. Sanchez-Gonzalez, J. Godwin, T. Pfaff, R. Ying, J. Leskovec, P. Battaglia: "*Learning to Simulate Complex Physics with Graph Networks*". Proceedings of the 37th International Conference on Machine Learning, PMLR 119 (2020). http://proceedings.mlr.press/v119/sanchez-gonzalez20a/sanchez-gonzalez20a.pdf
- Model System: Lorenz 96
- dynamics given by 40 nonlinear differential equations
- interesting (especially for earth systems): purely convolutional methods can be trained on partial system states -> subsample your data set in sub parts, but not data points, and train on these small parts
- 2D systems: learn emulators for shallow water equations
- did not work as well -> numerical solver works different here
## :question: Questions for the speaker
:bulb: Write down any questions or topics you wish to discuss during the seminar
_(either with your initials or anonymously)_
> Leave in-line comments! [color=#3b75c6]
:arrow_right: Q: How hard was it to get a well-performing emulator? How many different model architectures were tried etc.?
A: For Lorenz 96, you can see it on the slides. If you have enough layers to capture what is roughly going on and here even the neighbourhood was covered so this is what you need. You need a lot deeper neural networks.
## :question: Your Feedback
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_(either with your initials or anonymously)_
### Share something that you learned or liked :+1:
- Thank you for this really easy to follow and understandable talk! :)
### Share something that you didn’t like or would like us to improve :-1:
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