## Seminar

We organize a biweekly seminar on machine learning, every second Tuesday at 3pm (GMT+2). We discuss papers on ML, often (but not always) with connections to Earth science, climate and weather and materials science.

The seminar also allows members of the Hamburg machine learning community to connect and present their ongoing work. We meet in person at HZG, but we also welcome remote online participants and stream the meeting live on our YouTube channel.

To get updates about each meeting or suggest a topic, please join our mailing list.

## Future Topics

### 22. “Superdroplet Surprise” 23.02.21

On Tuesday, February 23 at 3 PM (GMT+1), we’ll discuss “Potential and Limitations of Machine Learning for Modeling Warm-Rain Cloud Microphysical Processes.”paper We’re excited to announce that the first author, Axel Seifert from the German Weather Service (DWD), will be joining us!

This paper address the microphysical processes through which water droplets combine to form raindrops in clouds. While climate and weather models use simplified parametrizations such as bulk moment schemes to describe the complex evolution of the droplet size distribution over time, the computationally intensive superdroplet schemepaper can give a more precise and realistic answer. We will review the basics of these approaches before delving into the main paper.

This paper uses machine learning to train a fast surrogate for the superdroplet scheme. Surprisingly, while a neural network can learn a faithful bulk-moment representation of superdroplet physics, the simplified parameterization performs better at capturing the long term dynamics of the droplet size distribution. The reasons for this are explained by the paper, which reveals some counterintuitive and important insights that are bound to be highly relevant for the design of ML-based physical parametrizations in the future.

## Past Topics

### 21. “Lessons from History” 09.02.21

We discuss “Correcting weather and climate models by machine learning nudged historical simulations,” Watt-Meyer et al., 2020. Geophysical Research Letters. pdf

This paper addresses an important problem that has come up often in previous seminars, as well as in many internal discussions in our research group: how can we learn improved parameterizations and corrections for climate and weather model, without differentiating through the model’s dynamics and physics? This is a very pressing issue in the near term as the gap between useful nondifferentiable models and differentiable toy models remains quite large.

This study offers a fresh and promising new approach. Instead of using expensive high-resolution simulations as training or imitating existing parameterizations with all their limitations, the authors propose learning additive corrections to the model so that it behaves more like an reanalysis dataset! We will discuss the specifics, advantages and limitations of this approach. The method uses random forests, which we covered previously in episode 19.

### 20. “Turning the Tide” 01.12.20

Zegou Zhang will present “Reconstruction of the Basin-Wide Sea Level Variability in the North Sea Using Coastal Data and Generative Adversarial Networks,”pdf recently published from the from the Hydrodynamics and Data Assimilation group at HZG together with Sebastian Grayek and Emil Stanev.

This paper uses adversarial networks to predict sea level across the North sea, and achieves excellent agreement with sophisticated operational forecasting systems by applying machine learning to only a small number of tidal gauge readings. It combines many important concepts we’ve seen in previous seminars, including forecasting, conditional GANs and U-nets. Unlike most of our previous papers, however, this work takes these concepts to the point of generating useful outputs for a real physical and geographic system.

Zegou will help us understand the data being used, the problem being solved, and how ML was applied. This presentation presents a great opportunity to ask questions to someone with hands on experience working with both oceanographic data and ML methods!

### 19. “Durable Physics” 17.11.20

Shivani Sharma will present “Use of neural networks for stable, accurate and physically consistent parameterization of subgrid atmospheric processes with good performance at reduced precision,” Yuval et al., 2020.pdf

As in Episode 10, this paper uses machine learning to replace physical parameterizations in an atmospheric model. However, the current paper is focused on a specific fundamental challenge: even when error appears low on training data with known inputs and outputs for the target parameterization, long-term simulations can “blow up” numerically, or exhibit unrealistic phenomena such as grid scale storms or double ITCZ.

To overcome this “fragility” in the coupled simulations, the authors propose a “durable” approach incorporating physical constraints, prediction of fluxes instead of tendencies and careful selection of diagnostic variables. They demonstrate this strategy using both random forests (which we will briefly review) and neural networks.

### 18. “Baking a Model from Scratch” 03.11.20

We discuss recent advances of using ML to learn dynamics from observational data.

In our last seminar, we already talked about transferring physical knowledge from a given dynamical model or parameterization to a ML model via training the latter on simulated data. An ambitious further step is to train an ML model directly on observational data, without the need of a physics-derived model of dynamics.

A big obstacle in this task is that observational data is usually noise-corrupted and incomplete. Our main paper for this week suggests to tackle this issue by combining ML with data assimilation. Using the Lorenz-96 model as a test-case, Brajard et al. [1] come up with an iterative method that uses an ensemble Kalman filter to provide better training data using a steadily improving neural network model of the system dynamics.

In a follow-up paper [2], which we will also briefly discuss, the authors explore a connection between their suggested method and Expectation-Maximization, a technique for optimizing statistical models in the presence of unobserved variables. This allows a Bayesian perspective on data-driven learning of dynamics.

Main paper:

[1] Brajard, J., Carassi, A., Bocquet, M., & Bertino, L. (2020). Combining data assimilation and machine learning to emulate a dynamical model from sparse and noisy observations: a case study with the Lorenz 96 model. arXiv preprint arXiv:2001.01520.

Supporting paper:

[2] Bocquet, M., Brajard, J., Carrassi, A., & Bertino, L. (2020). Bayesian inference of chaotic dynamics by merging data assimilation, machine learning and expectation-maximization. Foundations of Data Science, 2(1), 55-80. arXiv version

### 17. “Radiation Computation” 20.10.20

The radiative transfer calculations in general circulation models often impose a computational challenge owing to the complexity of the current radiation models. This week, guest presenter Anikesh Pal (IIT Kanpur) will give an overview of these calculations, and describe his recent work at Oak Ridge National Laboratory on using neural networks to accelerate these computations.

In this study, deep neural networks (DNNs) were implemented in the Super‐Parameterized Energy Exascale Earth System Model (SP‐E3SM) to imitate the shortwave and longwave radiative transfer calculations. These DNNs were able to emulate the radiation parameters with an accuracy of 90–95% at a cost of 8–10 times cheaper than the original radiation parameterization. A comparison of time‐averaged radiative fluxes and the prognostic variables manifested qualitative and quantitative similarity between the DNN emulation and the original parameterization. It has also been found that the differences between the DNN emulation and the original parameterization are comparable to the internal variability of the original parameterization. Although the DNNs developed in this investigation emulate the radiation parameters for a specific set of initial conditions, the results justify the need of further research to generalize the use of DNNs for the emulations of full model radiation and other parameterization for seasonal predictions and climate simulations.

Main paper:

[1] Pal, Anikesh, Salil Mahajan, and Matthew R. Norman. “Using Deep Neural Networks as Cost‐Effective Surrogate Models for Super‐Parameterized E3SM Radiative Transfer.” Geophysical Research Letters 46.11 (2019): 6069-6079. pdf

### “Known Unknowns” 06.10.20

In our seminars so fo far we’ve considered many applications of supervised learning: given an input, our neural network is tasked with producing a correct output as demonstrated in a training set. However, as we have seen in some episdoes, in addition to predicting the correct output, neural networks can also quantify uncertainty, expressing how sure they are about their solution to the task at hand. Just like the accuracy of the network’s predictions, we’d also like to quantify the accuracy of its uncertainty quantifications, asking in effect, “does the network know what it does and doesn’t know?”

The paper for this week investigates this in the context of image classification (assigning the correct label from a finite list of categories to each image), and comes up with a surprising result. While neural networks have increased in overall classification accuracy over the past two decades, their uncertainty quantifications have actually gotten worse! In particular these networks have become overconfident. The paper investigates several changes in network architecture and training procedures that may play a role in this change, and proposes a simple and effective procedure for making them less overconfident without strongly affecting their accuracy.

Main paper: Guo, C., Pleiss, G., Sun, Y. & Weinberger, K. Q. On calibration of modern neural networks. in Proceedings of the 34th International Conference on Machine Learning - Volume 70 1321–1330 (JMLR.org, 2017).

### “Smooth Criminals” 15. 22.09.20

This week we discuss “Learning Temporal Coherence via Self-Supervision for GAN-based Video Generation” by Chu et al. 2020. pdf [15]

They address the issue of GANs for video editing tasks usually would induce flickering or other artifacts. Thanks to the spatio-temporal discriminator together with their “Ping-Pong loss” they outperform many previous approaches.

The results are presented on the tasks of unpaired video translation, as well as video super resolution. In our seminar we will discuss how these techniques can be used in GANs for Earth-Science tasks.

[15] Chu, M., Xie, Y., Mayer, J., Leal-Taixé, L., & Thuerey, N. (2020). Learning temporal coherence via self-supervision for GAN-based video generation. ACM Transactions on Graphics (TOG), 39(4), 75-1.

### 14. “When are we?” 08.09.20

We discuss “Viewing Forced Climate Patterns Through an AI Lens,” Barnes et al. 2019 pdf

This paper takes up the task of finding features of meteorological fields (in this case temperature and precipitation) that be used to identify climate forcing (such as anthropogenic carbon emissions, or natural forcing due to volcanoes etc.).

The paper uses extremely small and simple feedforward neural networks, but with a clever trick – it trains these networks to predict the year of a climate simulation with simulated anthropogenic forcing from the meteorological fields. Remarkably, when trained in the right way these same networks then perform well at identifying the year from these same fields in historical observational datasets! The simple neural networks are then analyzed to determine which features they have learned.

### 13. “Model Data for the Data Models” 25.08.20

We discuss “Purely data-driven medium-range weather forecasting achieves comparable skill to physical models at similar resolution,” Rasp et al. 2020. This recent work builds machine learning tools for weather prediction to compete with physics based approaches. Stephan Rasp will return to the seminar to discuss his recent work on predicting temperature, geopotential and precipitation up to 5 days in the future, published just today on arXiv!

The Weatherbench benchmark for evaluating these techniques was proposed early this year, also by Rasp et al. A key contributor to the performance increases in the current work was expanding the training available data beyond the weather that has actually occurred in the recorded past, by including other hypothetical situations realized through global climate modeling.

We discuss many conceptual and practical questions that arise when attempting to predict weather in this way, and consider what the future might hold for data-driven weather prediction.

### 12. “The Big Picture” 11.08.20

We discuss “Adversarial Super-resolution of Climatological Wind and Solar Data” [1], a recent study using Generative Adversarial Networks (GANs) with convolutional layers to increase the resolution of wind and irradiance fields output by climate models. This study uses high-resolution data to train a neural network to generate high-res from low-res data.

This week’s topic is related to several previous themes: we covered GANs in episode 5 (“Real Fake Clouds”), and addressed a related problem of filling in missing data using convolutional networks in episode 8 (“Uncharted History”).

We’ll discuss the approach taken in this paper, describe the Machine Learning tool SRGAN which it uses [2], and debate the conceptual issues that arise when using ML to “invent” new pixel outputs for your model. We’ll also mention how GAN-based superresolution can introduce bias into results [3], and what this could mean for climate and earth science applications.

Main paper: [1] Stengel et al., “Adversarial super-resolution of climatological wind and solar data,” PNAS July, 2020. https://www.pnas.org/content/117/29/16805

Technical Background: [2] Ledi et al., “Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network”, arXiv 2016. https://arxiv.org/abs/1609.04802

Blog post on bias in GANs for SR: [3] https://www.theverge.com/21298762/face-depixelizer-ai-machine-learning-tool-pulse-stylegan-obama-bias

### 11. “Teach Yourself Physics in 2 Million Easy Steps” 28.07.20

In this episode we discuss “Learning to Simulate Complex Physics with Graph Networks” [1], a recent study using deep learning to emulate physical dynamical systems.

We have already encountered several approaches to predicting physical systems in previous seminars (episodes 3, 4, 7 & 9). Typically, a machine learning model is trained on data generated with a numerical solver to predict a (partial) system state many time steps ahead, using the current (partial) system state as input. The network solves the task in a way that bears little, if any resemblance to the numerical solver used to generate its training data.

Here, the authors follow another approach [2], where the machine learning model is trained explicitly to reproduce or “emulate” the behavior of the numerical solver over individual numerical integration steps. We will discuss how learning to carry out single-time-step updates offers certain advantages over learning to predict the future directly from the present as the learning problem is very well posed conceptually and mathematically. However, a critical concern is whether the solutions of this ‘learned simulation’ stay realistic over many integration steps when using the emulator network instead of the numerical solver.

Another twist for the upcoming session will be that the dynamical systems studied are multi-body systems, i.e. they consist of a fixed number of discrete interacting objects. To learn state predictions on this kind of data, the authors designed their own Interaction Network [3], which is a subclass of so-called Graph Neural Networks. GNNs [4] have become a very active and vast topic of research over the past years that we can only briefly touch upon in our session.

Main paper: [1] A. Sanchez-Gonzalez, J. Godwin, T. Pfaff, R. Ying, J. Leskovec, and P. W. Battaglia, “Learning to Simulate Complex Physics with Graph Networks,” arXiv:2002.09405 [physics, stat], Feb. 2020, Accessed: Jun. 27, 2020. http://arxiv.org/abs/2002.09405.

Additional Background: [2] R. Grzeszczuk, D. Terzopoulos, and G. E. Hinton, “Fast Neural Network Emulation of Dynamical Systems for Computer Animation,” in Advances in Neural Information Processing Systems 11, M. J. Kearns, S. A. Solla, and D. A. Cohn, Eds. MIT Press, 1999, pp. 882–888. https://papers.nips.cc/paper/1562-fast-neural-network-emulation-of-dynamical-systems-for-computer-animation

[3] P. W. Battaglia, R. Pascanu, M. Lai, D. Rezende, and K. Kavukcuoglu, “Interaction Networks for Learning about Objects, Relations and Physics,” arXiv:1612.00222 [cs], Dec. 2016, Accessed: Jul. 16, 2020. [Online]. Available: http://arxiv.org/abs/1612.00222.

Further reading: [4] J. Zhou et al., “Graph Neural Networks: A Review of Methods and Applications,” arXiv:1812.08434 [cs, stat], Jul. 2019, Accessed: Jul. 16, 2020. [Online]. Available: http://arxiv.org/abs/1812.08434.

### 10. “Try to look like a little black cloud” 14.07.20

In light of recent meteorological events in Hamburg, the next ML@HZG seminar will focus on clouds.

We will begin with a well-written 3-page review[1] that discusses how cloud resolving models (CRMs) can play an important role in our understanding of our climate and its potential changes in the future, but impose immense computational demands.

We’ll then discuss how small-scale CRMs can be used as cloud parameterizations for large-scale climate models, focusing on the Superparameterized Community Atmosphere Model (SPCAM) [2]. This approach aims to capture the two-way interactions between cloud physics and coarser-scale meteorological variables without paying the cost of a huge CRM simulation, but instead embedding a small CRM into each grid cell. Further work[3] showed how the embedded CRMs can be simplified without compromising accuracy.

Finally, we’ll discuss how machine learning can be used to imitate the effect of the miniature CRMs used in SPCAM, which in turn aims to imitate what a large-scale CRM might look like. Recent work[4] has shown the neural networks can be trained reproduce the feedback between coarse-scale climate model variables and each grid cell’s CRM, with a considerable reduction of computational.

As we’ll discuss, often the true test of these techniques is their ability to match observed phenomena in large, long simulations!

Postscript: as discussed in the seminar, it’s not totally clear why the MJO moves east, but there are some interesting theories as to why[5] (thanks to Eduardo Zorita for the reference).

[1] T. Schneider et al., “Climate goals and computing the future of clouds,” Nature Clim Change, vol. 7, no. 1, pp. 3–5, Jan. 2017, doi: 10.1038/nclimate3190.

[2] M. Khairoutdinov, D. Randall, and C. DeMott, “Simulations of the Atmospheric General Circulation Using a Cloud-Resolving Model as a Superparameterization of Physical Processes,” J. Atmos. Sci., vol. 62, no. 7, pp. 2136–2154, Jul. 2005, doi: 10.1175/JAS3453.1.

[3] M. S. Pritchard, C. S. Bretherton, and C. A. DeMott, “Restricting 32–128 km horizontal scales hardly affects the MJO in the Superparameterized Community Atmosphere Model v.3.0 but the number of cloud-resolving grid columns constrains vertical mixing,” Journal of Advances in Modeling Earth Systems, vol. 6, no. 3, pp. 723–739, 2014, doi: 10.1002/2014MS000340.

[4] S. Rasp, M. S. Pritchard, and P. Gentine, “Deep learning to represent subgrid processes in climate models,” PNAS, vol. 115, no. 39, pp. 9684–9689, Sep. 2018, doi: 10.1073/pnas.1810286115.

[5] B. Wang, F. Liu, and G. Chen, “A trio-interaction theory for Madden–Julian oscillation,” Geosci. Lett., vol. 3, no. 1, p. 34, Dec. 2016, doi: 10.1186/s40562-016-0066-z.

### 9. “The Best of All Possible Worlds” 30.06.20

We consider the critically important and monstrously difficult problem of tuning climate model parameters to match observations (reviewed in Hourdin et al., 2017).

This process is quite challenging, because:

- Testing new parameter combinations through simulation incurs an immense computational cost.
- The aspects of the data we wish to match (warming trends, long-term means and variances) require long, global simulations.

We discuss several approaches to this problem:

- Gradient-based Optimization attempts to adjust model parameters by following the gradients, or derivatives of climate model outputs with respect to parameters. A major challenge for this approach is that we usually lack the ability to calculate or even approximate these derivatives. Tett et al., 2017 get around this problem by using finite differencing, where derivatives are approximated using small perturbations to the parameters.
- History matching is a technique where nonlinear regression is used to learn an “emulator” or “metamodel” that maps directly between multiple tunable model parameters and real-world observables we’d like the original model to reproduce. Having estimated this parameter-observable relationship using a finite number of simulations, we can then identify all regions of parameter space for which the predicted model output is close to observations. Williamson et al., 2013 and Bellprat et al. 2012 use polynomial functions to build emulators for global and regional climate models resepctively. We also consider the more recent Li et al., 2019, which replaces the polynomial functions with simple neural networks.
- To demonstrate validation of a tuning scheme, Bellprat et al. 2016 use history matching on regional climate models for two different regions, and compare the results.

### 8. “Uncharted History” 16.06.20

We discuss the paper “Artificial intelligence reconstructs missing climate information”, Kadow et al. 2020, Nat. Geosci. pdf code

We are very happy to have the first-author of the paper with us to present the study!

The computer vision field of image inpainting paper uses several techniques to reconstruct broken images, paintings, etc. In recent years, more and more diverse machine learning techniques have boosted the field. A major step was taken by Liu et al. 2018 paper video in using partial convolutions in a CNN. The study shown here will transfer the technology to climate research. The presentation will show the journey of changing and applying the NVIDIA technique to one of the big obstacles in climate research: missing climate information of the past. Therefore a transfer learning approach is set up using climate model data. After evaluating test-suites, a reconstruction of HadCRUT4 - one of the most important climate data sets - is shown and analyzed.

### 7. “Compressed Pressure”, 02.06.20

The main paper for this session will be Latent Space Physics: Towards Learning the Temporal Evolution of Fluid Flow, Wiewel et al, 2019. Also see their blog post.

We will also briefly discuss a follow-up from Wiewel et al. 2020, and a related paper on generative fluid modelling from the same group, Kim et al. 2019. The latter is nicely summarized in this video.

For those interested in the underlying ML methods, this session will be about autoencoders and sequence-to-sequence models:

- Autoencoders train pairs of neural networks for unsupervised learning of data representations, and Wiewel et al. use them to compress the high-dimensional volumetric fluid data.
- Sequence-to-sequence models allow to predict a variable-length output sequence from a variable-length input sequence, using a pair of recurrent neural networks. “seq2seq” originated in natural language processing, but as we will see it can also be used to predict sequences of 3D images.

### 6. “Minimalist Chaos”, 19.05.20

We’ll discus the Lorenz `96 model (L96) and its myriad uses. In “Predictability - a problem partly solved”, Edward Lorenz introduced a simple mathematical model exhibiting many of Earth science’s core computational challenges.

Challenging features of L96 include chaotic dynamics, nonlinearity, combination of dissipative and conservative aspects and coupling of vastly differing scales in space and time. Chaos means that small perturbations in the model state due to numerical errors or observation noise will, over time, lead to large deviations in the future model state.

L96 is a frequent test case for algorithms tackling many fundamental problems. We consider two of these: parameter tuning, and parameterizing sub-grid processes:

- Marcel Nonnenmacher will describe work on identifying the 4 parameters of L96. This includes “Recovering the parameters underlying the Lorenz-96 chaotic dynamics,” Mouatadid et al. 2019, “Earth System Modeling 2.0”, Schneider et al., 2017, as well as his own unpublished work.
- “Coupled online learning as a way to tackle instabilities and biases in neural network parameterizations: general algorithms and Lorenz96 case study (v1.0)”, Rasp 2020. This paper and a related blog post discuss the design of parameterizations that approximate the effect of fast, fine-scale processes on slow, coarse scale ones. Linear and ML-based parameterizations are considered.
- Tobias Finn will guide us through stochastic parameterizations, which approximate deterministic chaos using randomness. “Machine Learning for Stochastic Parameterization: Generative Adversarial Networks in the Lorenz ‘96 Model”, Gagne et al., 2020, uses Generative Adversarial Networks (GANs, see episode 5) to describe uncertainty in the tendency of coarse, slow variables as a result of unseen fast, fine variables. It builds on previous stochastic parameterizations without ML.

Finally, we’ll revisit the original paper and the issue of predictability, nearly 25 years later.

### 5. “Real Fake Clouds” 05.05.20

We discuss the paper “Modeling Cloud Reflectance Fields using Conditional Generative Adversarial Networks,” Schmidt et al. 2020, arXiv. pdf code

This paper uses generative adversarial networks, or GANs. In the GAN framework, a generator network learns to generate “fake” data points while a second discriminator network learns to tell real from fake data. Schmidt et al. use GANs to predict cloud reflectance fields from meteorological variables such as temperature and wind speed. Given these meteorological variables, it can produce multiple realistic output patterns instead of an ensemble average. That is, the network attempts to learn the conditional probability distribution of reflectance given the input variables.

We start with a very brief introduction of GANs. More background can be found in Diego Gomez Mosquera’s high accessible blog post or Ian Goodfellow’s extensive tutorial.

Importantly, this paper wasn’t able to get good results just by applying the GAN framework out of the box, and had to use some of the latest specialized tricks as well. So we’ll briefly go through some of these tricks:

- Adding a term to the loss function that corresponds to supervised learning, as proposed for image to image translation tasks by Isola et al. 2018. pdf
- Multi-scale discriminator and generator networks, via Wang et al. 2018. pdf
- A least squares objective function, proposed by Mao et al. 2017 to avoid vanishing gradients. pdf

Additional links from the discussion: Variational Dropout and and the Local Reparameterization Trick pdf Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning pdf

### 4. “Far into the Future”, 21.04.20

Lennard Schmidt from UFZ present on his work. He applies machine learning to do quality control for hydrological measurement data. He also uses a sophisticated convLSTM architecture to predict hydrological dynamics in an Elbe catchment basin. Code for a convLSTM layer in tensorflow/keras can be found here.

Eduardo Zorita presents “Deep learning for multi-year ENSO forecasts,” Ham et al. 2019, Nature. link This paper uses machine learning algorithms to predict the El Niño/Southern Oscillation 1.5 years into the future, farther than previous methods have achieved. Notably, it trains on a combination of simulations and historical data.

Additional references on the predictability paradox in climate science: “Do seasonal‐to‐decadal climate predictions underestimate the predictability of the real world?” Eade et al. 2014, Geophys. Research Letters. link

“Skilful predictions of the winter North Atlantic Oscillation one year ahead.” Dunstone et al. 2016, Nature. link

### 3. “MetNet, Convolutional-Recurrent Nets, and the Self-Attention Principle” 07.04.20

Linda von Garderen presents on her work.

We cover Google Research’s recent work on weather prediction: “MetNet: A Neural Weather Model for Precipitation Forecasting,” Sønderby et al., 2020, arXiv. paper, blog post

To understand the ML tools that went into this work, we briefly review some concepts from earlier works:

- The convolutional LSTM, which combines convolutional and recurrent neural nets into a single architecture, as introduced by Xingjian et al. in 2015. paper. Review on LSTMs by Christopher Olah.
- Self-attention and the Transformer architecture, introduced by Vaswani et al. in 2017 https://arxiv.org/pdf/1706.03762.pdf, provide a new alternative to convolutional and recurrent nets. MetNet uses a specialized variant called Axial Attention (Ho et al., 2019)paper. We’ll turn to a blog post by Peter Bloem for helpful illustrations. For further reading on the attention concept, see Lillian Weng’s excellent blog post

With these concepts in mind, we examine how MetNet combines them, and consider their results from the perspectives of both ML and weather prediction.

Relevant discussion links:

- discussion between Stephan Rasp (TU Munich) and the MetNet authors on twitter. link
- F1 score used to quantify performance link
- code on github for axial self-attention link

### 2. “Don’t Fear the Sphere” 31.03.20

We cover “Spherical CNNs on Unstructured Grids,” Jiang et al. 2019, ICLR. We also survey other ML approaches to spherical data (more links in the description on YouTube). With 5 minute presentations by Julianna Carvalho, Tobias Finn and Lennart Marien.

### 1. “Hidden Fluid Mechanics” 24.03.20

We discuss the paper “Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations,” Raissi et al. 2020, Science, and the more technical study from the same group, “Physics Informed Neural Networks,” Raissi et al., 2019, J. Computational Physics. Tobias Weigel from DKRZ explains the ML support team that forms part of the local Helmholtz AI unit.