This talk was given at the Cologne AI and Machine Learning Meetup on April 13, 2023 (https://www.meetup.com/de-DE/cologne-ai-and-machine-learning-meetup/events/291513393/) by Philipp Wendland, PhD Student at Koblenz University of Applied Sciences, Group of Prof. Dr. Maik Kschischo: Neural ODEs - A state-of-the-art Deep Learning approach to process time series data Neural ODEs are a hybrid deep learning approach based on modelling the dynamic of hidden layers of a neural network in a continuous fashion as an Ordinary Differential Equation (ODE). Due to its continuous nature and promising performance Neural ODEs are a state-of-the-art approach to process (unevenly sampled) multivariate time-series data. Further promising and succesful applications of the Neural ODEs are image classifications, density estimation with continuous normalizing flows and the creation of multi-state survival models. In this talk we want to introduce the general framework of Neural ODEs with a particular focus on its applications to patient data. We will present our extension the so-called Multimodel Neural ODEs to generate highly realistic synthetic patient data based on both static and continuous covariates.

1. Motivation Methodological Background MultiNODEs Discussion References
Neural ODEs
A state-of-the-art Deep Learning approach to process time
series data
Philipp Wendland
Prof. Dr. Maik Kschischo
13.04.2023
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2. Motivation Methodological Background MultiNODEs Discussion References
Applications
Processing of time-series data
Image classifications
Density estimation with continuous normalizing flows
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3. Motivation Methodological Background MultiNODEs Discussion References
Applications
Time Series data
Generative model
Predictions
Classifications
Survival analysis

4. Motivation Methodological Background MultiNODEs Discussion References
Ordinary Differential Equations
Dynamical Systems
ẋ(t) = f(x(t))
y(t) = h(x(t))
x(t0) = xt0
All ClipArts from Pixabay.com

5. Motivation Methodological Background MultiNODEs Discussion References
Ordinary Differential Equations
Lotka-Volterra System
ẋ1(t) = αx1 (t) − βx1 (t) x2 (t)
ẋ2(t) = δx1 (t) x2 (t) − γx2 (t)
y(t) = x2 (t)
x(t0) = xt0
All ClipArts from Pixabay.com

6. Motivation Methodological Background MultiNODEs Discussion References
Neural ODEs (Chen et al., 2019)
Hidden layers are a continous
time dynamical system
Neural ODE
dx(t)
dt = fθ (x(t), t)
(p.1, fig.1, Chen et al., 2019)

7. Motivation Methodological Background MultiNODEs Discussion References
What makes Neural ODEs so special?
Data-driven modelling of continuous latent dynamics
Processing of time series data
Technically: Usage of ODE solvers
Constant memory cost at training time
Adaptive computation
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8. Motivation Methodological Background MultiNODEs Discussion References
Latent ODE Model
ẋ (t) = fθ (x (t) , t)
x (t0) = xt0 = henc yobs
(t)
ŷ (t) = hdec (x (t))

9. Motivation Methodological Background MultiNODEs Discussion References
Generative Latent ODE Model
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10. Motivation Methodological Background MultiNODEs Discussion References
Multimodal Neural ODEs (Wendland et al., 2022)
(p.2, fig.1, Wendland et al., 2022)
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11. Motivation Methodological Background MultiNODEs Discussion References
Synthetic patient data
(p.5, fig.4, Wendland et al., 2022)
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12. Motivation Methodological Background MultiNODEs Discussion References
Interpolation and Extrapolation
(p.6, fig.5, Wendland et al., 2022)
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13. Motivation Methodological Background MultiNODEs Discussion References
Spearman correlation
(p.4, fig.3, Wendland et al., 2022)
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14. Motivation Methodological Background MultiNODEs Discussion References
Conclusion
Neural ODEs are a powerful tool
Especially for processing time-series data
Neural ODEs can be used for many different tasks
Implementations in Pytorch, Jax and Tensorflow
Torchdyn package
https://github.com/DiffEqML/torchdyn
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15. Motivation Methodological Background MultiNODEs Discussion References
Acknowledgements
I would like to thank all the coauthors of the
MultiNODE publication!
Colin Birkenbihl (Shared First Co-Author)
Marc Gomez-Freixa
Meemansa Sood
Prof. Dr. Maik Kschischo
Prof. Dr. Holger Fröhlich
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16. Motivation Methodological Background MultiNODEs Discussion References
Chen, Ricky T. Q. et al. (Dec. 13, 2019). Neural Ordinary
Differential Equations. arXiv:1806.07366. type: article.
arXiv. arXiv: 1806.07366[cs,stat]. url:
http://arxiv.org/abs/1806.07366 (visited on
10/07/2022).
Wendland, Philipp et al. (Aug. 20, 2022). “Generation of
realistic synthetic data using Multimodal Neural Ordinary
Differential Equations”. In: npj Digital Medicine 5.1, p. 122.
issn: 2398-6352. doi: 10.1038/s41746-022-00666-x. url:
https://www.nature.com/articles/s41746-022-00666-x
(visited on 11/21/2022).
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