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Deep Learning for Scientific Computing - Two Stories on the Gap Between Theory & Practice - Ben Adcock
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- 1 Intro
- 2 Main collaborators
- 3 Deep Learning (DL) for scientific computing
- 4 This talk two stories on the theory-practice gap
- 5 Parametric modelling
- 6 Challenges
- 7 MLFA: examining the practical performance of DNNS
- 8 Limited performance for smooth, univariate approximation
- 9 Balancing architecture size
- 10 Smooth, multivariate functions
- 11 Piecewise smooth function approximation
- 12 Theoretical insights
- 13 DNN existence theory for holomorphic functions
- 14 Practical DNN existence theorem: Hilbert-valued case
- 15 Discussion
- 16 Deep learning for inverse problems
- 17 Further examples
- 18 These are not rare events
- 19 Unpredictable generalization
- 20 The universal instability theorem
- 21 Hallucinations in practice
- 22 Construction: unravelling and restarts
- 23 FIRENETS example
- 24 Conclusions
