Davide Murari
A PhD student in numerical analysis at the Norwegian University of Science and Technology.
From dynamical systems to neural networks and back
Davide Murari
davide.murari@ntnu.no
Problems of interest
Structuring Neural Networks
Approximating Dynamical Systems
Improving Numerical Methods
From dynamical systems to neural networks and back
\(\mathcal{N}=P\circ F_2\circ F_1\circ L\)
Structuring Neural Networks
\(X\) , Label : Plane
\(X+\delta\), \(\|\delta\|_2=0.3\) , Label : Cat
Structuring Neural Networks
\dot{x}(t) = F_{\theta}(x(t))\text{ such that}\\
\|x(T)-y(T)\|\leq \|x(0)-y(0)\|
From dynamical systems to deep learning and back
Data:
\(\{(x_i,\Phi^{\Delta t}(x_i),...,\Phi^{k\Delta t}(x_i))\}_{i=1}^N\)
Goal:
Find an ODE that
approximates accurately the
observations.
Example: predicting from images
True
Predicted
Thank you for the attention
PhD Seminar
By Davide Murari
PhD Seminar
Slides for the PhD Seminar of Tuesday 8th of November
