high order thesis

Author: FilippoMB

_theses/high-order.md

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+---
+layout: base
+title: "Graph Neural Networks for high-order relationships"
+keywords: "GNNs, high-order relationships"
+contact_person: "Lorenzo Livi, Filippo Maria Bianchi"
+---
+
+## 📝 Description
+Traditional Deep and Machine Learning algorithms operate in Euclidean spaces, however there are many problems that benefit from representation in non-Euclidean spaces. As an example, molecular systems such as proteins, DNA, RNA, protein-protein and protein-ligand interaction networks could be represented using their individual atom's coordinates, but this representation:
+
+- (i) is not invariant to common physical transformations;
+- (ii) does not describe the interaction between atoms/molecules, hence stressing the need to develop more advanced representations. 
+
+Graph-based representations offer a solution, as they encode pairwise relations between atoms that are not dependent on a specific framework of reference. However, in some relevant application domains, such as the free energy estimation from molecular dynamics simulations, modeling the relations between pairs of atoms is not enough to describe the potential energy, and thus the free energy of the molecular system of interest. 
+There are many other application domains where higher-order relations play an important role, such as wireless, social, and vehicular networks. Accordingly, there is a need to develop representations encoding higher-order relations and to develop novel machine learning methods capable of processing such complex data.
+
+
+## 📨 Contact:
+Lorenzo Livi <[email protected]>
+Filippo Maria Bianchi <[email protected]>