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In this thesis, we propose model order reduction techniques for high-dimensional PDEs that preserve structures of the original problems and develop a closure modeling framework leveraging the Mori-Zwanzig formalism and recurrent neural networks. Since high ...
This paper proposes a representational model for image pairs such as consecutive video frames that are related by local pixel displacements, in the hope that the model may shed light on motion perception in primary visual cortex (V1). The model couples the ...
We solve the Bin Packing problem in O^*(2^k) time, where k is the number of items less or equal to one third of the bin capacity. This parameter measures the distance from the polynomially solvable case of only large (i.e., greater than one third) items. O ...
Schloss Dagstuhl – Leibniz-Zentrum fur Informatik2022
In this work, we present a PDE-aware deep learning model for the numerical solution to the inverse problem of electrocardiography. The model both leverages data availability and exploits the knowledge of a physically based mathematical model, expressed by ...
Global spectral methods offer the potential to compute solutions of partial differential equations numerically to very high accuracy. In this work, we develop a novel global spectral method for linear partial differential equations on cubes by extending th ...
Modern manufacturing engineering is based on a ``design-through-analysis'' workflow. According to this paradigm, a prototype is first designed with Computer-aided-design (CAD) software and then finalized by simulating its physical behavior, which usually i ...
During the Artificial Intelligence (AI) revolution of the past decades, deep neural networks have been widely used and have achieved tremendous success in visual recognition. Unfortunately, deploying deep models is challenging because of their huge model s ...
Let G be either a simple linear algebraic group over an algebraically closed field of characteristic l>0 or a quantum group at an l-th root of unity. The category Rep(G) of finite-dimensional G-modules is non-semisimple. In this thesis, we develop new tech ...
This poster was presented at the IUTAM Symposium on Data-driven mechanics, taking place in Paris, France in Octoboer 2022. It shows a proof-of-concept for a new application of Data-Driven Computational Mechanics (DDCM): using it as a new type of adaptive r ...
Encapsulation techniques open up new possibilities to control the kinetics and location of the release of active ingredients. Despite the progresses achieved to obtain a better control over the dimensions and composition of the capsules, the encapsulation ...
