Description du projet
Combiner théorie et expérience permet de maintenir les algorithmes de diffusion dans la bonne direction
Imaginez une boule de billard frappée lors du premier coup d’une partie, se déplaçant avec une énergie cinétique importante vers le reste des boules, serrées les unes contre les autres en attendant leur sort. Ces boules se dispersent au moment de l’impact d’une manière facilement prévisible compte tenu de tous les paramètres physiques du système, tels que les masses, les coefficients de friction et les vecteurs de vitesse. La dispersion des ondes énergétiques dans d’autres situations, en raison des imperfections inhérentes au milieu de transmission, peut s’avérer beaucoup plus compliquée; des prévisions précises s’avèrent néanmoins essentielles pour les tâches à effectuer dans différents domaines allant de la biomédecine à la sismologie. Le projet SWING, financé par l’UE, prévoit de renforcer la puissance des algorithmes de calcul de la diffusion en combinant des approches théoriques et des approches fondées sur les données (apprentissage profond), tout en définissant les limites de chaque approche.
Objectif
Scattering of waves governs fundamental questions in science, from imaging molecules to fine-tuning concert hall acoustics. Efficient scattering computations rely on sparse representations of wavefields. Spurred by the empirical successes of deep learning, the emphasis has recently shifted to data-driven modeling. However, unlike signal-theoretic implementations that come with sharp approximation guarantees, it remains unclear whether the popular deep learning structures can represent important scattering operators.
In SWING, we address this question by leveraging advances in signal processing and machine learning. We propose theory and algorithms for the upcoming, learning-based wave of breakthroughs in forward and inverse scattering. SWING is built on three research thrusts:
1. To design efficient computational structures with approximation guarantees for learning scattering operators. We will focus on minimal structures for Fourier integral operators which model key problems.
2. To treat learning for inverse scattering as a sampling problem and derive practical sample complexity results. We will explore connections between learning theory and stability of inverse problems, and examine the regularization roles of data, physics and nonlinearity.
3. To apply our techniques to two classes of inverse problems: (i) emerging modalities in molecular imaging, giving rise to problems in geometry and unlabeled sampling; and (ii) seismic tomography of Earth and Mars, with data-driven discretizations of scattering operators playing a central role.
With the growth of wave-based sensing, there is an urgency to quantify the limits of the data-driven paradigm in scattering problems. The power of data in fitting models is indisputable: it is certainly the next frontier. We believe, however, that the best designs combine data-based models with an understanding of the underlying physics.
Champ scientifique
- engineering and technologyelectrical engineering, electronic engineering, information engineeringelectronic engineeringsignal processing
- natural sciencesphysical sciencesacoustics
- natural sciencescomputer and information sciencesartificial intelligencemachine learningdeep learning
- natural sciencesmathematicspure mathematicsgeometry
Programme(s)
Thème(s)
Régime de financement
ERC-STG - Starting GrantInstitution d’accueil
4051 Basel
Suisse