Descrizione del progetto
Teoria combinata all’esperienza per controllare gli algoritmi di dispersione
Immaginate una palla da biliardo colpita nella prima mossa di una partita, che viaggia con una forte energia cinetica verso il resto delle palle ammassate, in attesa del loro destino. Queste palle si sparpaglieranno all’impatto secondo modalità che possono essere facilmente predette conoscendo tutti i parametri fisici come massa, coefficiente di attrito e vettori di velocità. In altre situazioni, la dispersione delle onde energetiche causata dalle imperfezioni del mezzo di trasmissione può essere molto più complicata; tuttavia, una previsione accurata è fondamentale per attività in campi che vanno dalla biomedicina alla sismologia. Il progetto SWING, finanziato dall’UE, prevede di aumentare la potenza degli algoritmi computazionali di dispersione combinando approcci teorici con approcci basati sui dati (apprendimento profondo), definendo al contempo i limiti di ciascuno di essi.
Obiettivo
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.
Campo scientifico
- engineering and technologyelectrical engineering, electronic engineering, information engineeringelectronic engineeringsignal processing
- natural sciencesphysical sciencesacoustics
- natural sciencescomputer and information sciencesartificial intelligencemachine learningdeep learning
- natural sciencesmathematicspure mathematicsgeometry
Programma(i)
Argomento(i)
Meccanismo di finanziamento
ERC-STG - Starting GrantIstituzione ospitante
4051 Basel
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