Descripción del proyecto
La combinación de teoría y experiencia mantiene los algoritmos de dispersión por el buen camino
Imaginen una bola blanca golpeada en la primera jugada de una partida de billar, viajando con una importante energía cinética hacia el resto de las bolas acurrucadas en masa que esperan su destino. Estas bolas se dispersan en el momento del impacto de manera que esto se puede predecir fácilmente según todos los parámetros físicos del sistema como masas, coeficientes de fricción y vectores de velocidad. La dispersión de las ondas energéticas en otras situaciones debido a las imperfecciones del medio de transmisión puede ser mucho más complicada. Sin embargo, una predicción precisa es fundamental para las tareas en ámbitos que van desde la biomedicina hasta la sismología. El proyecto SWING, financiado con fondos europeos, tiene previsto aumentar la potencia de los algoritmos computacionales de dispersión mediante la combinación de métodos teóricos con los basados en datos (aprendizaje profundo) y la definición de los límites de cada uno de ellos.
Objetivo
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.
Ámbito científico
- engineering and technologyelectrical engineering, electronic engineering, information engineeringelectronic engineeringsignal processing
- natural sciencesphysical sciencesacoustics
- natural sciencescomputer and information sciencesartificial intelligencemachine learningdeep learning
- natural sciencesmathematicspure mathematicsgeometry
Programa(s)
Régimen de financiación
ERC-STG - Starting GrantInstitución de acogida
4051 Basel
Suiza