Description du projet
Vers de nouvelles applications neuromorphes
L’informatique neuromorphique imite la façon dont les réseaux neuronaux du cerveau se reconnectent dynamiquement pour prendre des décisions en réponse à des stimuli particuliers. Elle utilise de nouvelles approches algorithmiques pour améliorer la puissance et les performances de la prochaine génération d’ordinateurs, tout en leur apportant des capacités sans précédent. Le projet NEUROMORPH, financé par l’UE, a pour objectif de développer des modèles mathématiques et des méthodes numériques innovantes en combinant des concepts issus de la thermodynamique, de la biologie cellulaire et du génie électrique. Les chercheurs concevront des modèles qui récapitulent le comportement des synapses et la connectivité neuronale. L’ensemble de ces travaux devrait déboucher sur de nouveaux dispositifs à memristors pour une électronique ultra-dense capable de stocker, d’apprendre et de traiter les mégadonnées.
Objectif
Network structures arise in many applications like for biological tissues, neuron systems, and nanoelectronic devices. Neuronal network structures are inspiring novel neuromorphic computer architectures, overcoming physical scaling limits in traditional hardware. The project NEUROMORPH focuses on the interplay of emerging structures in biological neuron systems and electronic circuit models. The problems we address are formulated in terms of nonlinear partial differential systems, including stochastic and nonlocal terms. Examples include transport through ion channels, chemotaxis-fluid systems, mean-field network models, and memristor networks.
The aims of this mathematics-oriented project are to explore the structure of the multiscale systems, prove their well-posedness, and devise structure-preserving numerical methods. Mathematical challenges are coming from the cross-diffusion character, the coupling of different types of equations (partially diffusive, stochastic, algebraic), the nonstandard degeneracies of the equations, and the hierarchy of scales, ranging from the molecular to the cellular to the network level.
To achieve these goals, we develop new tools by combining variants of the boundedness-by-entropy method, compensated compactness, stability theory, and stochastic analysis. We build on the expertise of the PI on semiconductor device modeling, theory of cross-diffusion systems, numerical analysis, and recent work on stochastic differential equations. Concepts from thermodynamics, cell biology, and electrical engineering will be condensed into innovative mathematical theories for cross-diffusion systems and multiscale models.
The project culminates in the simulation of small bio-inspired neuromorphic circuits, where memristor devices model the behavior of synapses or ion channels and mimic neuronal connectivity. The combination of bio-physical and device-circuit models is expected to make a vital progress for the design of neuromorphic structures.
Champ scientifique
- natural sciencesmathematicspure mathematicsmathematical analysisdifferential equations
- natural sciencesphysical sciencesthermodynamics
- natural sciencesbiological sciencescell biology
- natural sciencesphysical scienceselectromagnetism and electronicssemiconductivity
- natural sciencesmathematicsapplied mathematicsnumerical analysis
Programme(s)
Thème(s)
Régime de financement
ERC-ADG - Advanced GrantInstitution d’accueil
1040 Wien
Autriche