Mathematisches Kolloquium: Drift-diffusion models and brain-inspired neuromorphic computing with memristors

Wann
Donnerstag, 15. Dezember 2022
17 bis 0 Uhr

Wo
Universität Konstanz A702

Veranstaltet von

Vortragende Person/Vortragende Personen:
Ansgar Jüngel (TU Wien)

More than 50 years ago, Moore predicted that the number of transistors on a microchip doubles every two years. This exponential growth is ending today because of physical limits, and new technologies are needed. Neuromorphic computing seems to be a promising avenue. An encouraging device as technology enabler of neuromorphic computing is the memristor. Memristors can be seen as nonlinear resistors with memory, mimicking the conductance response of biological synapses.

This talk is concerned with the mathematical analysis of three-species drift-diffusion equations for memristors. Previous results in the literature regard only two species or two space dimensions. We are able to prove the global existence of weak solutions in any space dimension as well as the uniform-in-time boundedness of the solutions and the fast-relaxation limit in two dimensions. The key ideas of the proof are the use of the entropy method and a combination of local and global compactness results. Numerical experiments in one dimension reproduce hysteresis effects in the current-voltage characteristics, which are a fingerprint for memristive devices.