DEPARTMENT OF COMPUTATIONAL AND DATA SCIENCES
M.Tech Research Thesis Colloquium
Speaker : Mr. Jayanta Pari
S.R. Number : 06-18-01-10-12-22-2-22270
Title : ” Differential-Algebraic Equation(DAE) based model of Avalanche Dynamics in Ag-hBN memristor and Reservoir Computing.”
Research Supervisor : Prof. Soumyendu Raha
Date & Time : January 21, 2026, 15.00 PM
Venue : # 202 CDS Class Room
ABSTRACT
Memristive devices based on percolative tunnelling networks exhibit complex collective dynamics arising from the interaction of many nanoscale conductive paths. In particular, Ag–hBN memristive systems have been experimentally shown to display avalanche-like current fluctuations and signatures of self-organized criticality. However, the internal mechanisms responsible for these emergent behaviours are difficult to access experimentally due to the highly disordered and hidden nature of the network. This thesis develops a mathematical and computational framework to model and analyse avalanche dynamics in such memristive networks and to explore their potential for reservoir computing.
The device is modeled as a graph of nodes and edges, where each edge represents a tunnelling or filamentary conduction channel whose conductance evolves in time. Kirchhoff’s circuit laws are enforced through an algebraic constraint, while the internal filament dynamics are described by nonlinear differential equations, leading to a coupled differential–algebraic equation (DAE) system. Proper boundary conditions are imposed to ensure a well-posed, index-1 formulation suitable for stable numerical integration. Joule heating–induced filament dissolution is incorporated through a discrete update rule.
Numerical simulations are performed for both two-dimensional and quasi-three-dimensional network geometries. The resulting conductance time series exhibits intermittent burst-like activity. Statistical analysis of these fluctuations reveals power-law distributions of avalanche size and duration, long-range temporal correlations, and consistency with crackling-noise scaling relations.
The same DAE-based framework is then used as a physical reservoir for temporal information processing. A scalar input signal is applied as a sequence of voltages to multiple input nodes, and the resulting currents at multiple output nodes form a high-dimensional reservoir state. Linear readout training is performed using ridge regression to evaluate performance on benchmark temporal tasks. The results demonstrate that the intrinsic dynamics of percolative memristive networks can simultaneously support avalanche criticality and reservoir computing. All these highlight a direct connection between material-level dynamics and computation in neuromorphic systems.
ALL ARE WELCOME
