As feature-size scaling and "Moore's Law" in integrated CMOS circuits further slows down, attention is shifting to computing by non-von Neumann and non-Boolean computing models. Reservoir computing (RC) is a new computing paradigm that allows to harness the intrinsic dynamics of a "reservoir" to perform useful computations. The reservoir, or compute core, must only provide sufficiently rich dynamics that are then mapped onto a low-dimensional space by an readout layer. One of the key advantages of this approach is that only the readout layer needs to be adapted to perform the desired computation. The reservoir itself remains unchanged. In this paper we use for the first time memristive components as reservoir building blocks that are assembled into device networks. Memristive components are particularly interesting for this purpose because of their non-linear and memory characteristics. In addition, they can be integrated very densely and provide rich dynamics with a few components only. We use pattern recognition and associative memory tasks to illustrate the memristive reservoir computing approach. For that purpose, we have built a software framework that allows to create valid memristor networks, to simulate and evaluate them in Ngspice, and to train the readout layer by means of a Genetic Algorithm (GA). Our results show that we can efficiently and robustly classify temporal patterns. The approach presents a promising new computing paradigm that harnesses the non-linear, time-dependent, and highly-variable properties of current memristive components for solving computational tasks.

An associative memory is an essential building block for high-level networks for cognitive or brain-like computing. In this paper we consider the problem of designing associative memories using nanoscale memristors. Until now, memristors have been exploited solely as a synapse in neural networks. Our approach is novel because it exploits the analog, timedependent properties of memristors, resulting in more efficient and simpler designs. We have designed two complementary evolutionary frameworks for the automated discovery of circuits. The memristor-based circuits are evaluated using ngspice. Our best circuit only uses three memristors for a fully functional associative memory of two inputs. HP has demonstrated practical memristors working at 3nm x 3nm sizes in terms of area. At these densities our associative memory could easily rival even the current sub-25 nm flash memory technology.

In today's nanoscale era, scaling down to even smaller feature sizes poses a significant challenge in the device fabrication, the circuit, and the system design and integration. On the other hand, nanoscale technology has also led to novel materials and devices with unique properties. The memristor is one such emergent nanoscale device that exhibits non-linear current-voltage characteristics and has an inherent memory property, i.e., its current state depends on the past. Both the nonlinear and the memory property of memristors have the potential to enable solving spatial and temporal pattern recognition tasks in radically different ways from traditional binary transistor-based technology. The goal of this thesis is to explore the use of memristors in a novel computing paradigm called "Reservoir Computing" (RC). RC is a new paradigm that belongs to the class of artificial recurrent neural networks (RNN). However, it architecturally differs from the traditional RNN techniques in that the pre-processor (i.e., the reservoir) is made up of random recurrently connected non-linear elements. Learning is only implemented at the readout (i.e., the output) layer, which reduces the learning complexity significantly.To the best of our knowledge, memristors have never been used as reservoir components. We use pattern recognition and classification tasks as benchmark problems.Real world applications associated with these tasks include process control, speech recognition, and signal processing. We have built a software framework, RCspice (Reservoir Computing Simulation Program with Integrated Circuit Emphasis), for this purpose. The framework allows to create random memristor networks, to simulate and evaluate them in Ngspice, and to train the readout layer by means of Genetic Algorithms (GA). We have explored reservoir-related parameters, such as the network connectivity and the reservoir size along with the GA parameters.i Our results show that we are able to efficiently and robustly classify time-series patterns using memristor-based dynamical reservoirs. This presents an important step towards computing with memristor-based nanoscale systems.ii Acknowledgements