Although synaptic behaviours of memristors have been widely demonstrated, implementation of an even simple artificial neural network is still a great challenge. In this work, we demonstrate the associative memory on the basis of a memristive Hopfield network. Different patterns can be stored into the memristive Hopfield network by tuning the resistance of the memristors, and the pre-stored patterns can be successfully retrieved directly or through some associative intermediate states, being analogous to the associative memory behaviour. Both single-associative memory and multi-associative memories can be realized with the memristive Hopfield network.

We study the paired-pulse-induced response of a NiO_x-based memristor. The behavior of the memristor is surprisingly similar to the paired-pulse facilitation of a biological synapse. When the memristor is stimulated with a pair of electrical pulses, the current of the memristor induced by the second pulse is larger than that by the first pulse. In addition, the magnitude of the facilitation decreases with the pulse interval, while it increases with the pulse magnitude or pulse width.

In this study, multilayer perceptron artificial neural networks are used to predict orthodontic treatment plans, including the determination of extraction-nonextraction, extraction patterns, and anchorage patterns. The neural network can output the feasibilities of several applicable treatment plans, offering orthodontists flexibility in making decisions. The neural network models show an accuracy of 94.0% for extraction-nonextraction prediction, with an area under the curve (AUC) of 0.982, a sensitivity of 94.6%, and a specificity of 93.8%. The accuracies of the extraction patterns and anchorage patterns are 84.2% and 92.8%, respectively. The most important features for prediction of the neural networks are “crowding, upper arch” “ANB” and “curve of Spee”. For handling discrete input features with missing data, the average value method has a better complement performance than thek-nearest neighbors (k-NN) method; for handling continuous features with missing data,k-NN performs better than the other methods most of the time. These results indicate that the proposed method based on artificial neural networks can provide good guidance for orthodontic treatment planning for less-experienced orthodontists.

The well-known Ebbinghaus forgetting curve, which describes how information is forgotten over time, can be emulated using a NiO-based memristor with conductance that decreases with time after the application of electrical pulses. Here, the conductance is analogous to the memory state, while each electrical pulse represents a memory stimulation or learning event. The decrease in the conductance with time depends on the stimulation parameters, including pulse height and width and the number of pulses, which emulates memory loss behavior well in that the time taken for the memory to be lost depends on how the information is learned.

Synaptic memristor has attracted much attention for its potential applications in artificial neural networks (ANNs). However useful applications in real life with such memristor-based networks have seldom been reported. In this paper, an ANN based on memristors is designed to learn a multi-variable regression model with a back-propagation algorithm. A weight unit circuit based on memristor, which can be programed as an excitatory synapse or inhibitory synapse, is introduced. The weight of the electronic synapse is determined by the conductance of the memristor, and the current of the synapse follows the charge-dependent relationship. The ANN has the ability to learn from labeled samples and make predictions after online training. As an example, the ANN was used to learn a regression model of the house prices of several Boston towns in the USA and the predicted results are found to be close to the target data.

Although there is a huge progress in complementary-metal-oxide-semiconductor (CMOS) technology, construction of an artificial neural network using CMOS technology to realize the functionality comparable with that of human cerebral cortex containing 10¹⁰–10¹¹ neurons is still of great challenge. Recently, phase change memristor neuron has been proposed to realize a human-brain level neural network operating at a high speed while consuming a small amount of power and having a high integration density. Although memristor neuron can be scaled down to nanometer, integration of 10¹⁰–10¹¹ neurons still faces many problems in circuit complexity, chip area, power consumption, etc. In this work, we propose a CMOS compatible HfO₂ memristor neuron that can be well integrated with silicon circuits. A hybrid Convolutional Neural Network (CNN) based on the HfO₂ memristor neuron is proposed and constructed. In the hybrid CNN, one memristive neuron can behave as multiple physical neurons based on the Time Division Multiplexing Access (TDMA) technique. Handwritten digit recognition is demonstrated in the hybrid CNN with a memristive neuron acting as 784 physical neurons. This work paves the way towards substantially shrinking the amount of neurons required in hardware and realization of more complex or even human cerebral cortex level memristive neural networks.