Mixture density networks as a probabilistic surrogate for cycle-to-cycle variability in filamentary HfOx-memristive devices: Data and code

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This zip-file contains the code and example data sets to rebuild the models, analysis and plots of the publication. Abstract: Memristive devices are promising candidates for next-generation computing hardware because they combine memoryand computation in a single scalable device. However, their resistive switching behavior is inherently stochastic,causing significant variability that complicates device characterization and predictive modeling. Existing modeling approachesoften rely on simplified variability descriptions and therefore do not fully capture the full probabilistic natureof switching behavior. In this work, we present a probabilistic surrogate model of HfOx-based memristive devicesbased on mixture density networks (MDNs). The network predicts the full conditional probability distribution of postpulseconductance values given the applied voltage, the prior conductance state, and the switching polarity. Trained andevaluated on experimental data, the MDN is able to capture unimodal distributions observed at low and high resistivestates and the multimodal distributions arising in between. Model performance is quantified using the coefficient ofdetermination R2 and the continuous ranked probability score (CRPS). The MDN achieves R2 = 0.95, explaining 95%of the observed variance in post-pulse conductance, and a CRPS of 4.8 μS, which corresponds to an average calibrationerror of only ≈3.5% of the full range, indicating well-calibrated predictive distributions with sufficient sharpness toresolve cycle-to-cycle variability. The MDN captures the dominant switching statistics with as few as 125 trainingsamples. The approach provides a practical, automatable framework for a data-efficient surrogate model of inherentlystochastic memristive devices and prediction of post-pulse conductance distributions. Details about the repository: This repository contains the relevant data, scripts and figures for the APL Machine Learning publication "Mixture density networks as a probabilistic surrogate for cycle-to-cycle variability in filamentary HfOx-memristive devices". If you are further interested in this work, please contact the author: tbe@tf.uni-kiel.de. The main scripts are described below: training_and_validation.py is the training and validation script. The number of training samples (from (data/train_val_samples_removed_outliers.csv)) to be used to train the MDNs, needs to be specified. predictions_for_testset.py uses the trained models to predict the probability density function of the conductance distribution for the input data from the test dataset (data/test_samples_removed_outliers.csv). evaluate_predictions_crps.py computes crps for all models. compute_r_squared.py computes R2 for all models. compute_specific_predictions_for_comparison.py is a script needed for Figure 4. MDN.py, MDN_loss.py and MDN_predict.py are helper functions for 1. and 2. . The folders are named straight forward: "data" contains preprocessed data samples that allow the use of the scripts. "figures" contains all scripts to recreate the data-based figures. "models" contains the trained models and scalers as a result of training_and_validation.py. "predictions" contains the predictions on the testset data as a result of predictions_for_testset.py. "results" contains the CRPS and R2 results. "runs" is a log-folder that is filled during the run of training_and_validation.py and coontais tensorboard files to track and analyze the training and validation process, if needed.

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