Delayed random walks: Identification with neural networks

Dávid András Horváth and Tamás Kalmár-Nagy

Chaos, Solitons & Fractals, 2026, vol. 210, issue P2

Abstract: Delayed random walks represent a simple model capturing feedback delay and noise, relevant for understanding metastable dynamics and stochastic resonance. We construct neural network models that can capture statistical properties of delayed random walks as well as generate random sequences with these statistical properties. We introduce two architectures based on the Long Short-Term Memory (LSTM), a variant of recurrent neural networks: the delay LSTM, which infers the time delay from a time series, and the timeseries LSTM, which forecasts transition probabilities at each timestep. For comparison, we derive a Maximum Likelihood Estimator (MLE) to directly recover the governing parameters (transition probability and delay) from the data. The delay LSTM not only provides better parameter estimates than the MLE, but is applicable to systems lacking an analytical MLE. The timeseries LSTM is trained on the delayed random walks and can generate random sequences (surrogate series) that correctly capture statistical properties, such as the root mean square position of the original process. The distribution of the generated sequences shows little deviation from that of the random walks.

Keywords: Neural networks; Machine learning; Delayed random walks; Time delay (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:210:y:2026:i:p2:s0960077926008520

DOI: 10.1016/j.chaos.2026.118711

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