# A recursive Bayesian neural network for constitutive modeling of sands under monotonic and cyclic loading

arXiv: https://arxiv.org/abs/2501.10088 · HTML: https://mlsanity.com/paper/2501.10088/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 65 references that are in the map.
- First posted on arXiv 17 Jan 2025.

## Builds on (most cited first, 10 of 10)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [Scheduled Sampling for Sequence Prediction with Recurrent Neural Networks](https://mlsanity.com/paper/1506.03099/) (2015)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [A Primer on PAC-Bayesian Learning](https://mlsanity.com/paper/1901.05353/) (2019)
- [TensorFlow Distributions](https://mlsanity.com/paper/1711.10604/) (2017)
- [Priors in Bayesian Deep Learning: A Review](https://mlsanity.com/paper/2105.06868/) (2021)
- [Generalized Variational Inference: Three arguments for deriving new Posteriors](https://mlsanity.com/paper/1904.02063/) (2019)
- [Robust Generalised Bayesian Inference for Intractable Likelihoods](https://mlsanity.com/paper/2104.07359/) (2021)

## Abstract (arXiv)

In geotechnical engineering, constitutive models are central to capturing soil behavior across diverse drainage conditions, stress paths,and loading histories. While data driven deep learning (DL) approaches have shown promise as alternatives to traditional constitutive formulations, their deployment requires models that are both accurate and capable of quantifying predictive uncertainty. This study introduces a recursive Bayesian neural network (rBNN) framework that unifies temporal sequence learning with generalized Bayesian inference to achieve both predictive accuracy and rigorous uncertainty quantification. A key innovation is the incorporation of a sliding window recursive structure that enables the model to effectively capture path dependent soil responses under monotonic and cyclic loading. By treating network parameters as random variables and inferring their posterior distributions via generalized variational inference, the rBNN produces well calibrated confidence intervals alongside point predictions.The framework is validated against four datasets spanning both simulated and experimental triaxial tests: monotonic loading using a Hardening Soil model simulation and 28 CD tests on Baskarp sand, and cyclic loading using an exponential constitutive simulation of CD CU tests and 37 experimental cyclic CU tests on Ottawa F65 sand. This progression from monotonic to cyclic and from simulated to experimental data demonstrates the adaptability of the proposed approach across varying levels of data fidelity and complexity. Comparative analyses with LSTM, Encoder Decoder,and GRU architectures highlight that rBNN not only achieves competitive predictive accuracy but also provides reliable confidence intervals.