Soban Nasir Lone

Soban Nasir Lone, Subhayan De, Rajdip Nayek

We introduce a novel deep operator network (DeepONet) framework that incorporates generalised variational inference (GVI) using Rényi's $α$-divergence to learn complex operators while quantifying uncertainty. By incorporating Bayesian neural networks as the building blocks for the branch and trunk networks, our framework endows DeepONet with uncertainty quantification. The use of Rényi's $α$-divergence, instead of the Kullback-Leibler divergence (KLD), commonly used in standard variational inference, mitigates issues related to prior misspecification that are prevalent in Variational Bayesian DeepONets. This approach offers enhanced flexibility and robustness. We demonstrate that modifying the variational objective function yields superior results in terms of minimising the mean squared error and improving the negative log-likelihood on the test set. Our framework's efficacy is validated across various mechanical systems, where it outperforms both deterministic and standard KLD-based VI DeepONets in predictive accuracy and uncertainty quantification. The hyperparameter $α$, which controls the degree of robustness, can be tuned to optimise performance for specific problems. We apply this approach to a range of mechanics problems, including gravity pendulum, advection-diffusion, and diffusion-reaction systems. Our findings underscore the potential of $α$-VI DeepONet to advance the field of data-driven operator learning and its applications in engineering and scientific domains.

Toiba Noor, Soban Nasir Lone, G. V. Ramana et al.

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.