Sina Aghaee Dabaghan Fard

Sina Aghaee Dabaghan Fard, Marie Maros, Jaesung Lee

We introduce an efficient Bayesian deep ensemble method for predictive regression designed to enhance interpretability while maintaining competitive predictive performance and computational efficiency. Our method combines the statistical rigor of Bayesian inference with the scalability of deep ensembles, providing calibrated uncertainty estimates that enable its use not only for standalone prediction but also as a component within broader learning systems. To achieve these goals, our work relies on three key design components: (i) low-dimensional ensemble representation: predictions are expressed as a combination of a small number of trained neural predictors, enabling scalable inference whose cost depends on ensemble size rather than dataset size; (ii) closed-form Bayesian aggregation: ensemble predictions are combined using Bayesian linear regression, yielding interpretable posterior weights and calibrated uncertainty without approximate inference; and (iii) Independent ensemble training: multiple neural networks are trained separately, producing diverse predictive representations that improve robustness and uncertainty calibration. Empirical results on standard regression benchmarks demonstrate that the proposed approach achieves competitive predictive performance while maintaining reliable uncertainty estimates across settings.

Tatthapong Srikitrungruang, Matthew Lemon, Sina Aghaee Dabaghan Fard et al.

Accurately estimating spatially heterogeneous elasticity parameters, particularly Young's modulus and Poisson's ratio, from noisy displacement measurements remains significantly challenging in inverse elasticity problems. Existing inverse estimation techniques are often limited by instability, pronounced sensitivity to measurement noise, and difficulty in recovering absolute-scale Young's modulus. This work presents a novel Inverse Elasticity Physics-Informed Neural Network (IE-PINN) specifically designed to robustly reconstruct heterogeneous distributions of elasticity parameters from noisy displacement data based on linear elasticity physics. IE-PINN integrates three distinct neural network architectures dedicated to separately modeling displacement fields, strain fields, and elasticity distributions, thereby significantly enhancing stability and accuracy against measurement noise. Additionally, a two-phase estimation strategy is introduced: the first phase recovers relative spatial distributions of Young's modulus and Poisson's ratio, and the second phase calibrates the absolute scale of Young's modulus using imposed loading boundary conditions. Additional methodological innovations, including positional encoding, sine activation functions, and a sequential pretraining protocol, further enhance the model's performance and robustness. Extensive numerical experiments demonstrate that IE-PINN effectively overcomes critical limitations encountered by existing methods, delivering accurate absolute-scale elasticity estimations even under severe noise conditions. This advancement holds substantial potential for clinical imaging diagnostics and mechanical characterization, where measurements typically encounter substantial noise.