Analyzing the effects of uncertainties on complex multidisciplinary and coupled systems is a challenging problem when high-fidelity mathematical models of such systems are expensive to evaluate. Surrogate modeling methods can be used to overcome the computational challenge. However, most surrogate methods cannot be scaled to large-scale multidisciplinary systems or they do not resolve the coupling between disciplines. This paper proposes a novel surrogate modeling methodology called multidisciplinary iterative neural networks (MINNs). The proposed approach consists of replacing discipline models with neural network models that are trained using an iterative procedure to couple the networks. The MINNs approach is characterized using an analytical two-discipline multidisciplinary problem. The trained models are used to perform uncertainty propagation and analyze the sensitivity of one discipline to the other. The results demonstrated that the MINN formulation can achieve less than 1
Solving the p-Laplace equation numerically is challenging due to inherent degeneracies and singularities. We present a new hybrid strategy combining Continuous Data Assimilation, Picard iteration with Anderson Acceleration, and Newton’s Method. By incorporating coarse-mesh observations via a nudging term, the scheme provides essential spatial regularization. Our results show that this integration stabilizes nonlinear iterations and significantly improves convergence speed. Notably, the CDA-enhanced solver captures localized singular behaviors and suppresses oscillations in highly nonlinear regimes where standard methods typically fail.
The solution of large, sparse linear systems often dominates the computational effort of scientific applications and is a frequent optimization target. Modern libraries provide numerous solver and preconditioner configurations, but their performance varies significantly across problem instances. Previous works have addressed the selection of an optimal solver, but are typically limited by the problem set addressed (e.g., only symmetric positive definite matrices), the use of expensive matrix features, or the complexity of the approach. This work proposes a modular, low-cost embedding-based framework for solver selection that decouples performance modeling from feature representation and downstream prediction. Solver-problem relationships are learned directly from observed performance data, while inexpensive numerical features are used to project unseen problems into the learned embedding space. The framework focuses on multilabel prediction and evaluation using user-centric metrics, such as MAPE and nDCG, which better reflect relative performance. Experiments on 621 matrices from the SuiteSparse matrix collection across 101 PETSc solver configurations demonstrate a 17
Understanding nonlinear feature interactions is crucial in science and engineering, yet standard multilayer perceptrons (MLPs) often capture such interactions only implicitly, leading to entangled representations that can impair robustness and interpretability. We investigate product-unit residual networks (PURe) that integrate multiplicative product units with residual connections to explicitly model cross-feature couplings while stabilizing optimization. We conduct a systematic evaluation on an interaction-driven synthetic benchmark and two real-world datasets, assessing predictive accuracy, robustness to Gaussian feature noise, and performance under limited training data, and we compare real- and complex-valued variants under a matched parameter budget. Beyond accuracy, SHapley Additive exPlanations (SHAP)-based interaction analyses show that PURe learns more concentrated and structurally coherent interaction patterns than MLP baselines. Overall, PURe achieves competitive or improved performance, better robustness and sample efficiency in low-data regimes, and enhanced interaction-level interpretability.
In CT angiography, the accurate segmentation of abdominal aortic aneurysms (AAAs) is difficult due to large anatomical variability, low-contrast vessel boundaries, and the close proximity of organs whose intensities resemble vascular structures, often leading to false positives. To address these challenges, we propose an anatomy-aware segmentation framework that integrates organ exclusion masks derived from TotalSegmentator into the training process. These masks encode explicit anatomical priors by identifying non-vascular organsand penalizing aneurysm predictions within these regions, thereby guiding the U-Net to focus on the aorta and its pathological dilation while suppressing anatomically implausible predictions. Despite being trained on a relatively small dataset, the anatomy-aware model achieves high accuracy, substantially reduces false positives, and improves boundary consistency compared to a standard U-Net baseline. The results demonstrate that incorporating anatomical knowledge through exclusion masks provides an efficient mechanism to enhance robustness and generalization, enabling reliable AAA segmentation even with limited training data.
