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Bayesian method is capable of capturing real world uncertainties/incompleteness and properly addressing the over-fitting issue faced by deep neural networks. In recent years, Bayesian Neural Networks (BNNs) have drawn tremendous attentions…
Segmentation of nuclei regions from histological images enables morphometric analysis of nuclei structures, which in turn helps in the detection and diagnosis of diseases under consideration. To develop a nuclei segmentation algorithm,…
The aim of this work is to present a model reduction technique in the framework of optimal control problems for partial differential equations. We combine two approaches used for reducing the computational cost of the mathematical numerical…
We present a data-enabled physics-informed neural network (DEPINN) with comprehensive numerical study for solving industrial scale neutron diffusion eigenvalue problems (NDEPs). In order to achieve an engineering acceptable accuracy for…
Power delivery network (PDN) design is a nontrivial, time-intensive, and iterative task. Correct PDN design must account for considerations related to power bumps, currents, blockages, and signal congestion distribution patterns. This work…
The analysis of variance (ANOVA) decomposition offers a systematic method to understand the interaction effects that contribute to a specific decision output. In this paper we introduce Neural-ANOVA, an approach to decompose neural networks…
Recently, several optimization methods have been successfully applied to the hyperparameter optimization of deep neural networks (DNNs). The methods work by modeling the joint distribution of hyperparameter values and corresponding error.…
Decentralized state estimation in a communication-constrained sensor network is considered. The exchanged estimates are dimension-reduced to reduce the communication load using a linear mapping to a lower-dimensional space. The mean squared…
Large optimal transport problems can be approached via domain decomposition, i.e. by iteratively solving small partial problems independently and in parallel. Convergence to the global minimizers under suitable assumptions has been shown in…
Most machine vision tasks (e.g., semantic segmentation) are based on images encoded and decoded by image compression algorithms (e.g., JPEG). However, these decoded images in the pixel domain introduce distortion, and they are optimized for…
Most state of the art deep neural networks are overparameterized and exhibit a high computational cost. A straightforward approach to this problem is to replace convolutional kernels with its low-rank tensor approximations, whereas the…
Neural networks are one tool for approximating non-linear differential equations used in scientific computing tasks such as surrogate modeling, real-time predictions, and optimal control. PDE foundation models utilize neural networks to…
Deep neural networks ( DNNs ) are becoming a key enabling technology for many application domains. However, on-device inference on battery-powered, resource-constrained embedding systems is often infeasible due to prohibitively long…
A challenging part of dynamic probabilistic risk assessment for nuclear power plants is the need for large amounts of temporal simulations given various initiating events and branching conditions from which representative feature extraction…
This paper presents a power distribution network (PDN) decoupling capacitor optimization application with three primary goals: reduction of solution times for large networks, development of flexible network scoring routines, and a…
This article presents an original methodology for the prediction of steady turbulent aerodynamic fields. Due to the important computational cost of high-fidelity aerodynamic simulations, a surrogate model is employed to cope with the…
The majority of AI models in imaging and vision are customized to perform on specific high-precision task. However, this strategy is inefficient for applications with a series of modular tasks, since each requires a mapping into a disparate…
Long-range interactions play a central role in electron transport. At the same time, they present a challenge for direct computer simulations, since sufficiently large portions of the bath have to be included in the computation to…
A classic approach for solving differential equations with neural networks builds upon neural forms, which employ the differential equation with a discretisation of the solution domain. Making use of neural forms for time-dependent…
A nonlinear-manifold reduced order model (NM-ROM) is a great way of incorporating underlying physics principles into a neural network-based data-driven approach. We combine NM-ROMs with domain decomposition (DD) for efficient computation.…