A systematic approach is developed for constructing proper trial solutions to Partial Differential Equations (PDEs) of up to second order, using neural forms that satisfy prescribed initial, boundary and interface conditions. The spatial domain considered is of the rectangular hyper-box type. On each face either Dirichlet or Neumann conditions may apply. Robin conditions may be accommodated as well. Interface conditions that induce discontinuities, have not been treated to date in the relevant neural network literature. As an illustration a common problem of heat conduction through a system of two rods in thermal contact is considered.

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Nuclear Power Plants (NPPs) are nowadays facing a transition from analog to digital control rooms, mainly in the form of new interfaces for displaying sensor information as of Human Machine Interface (HMI) were one-sided, taking into consideration either the human or the machine perspective. The approach presented in the present article considers human machine interfaces met in nuclear power plants as a joint system, where the performance of the NPP operator is evaluated according to the cooperation level achieved with the machine. In particular, the purpose of this study is to provide a methodology to evaluate the degree of flexibility of an operator during the transition period from an analog to a digital system. The proposed methodology has been implemented by utilizing fuzzy logic inference and realized with the fuzzy toolbox embedded in Matlab software.

Stochastic Gradient Descent (SGD) is perhaps the most frequently used method for large scale training. A common example is training a neural network over a large data set, which amounts to minimizing the corresponding mean squared error (MSE). Since the convergence of SGD is rather slow, acceleration techniques based on the notion of “Mini-Batches” have been developed. All of them however, mimicking SGD, impose diminishing step-sizes as a means to inhibit large variations in the MSE objective. In this article, we introduce random sets of mini-batches instead of individual mini-batches. We employ an objective function that minimizes the average MSE and its variance over these sets, eliminating so the need for the systematic step size reduction. This approach permits the use of state-of-the-art optimization methods, far more efficient than the gradient descent, and yields a significant performance enhancement.

Detection and identification of special nuclear materials (SNMs) are an essential part of the US nonproliferation effort. Modern cutting-edge SNM detection methodologies rely more and more on modeling and simulation techniques. Experiments with radiological samples in realistic configurations, is the ultimate tool that establishes the minimum detection limits of SNMs in a host of different geometries. Modern modeling and simulation approaches have the potential to significantly reduce the number of experiments with radioactive sources needed to determine these detection limits and reduce the financial barrier to SNM detection. Unreliable nuclear data is one of the principal causes of uncertainty in modeling and simulating nuclear systems. In particular, nuclear cross sections introduce a significant uncertainty in the nuclear data. The goal of this research is to develop a methodology that will autonomously extract the correct nuclear resonance characteristics of experimental data in a reliable way, a task previously left to expert judgement. Accurate nuclear data will in turn allow contemporary modeling and simulation to become far more reliable, de-escalating the extent of experimental testing. Consequently, modeling and simulation techniques reduce the use and distribution of radiological sources, while at the same time increase the reliability of the currently used methods for the detection and identification of SNMs.