Product Unit Networks Research Articles

Predicting nuclear masses with product-unit networks

Accurate estimation of nuclear masses and their prediction beyond the experimentally explored domains of the nuclear landscape are crucial to an understanding of the fundamental origin of nuclear properties and to many applications of nuclear science, most notably in quantifying the r-process of stellar nucleosynthesis. Neural networks have been applied with some success to the prediction of nuclear masses, but they are known to have shortcomings in application to extrapolation tasks. In this work, we propose and explore a novel type of neural network for mass prediction in which the usual neuron-like processing units are replaced by complex-valued product units that permit multiplicative couplings of inputs to be learned from the input data. This generalized network model is tested on both interpolation and extrapolation data sets drawn from the Atomic Mass Evaluation. Its performance is compared with that of common neural-network architectures, substantiating its suitability for nuclear-mass prediction. Additionally, a prediction-uncertainty measure for such complex-valued networks is proposed that allows identifying nuclides of expected large prediction error. Within and beyond the experimentally explored domain, model predictions are evaluated by computing deviations from the Garvey-Kelson relations.

Influence of the choice of stream temperature model on the projections of water temperature in rivers

In the majority of studies aiming at stream temperature warming due to climate change just a single water temperature model is used. Choosing a single model may highly impact the conclusions from the study. In this paper four relatively different empirical or semi-empirical models: perceptron neural networks, product unit networks, extended logistic regression and air2stream were applied to project the impact of climate change on water temperature in rivers located in temperate climatic zones of the USA and Poland. The models were driven by daily air temperature and streamflow projected by the rainfall-runoff model. In the first step, the models were calibrated and validated. Then the projections of water temperature were derived for the historical periods and two future periods taking into account: (a) climate simulations from the CORDEX initiative (NA-CORDEX and EURO-CORDEX), (b) the GR4J rainfall-runoff model and (c) different water temperature models. The obtained results indicate that due to global warming, the stream temperatures are expected to increase by about 1–2 °C for 2021–2050 and by 2–3 °C for 2071–2100 periods. These changes are not uniformly distributed throughout the year. The largest warming in the USA is found in the summertime, in Poland – in spring and autumn. For some months the discrepancies in the projected stream temperature between various stream temperature models are large. Product unit neural network, logistic regression-based model or air2stream occasionally led to projections that differ from those obtained by the majority of models even by 2 °C. We strongly recommend using at least a few stream temperature models for analysing the impact of climate change on water temperatures or the fate of the aquatic ecosystem.

Analysis of the energy potential of tidal streams on the Faroe Shelf

A first estimate of the energy potential in the tidal streams on the Faroe Shelf is derived from a barotropic numerical model with 100 m resolution. A total of 13 sites are identified as potential candidates for the harvest of the tidal stream energy with a total available mean energy flux in transects through these locations exceeding 2 GW. Of this 214–886 MW is in areas with depths larger than 40 m and peak velocities above 2.5 ms−1, where the lower estimate is for the mean tide and the higher estimate is with 8 constituents included in the assessment. Lowering the criteria for the peak velocities expands the potential areas significantly. A relatively large diversity of tidal phasing between the sites is identified suggesting good opportunities to construct a network of production units with a low ebb/flood variability.

E|Flow - From Production Line Concept to a Physically and Digitally Full-Meshed Production Network

The continuous change of the consumers’ behavior combined with the impact of new technologies to the shop-floor is a challenge for the classic and established line production. Due to the effects of mass-customization there is an increase of the variants of the products combined with a reduction of the number of units per variation. Therefore, it is necessary that the next generations of production lines, especially the assembling devices, have to be designed more adaptable. Regarding to business information systems this trend is realized by a progressive digital integration of the particular units. However, at the physical level of the value stream the sequenced units are linked to each other and arranged flow-orientated since Taylor. Particularly, for mass production the so called “line concept” is well established. This inflexibility of the physical material flow blocks the spread of mass-customization into established industrial sectors where linked manufacturing steps are common use. A product which is very individualized is not, or only with an additional expense, producible on such linked lines. Therefore, it is necessary to resolve the linking of the physical material flow similar to the digital integration of the work flow. The result will be a physically and digitally full-meshed network of production units with a high variability. Especially for a production of goods with a high variant diversity the benefits of a physically meshed production site are obvious. Each part gets its own and individual routing, which depends on the current machine availability, the set-up and other factors. Furthermore, a change of the general conditions during the manufacturing of the part can be considered and lead to an adaption of the routing. One of the most important parts of a flexible physical production network is the transport system, consisting of autonomous and smart entities which are interconnected with business information systems, products and machines.

An optimised product-unit neural network with a novel PSO–BP hybrid training algorithm: Applications to load–deformation analysis of axially loaded piles

In general, neural network training is a nonlinear multivariate optimisation problem. Unlike previous studies, in the present study, particle swarm optimisation (PSO) and back-propagation (BP) algorithms were coupled to develop a robust hybrid training algorithm with both local and global search capabilities. To demonstrate the capacity of the proposed model, we applied the model to the predictions of the load–deformation behaviour of axially loaded piles. This is a soil–structure interaction problem, involving a complex mechanism of load transfer from the pile to the supporting geologic medium. A database of full scale pile loading tests is used to train and validate the product-unit network. The results show that the proposed hybrid learning algorithm simulates the load–deformation curve of axially loaded piles more accurately than other BP, PSO, and existing PSO–BP hybrid methods. The network developed using the proposed algorithm also turns out to be more accurate than hyperbolic and t−z models.

Improvement of accuracy in a sound synthesis method using Evolutionary Product Unit Networks

Auralization through binaural transfer path analysis and synthesis is a useful tool to analyze how contributions from different sources affect the perception of sound. This paper presents a novel model based on the auralization of sound sources through the study of the behavior of the system with respect to frequency. The proposed approach is a combined model using the airborne source quantification (ASQ) technique for low-mid frequencies (⩽2.5kHz) and Evolutionary Product-Unit Neural Networks (EPUNNs) for high frequencies (>2.5kHz), which improve overall accuracy. The accuracy of all models has been evaluated in terms of the Mean Squared Error (MSE) and the Standard Error of Prediction (SEP), the combined model obtaining the smallest value for high frequencies. Moreover, the best prediction model was established based on sound quality metrics, the proposed method showing better accuracy than the ASQ technique at high frequencies in terms of loudness, sharpness and 1/3rd octave bands.

Firm-network characteristics and economic robustness to natural disasters

This article proposes a theoretical framework to investigate economic robustness to exogenous shocks such as natural disasters. It is based on a dynamic model that represents a regional economy as a network of production units through the disaggregation of sector-scale input–output tables. Results suggest that disaster-related output losses depend on direct losses heterogeneity and on the economic network structure. Two aggregate indexes – concentration and clustering – appear as important drivers of economic robustness, offering opportunities for robustness-enhancing strategies. Modern industrial organization seems to reduce short-term robustness in a trade-off against higher efficiency in normal times.

Assessing the Consequences of Natural Disasters on Production Networks: A Disaggregated Approach

This article proposes a framework to investigate the consequences of natural disasters. This framework is based on the disaggregation of Input-Output tables at the business level, through the representation of the regional economy as a network of production units. This framework accounts for (i) limits in business production capacity; (ii) forward propagations through input shortages; and (iii) backward propagations through decreases in demand. Adaptive behaviors are included, with the possibility for businesses to replace failed suppliers, entailing changes in the network structure. This framework suggests that disaster costs depend on the heterogeneity of losses and on the structure of the affected economic network. The model reproduces economic collapse, suggesting that it may help understand the difference between limited-consequence disasters and disasters leading to systemic failure.

Macro-invertebrates in a dynamic river environment: analysis of time series from artificial substrates, using a ‘white box’ neural network modelling method

New statistical modelling methods, such as neural networks (NNs), allow us to take a step further in the understanding of complex relations in aquatic ecosystems. In this paper the results from the analysis of macro-invertebrate communities in a complex riverine environment are presented. We attempted to explain observed changes in species composition and abundance with neural network modelling methods and compared the results to linear regression. The NN method used is an improved form of the RF5 algorithm, developed to effectively discover numeric laws from data. RF5 uses Product Unit Networks (PUNs), which are in effect multivariate non-discrete power functions. The data set consisted of a 10-year time series of monthly samples of macro-invertebrates on artificial substrates in the rivers Rhine and Meuse in the Netherlands. During this period the invertebrate community has largely changed coinciding with the invasion of Ponto-Caspian crustaceans. We used physical –chemical data and data on the abundance of the invasive taxa Corophium curvispinum and Dikerogammarus villosis to explain the observed changes in the resident invertebrate community. The analyses showed temperature, abundance of invasive taxa and peak discharges as important factors. Comparison of the results from NN modelling to linear regression revealed that the factors temperature and abundance of Dikerogammarus villosis explained equally well in both cases. Only the neural network was able to use information on peak discharge and timing of the peak in the previous winter to improve model performances. Neural networks are known to yield excellent modelling results, a drawback however is their lack of transparency or their ‘black box’ character. The use of relatively easy interpretable (white box) PUNs allows us to investigate the extracted relations in more detail and can enhance our understanding of ecosystem functioning. Our results show that peak discharges might be an important factor structuring invertebrate communities in rivers and hint on the existence of interacting effects from invasive species and discharge peaks. They finally show the value of biological data sets that are collected over a long period and in a highly standardised way.

On the complexity of computing and learning with multiplicative neural networks.

In a great variety of neuron models, neural inputs are combined using the summing operation. We introduce the concept of multiplicative neural networks that contain units that multiply their inputs instead of summing them and thus allow inputs to interact nonlinearly. The class of multiplicative neural networks comprises such widely known and well-studied network types as higher-order networks and product unit networks. We investigate the complexity of computing and learning for multiplicative neural networks. In particular, we derive upper and lower bounds on the Vapnik-Chervonenkis (VC) dimension and the pseudo-dimension for various types of networks with multiplicative units. As the most general case, we consider feedforward networks consisting of product and sigmoidal units, showing that their pseudo-dimension is bounded from above by a polynomial with the same order of magnitude as the currently best-known bound for purely sigmoidal networks. Moreover, we show that this bound holds even when the unit type, product or sigmoidal, may be learned. Crucial for these results are calculations of solution set components bounds for new network classes. As to lower bounds, we construct product unit networks of fixed depth with super-linear VC dimension. For sigmoidal networks of higher order, we establish polynomial bounds that, in contrast to previous results, do not involve any restriction of the network order. We further consider various classes of higher-order units, also known as sigma-pi units, that are characterized by connectivity constraints. In terms of these, we derive some asymptotically tight bounds. Multiplication plays an important role in both neural modeling of biological behavior and computing and learning with artificial neural networks. We briefly survey research in biology and in applications where multiplication is considered an essential computational element. The results we present here provide new tools for assessing the impact of multiplication on the computational power and the learning capabilities of neural networks.

An Aggregation Procedure for the Continuous Simulation of Production Units Organised in Network

The present tendency in industry is more and more cooperation between production units (workshops, factories, facilities, etc.). Then, the need of global evaluation of production units organised in network has emerged. In continuous simulation, the number of equations generated by the flows become impossible to take into account as soon as the number of units and the number of products increase. Then, to manage a reasonable number of equations, an aggregation procedure is required. Thus, the objective of this paper is to propose an aggregation procedure to reduce the number of flows exchanged inside a network of production units. This paper presents a five step aggregation procedure, respecting rules. This procedure is applied to an illustrative example at the end of the paper.

Dynamic hierarchical control for distributed problem solving

Distributed problem solving (DPS) has become one of the central topics in AI. Much research has been concerned with finding an appropriate distributed control regime. We propose the concept of dynamic, hierarchical control (DHC) for distributed problem solving. In many domains, DPS has a natural hierarchy or a subproblem hierarchy can be imposed by utilizing appropriate decomposition techniques. DHC aims at exploiting the power inherent in the hierarchical approach. It also enables the control of the problem solving process to fit the structure of a domain. This results in well-coordinated cooperation and coherent negotiation among distributed controllers. We have used the DHC to perform plant combine production planning (PCPP). This task involves the activity of a network of production units, each with possibly different characteristics, collaborating to produce various items under dynamically changing conditions. We also describe the general structure of a single controller which adopts a blackboard and a knowledge source (KS) scheduling mechanism to carry out dynamic process execution. The paper describes the results of our first solution to this problem. Finally, we discuss on-going research that aims at handling additional problems.