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For any given neural network architecture a permutation of weights and biases results in the same functional network. This implies that optimization algorithms used to 'train' or 'learn' the network are faced with a very large number (in the millions even for small networks) of equivalent optimal solutions in the parameter space. To the best of our knowledge, this observation is absent in the literature. In order to narrow down the parameter search space, a novel technique is introduced in order to fix the bias vector configurations to be monotonically increasing. This is achieved by augmenting a typical learning problem with inequality constraints on the bias vectors in each layer. A Moreau-Yosida regularization based algorithm is proposed to handle these inequality constraints and a theoretical convergence of this algorithm is established. Applications of the proposed approach to standard trigonometric functions and more challenging stiff ordinary differential equations arising in chemically reacting flows clearly illustrate the benefits of the proposed approach. Further application of the approach on the MNIST dataset within TensorFlow, illustrate that the presented approach can be incorporated in any of the existing machine learning libraries.

 

Purpose The purpose of this study is to compare interpolation algorithms and deep neural networks for inverse transfer problems with linear and nonlinear behaviour. Design/methodology/approach A series of runs were conducted for a canonical test problem. These were used as databases or “learning sets” for both interpolation algorithms and deep neural networks. A second set of runs was conducted to test the prediction accuracy of both approaches. Findings The results indicate that interpolation algorithms outperform deep neural networks in accuracy for linear heat conduction, while the reverse is true for nonlinear heat conduction problems. For heat convection problems, both methods offer similar levels of accuracy. Originality/value This is the first time such a comparison has been made. 

A high fidelity model for the propagation of pathogens via aerosols in the presence of moving pedestrians is proposed. The key idea is the tight coupling of computational fluid dynamics and computational crowd dynamics in order to capture the emission, transport and inhalation of pathogen loads in space and time. An example simulating pathogen propagation in a narrow corridor with moving pedestrians clearly shows the considerable effect that pedestrian motion has on airflow, and hence on pathogen propagation and potential infectivity.

 

Purpose The purpose of this study is to determine the possibility of an accurate assessment of the spatial distribution of material properties such as conductivities or impedances from boundary measurements when the governing partial differential equation is a Laplacian. Design/methodology/approach A series of numerical experiments were carefully performed. The results were analyzed and compared. Findings The results to date show that while the optimization procedure is able to obtain spatial distributions of the conductivity k that reduce the cost function significantly, the resulting conductivity k is still significantly different from the target (or real) distribution sought. While the normal fluxes recovered are very close to the prescribed ones, the tangential fluxes can differ considerably. Research limitations/implications At this point, it is not clear why rigorous mathematical proofs yield results of convergence and uniqueness, while in practice, accurate distributions of the conductivity k seem to be elusive. One possible explanation is that the spatial influence of conductivities decreases exponentially with distance. Thus, many different conductivities inside a domain could give rise to very similar (infinitely close) boundary measurements. Practical implications This implies that the estimation of field conductivities (or generally field data) from boundary data is far more difficult than previously assumed when the governing partial differential equation in the domain is a Laplacian. This has consequences for material parameter assessments (e.g. for routine maintenance checks of structures), electrical impedance tomography, and many other applications. Originality/value This is the first time such a finding has been reported in this context.