<abstract><p>In this paper, we approximate traveling wave solutions via artificial neural networks. Finding traveling wave solutions can be interpreted as a forward-inverse problem that solves a differential equation without knowing the exact speed. In general, we require additional restrictions to ensure the uniqueness of traveling wave solutions that satisfy boundary and initial conditions. This paper is based on the theoretical results that the bistable three-species competition system has a unique traveling wave solution on the premise of the monotonicity of the solution. Since the original monotonic neural networks are not smooth functions, they are not suitable for representing solutions of differential equations. We propose a method of approximating a monotone solution via a neural network representing a primitive function of another positive function. In the numerical integration, the operator learning-based neural network resolved the issue of differentiability by replacing the quadrature rule. We also provide theoretical results that a small training loss implies a convergence to a real solution. The set of functions neural networks can represent is dense in the solution space, so the results suggest the convergence of neural networks with appropriate training. We validate that the proposed method works successfully for the cases where the wave speed is identical to zero. Our monotonic neural network achieves a small error, suggesting that an accurate speed and solution can be estimated when the sign of wave speed is known.</p></abstract>

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Seismic performance evaluation of existing building usually needs much time and man power, especially in case of nonlinear analysis. Many data interaction steps for model transfer are needed and engineers should spend much time with simple works like data entry. Those time-consuming steps could be reduced by applying computerized and automated modules. In this study, computational platform for seismic performance evaluation was made with several computerized modules. StrAuto and floor load transfer module offers a path that can transfer most linear model data to nonlinear analysis model so that engineers can avoid a lot of repetitive work for input information for the nonlinear analysis model. And the new nonlinear property generator also helps to get the nonlinear data easily by importing data from structural design program. To evaluate the effect of developed modules on each stages, seismic performance evaluation of example building was carried out and the lead time was used for the quantitative evaluation.

<abstract><p>We consider the mathematical model of chemotaxis introduced by Patlak, Keller, and Segel. Aggregation and progression waves are present everywhere in the population dynamics of chemotactic cells. Aggregation originates from the chemotaxis of mobile cells, where cells are attracted to migrate to higher concentrations of the chemical signal region produced by themselves. The neural net can be used to find the approximate solution of the PDE. We proved that the error, the difference between the actual value and the predicted value, is bound to a constant multiple of the loss we are learning. Also, the Neural Net approximation can be easily applied to the inverse problem. It was confirmed that even when the coefficient of the PDE equation was unknown, prediction with high accuracy was achieved.</p></abstract>