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Konstantin Volkov
The opportunities provided by new information technologies, object-oriented programming tools, and modern operating systems for solving boundary value problems in CFD described by partial differential equations are discussed. An approach to organizing ve...
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Christos Tzimopoulos, Kyriakos Papadopoulos, Nikiforos Samarinas, Basil Papadopoulos and Christos Evangelides
In this work, a novel fuzzy FEM (Finite Elements Method) numerical solution describing the recession flow in unconfined aquifers is proposed. In general, recession flow and drainage problems can be described by the nonlinear Boussinesq equation, while th...
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Shancheng Tang, Ying Zhang, Zicheng Jin, Jianhui Lu, Heng Li and Jiqing Yang
The number of defect samples on the surface of aluminum profiles is small, and the distribution of abnormal visual features is dispersed, such that the existing supervised detection methods cannot effectively detect undefined defects. At the same time, t...
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Andrea D?Ambrosio and Roberto Furfaro
This paper demonstrates the utilization of Pontryagin Neural Networks (PoNNs) to acquire control strategies for achieving fuel-optimal trajectories. PoNNs, a subtype of Physics-Informed Neural Networks (PINNs), are tailored for solving optimal control pr...
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Lin Guo, Anand Balu Nellippallil, Warren F. Smith, Janet K. Allen and Farrokh Mistree
When dealing with engineering design problems, designers often encounter nonlinear and nonconvex features, multiple objectives, coupled decision making, and various levels of fidelity of sub-systems. To realize the design with limited computational resou...
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Ferenc Izsák and Rudolf Izsák
A neural-network-assisted numerical method is proposed for the solution of Laplace and Poisson problems. Finite differences are applied to approximate the spatial Laplacian operator on nonuniform grids. For this, a neural network is trained to compute th...
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Ferenc Izsák and Taki Eddine Djebbar
We propose neural-network-based algorithms for the numerical solution of boundary-value problems for the Laplace equation. Such a numerical solution is inherently mesh-free, and in the approximation process, stochastic algorithms are employed. The chief ...
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James T. Jenkins and Michele Larcher
Kinetic theory is used to propose and solve boundary value problems for fully developed, steady, dense gravity-driven flows of mixtures composed of identical inelastic spheres and water over both inclined erodible beds and rigid, bumpy bases confined by ...
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Elettra Agliardi and Rossella Agliardi
A new explicit form is provided for the solution of optimal stopping problems involving a multidimensional geometric Brownian motion. A free-boundary value approach is adopted and the value function is obtained via fundamental solution methods. There are...
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Efthimios Providas and Ioannis Nestorios Parasidis
Integro-differential equations involving Volterra and Fredholm operators (VFIDEs) are used to model many phenomena in science and engineering. Nonlocal boundary conditions are more effective, and in some cases necessary, because they are more accurate me...
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