A $1 million prize awaits anyone who can show where the math of fluid flow breaks down. With specially trained AI systems, ...
Tessellations aren’t just eye-catching patterns—they can be used to crack complex mathematical problems. By repeatedly ...
Abstract: In this study, we presented numerical methods for determining the minimum energy state among three dynamic systems governed by a class of integro-differential equation with weakly singular ...
Abstract: Physics-Informed Neural Networks (PINNs) have recently emerged as a powerful method for solving differential equations by leveraging machine learning techniques. However, while neural ...
The parabolic equation (PE) serves as a fundamental methodology for modeling underwater acoustic propagation. The computational efficiency of this approach derives from the far-field approximation of ...
Physics-Informed Neural Networks (PINNs) provide a mesh-free approach for solving differential equations by embedding physical constraints into neural network training. However, PINNs tend to overfit ...
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