We developed a physics-informed neural network based on a mixture of Cartesian grid sampling and Latin hypercube sampling to solve forward and backward modified diffusion equations. We optimized the ...

Physics-Informed Neural Networks (PINNs) augment traditional neural architectures by embedding the governing equations of physical systems directly into the loss function. Instead of solely minimising ...

Whether it's physical phenomena, share prices or climate models—many dynamic processes in our world can be described mathematically with the aid of partial differential equations. Thanks to ...

We mentioned before about the \(+ c\) term. We are now going to look at how to find the value of \(c\) when additional information is given in the question.

When integrating simple expressions, the constant of integration, the \(+ c\) term, may remain an unknown. The value of \(c\) can be worked out when additional information is given in the question, .

We all know how differential equations are a crucial part of engineering design and analysis. We have some powerful software tools for this today. Well, here is what led up to our modern analysis ...