PINN-Practice

Physical Informed Neural Network Practice

Diffusion Equation

我们要求解的一个微分方程, 其中 $x, t\in[0,1]$, $$ \left{ \begin{aligned} u_t(x,t) &= \ u_{xx}(x,t) -c*sin(2\pi x)*u(x,t) \ u(x,t)& = \ u(x+1,t) \ u(x,0) & = 1 \end{aligned} \right. (1) $$

定义$f(x,t)$ , $g(x,t)$ , $h(x)$分别为:

$$ \left{ \begin{aligned} f: &=u_t(x,t) - \ u_{xx}(x,t) +c*sin(2\pi x)*u(x,t) \ g :&= u(x,t) - u(x+1,t) \ h :&= u(x,0) - 1 \end{aligned} \right. (2) $$