PINN API

Physics-Informed Neural Networks

PINNModule

Base class for physics-informed models. Defines the pde_residual method.

class HeatEquationPINN(PINNModule):
    def pde_residual(self, x, t, u):
        u_t = grad(u, t)
        u_xx = grad(grad(u, x), x)
        return u_t - self.D * u_xx

Samplers

CollocationSampler

Samples points in the domain \(\Omega \times [0, T]\) for PDE loss computation.

• UniformSampler: Uniform grid.
• LatinHypercubeSampler: LHS sampling for better coverage.

Boundary Conditions

DirichletBC

Fixed value boundary condition: \(u(x) = g(x)\).

NeumannBC

Fixed derivative boundary condition: \(\frac{\partial u}{\partial n} = h(x)\).