Module gpu_neural_solver 

GPU neural network solver for physics (CPU mock backend).

Provides a multi-layer perceptron (MLP) framework and physics-informed neural network (PINN) utilities:

• NeuralLayer: single dense layer with several activation modes.
• GpuNeuralSolver: stacked MLP forward pass.
• PhysicsNeuralNet: PINN wrapper with PDE + boundary-condition loss.
• Activation functions: ns_relu, ns_sigmoid, ns_softmax.
• Loss functions: ns_mse_loss, ns_mae_loss.
• PINN residuals: pinn_residual, pinn_boundary_loss.

Structs

GpuNeuralSolver

Multi-layer perceptron running on the CPU mock GPU backend.

NeuralLayer

A single fully-connected (dense) neural network layer.

PhysicsNeuralNet

Physics-informed neural network (PINN).

Functions

ns_mae_loss

Mean absolute error loss: mean(|predicted_i − target_i|).

ns_mse_loss

Mean-squared error loss: mean((predicted_i − target_i)²).

ns_relu

Rectified linear unit activation: max(0, x).

ns_sigmoid

Logistic sigmoid activation: 1 / (1 + e^{-x}).

ns_softmax

Softmax of a slice: normalised exponentials exp(x_i) / Σ exp(x_j).

pinn_boundary_loss

Boundary-condition loss: MSE between the predicted boundary values and the prescribed Dirichlet data.

pinn_residual

Physics-informed residual for the 1-D Poisson equation −u_xx = source.