pinn/model.py

import torch
import torch.nn as nn
import config


class HeatPINN(nn.Module):
    def __init__(self):
        super().__init__()
        h = config.HIDDEN_SIZE
        layers = [nn.Linear(2, h), nn.Tanh()]
        for _ in range(config.N_HIDDEN_LAYERS - 1):
            layers += [nn.Linear(h, h), nn.Tanh()]
        layers.append(nn.Linear(h, 1))
        self.net = nn.Sequential(*layers)

    def forward(self, xt):
        x = xt[:, :1] / config.L
        t = xt[:, 1:] / config.T_END
        return config.T_AMB + (config.Q_VAL * config.L / config.K) * self.net(torch.cat([x, t], dim=1))


# Precomputed loss scales (depend only on config constants)
_T_char    = config.Q_VAL * config.L / config.K   # ~150 °C — temperature scale
# _pde_scale covers both dT/dt and the Gaussian source peak (dominant with small sigma)
_src_peak  = config.ALPHA * config.Q_VAL / (config.K * config.GAUSS_SIGMA * (2 * 3.141592653589793) ** 0.5)
_pde_scale = max((_T_char / config.T_END) ** 2, _src_peak ** 2) + 1e-8
# Robin BC residual scale: max(dT/dx, H_CONV/K * T_char) — convective term dominates when H*L/K >> 1
_bc_scale  = max(config.Q_VAL / config.K,
                 config.H_CONV * _T_char / config.K) ** 2


def heat_pinn_loss(model, x_f, t_f, x_ic, t_bc,
                   w_pde=None, w_ic=None, w_bc=None):
    if w_pde is None: w_pde = config.W_PDE
    if w_ic  is None: w_ic  = config.W_IC
    if w_bc  is None: w_bc  = config.W_BC
    T_char = _T_char

    # PDE residual: dT/dt - alpha * d2T/dx2 - source(x,t) = 0  (normalized by T_char/t_char)
    x_f = x_f.detach().requires_grad_(True)
    t_f = t_f.detach().requires_grad_(True)
    T_f = model(torch.stack([x_f, t_f], dim=1))
    dT_dt, dT_dx = torch.autograd.grad(T_f.sum(), [t_f, x_f], create_graph=True)
    d2T_dx2 = torch.autograd.grad(dT_dx.sum(), x_f, create_graph=True)[0]
    Q_t_f = torch.where(t_f >= config.T_STEP,
                        torch.tensor(config.Q_VAL, device=t_f.device, dtype=t_f.dtype),
                        torch.tensor(0.0,          device=t_f.device, dtype=t_f.dtype))
    sigma = config.GAUSS_SIGMA
    gauss = torch.exp(-0.5 * ((x_f - config.X_SRC) / sigma) ** 2) / (sigma * (2 * torch.pi) ** 0.5)
    source_term = (config.ALPHA / config.K) * Q_t_f * gauss
    L_pde = ((dT_dt - config.ALPHA * d2T_dx2 - source_term) ** 2).mean() / _pde_scale

    # IC: T(x, 0) = T0 — normalized by T_char²
    T_ic_pred = model(torch.stack([x_ic, torch.zeros_like(x_ic)], dim=1))
    T_ic_true = torch.full_like(T_ic_pred, config.T0)
    L_ic = ((T_ic_pred - T_ic_true) ** 2).mean() / (_T_char ** 2 + 1e-8)

    # BC x=0: Robin — dT/dx + H_CONV/K * (T(0,t) - T_AMB) = 0
    x_left = torch.zeros(t_bc.shape[0], device=t_bc.device).requires_grad_(True)
    T_left = model(torch.stack([x_left, t_bc.detach()], dim=1))
    dT_dx_left = torch.autograd.grad(T_left.sum(), x_left, create_graph=True)[0]
    L_bc_left = ((dT_dx_left - (config.H_CONV / config.K) * (T_left.squeeze() - config.T_AMB)) ** 2).mean() / _bc_scale

    # BC x=L: Robin — dT/dx + H_CONV/K * (T(L,t) - T_AMB) = 0
    x_right = torch.full((t_bc.shape[0],), config.L, device=t_bc.device).requires_grad_(True)
    T_right = model(torch.stack([x_right, t_bc.detach()], dim=1))
    dT_dx_right = torch.autograd.grad(T_right.sum(), x_right, create_graph=True)[0]
    L_bc_right = ((dT_dx_right + (config.H_CONV / config.K) * (T_right.squeeze() - config.T_AMB)) ** 2).mean() / _bc_scale

    L_bc = L_bc_left + L_bc_right
    total = w_pde * L_pde + w_ic * L_ic + w_bc * L_bc
    return total, L_pde, L_ic, L_bc