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# CLAUDE.md
This file provides guidance to Claude Code (claude.ai/code) when working with code in this repository.
## Project Overview
**Heat Equation PINN** — A Physics-Informed Neural Network that solves the 1D time-varying heat equation with physical boundary conditions:
```
∂T/∂t = α ∂²T/∂x² x ∈ [0, L], t ∈ [0, T_END]
```
- **IC:** `T(x, 0) = T0` (uniform)
- **BC x=0:** Neumann — heat flux step: `k ∂T/∂x = Q(t)` where `Q = Q_VAL` if `t ≥ T_STEP` else `0`
- **BC x=L:** Robin — convection: `k ∂T/∂x = h (T T_AMB)`
No experimental data is needed. A `fdm/` module provides a reference numerical solution (FTCS explicit scheme) used for evaluation and visualization comparison.
All physical and numerical parameters live in `config.py`.
## Running
Always activate the virtual environment first:
```bash
source .venv/bin/activate
```
**PINN:**
```bash
python app.py # Train / Evaluate (L2 vs FDM) / Visualize
```
**FDM reference solver:**
```bash
python fdm/app.py # Solve / Heatmap / Animation / Time-series
```
Saved artifacts (git-ignored): `models/best_heat_pinn_model.pth`, HTML plots in `animations/` and `animations/fdm/`.
To retrain from scratch: `rm models/best_heat_pinn_model.pth` before running option 1.
## Dependencies
`requirements.txt` exists. Key packages: `torch`, `numpy`, `plotly`. No `pandas` or `scikit-learn` needed.
GPU is auto-detected (`cuda``mps``cpu`) in `engine.py:_get_device()`.
## Architecture
```
config.py ← all physical + numerical parameters (edit here to change the problem)
app.py ← PINN CLI menu
model.py ← HeatPINN + heat_pinn_loss()
engine.py ← data sampling, Adam+L-BFGS training, evaluation vs FDM, visualization call
visualizer.py ← PINN vs FDM: heatmap, animated T(x), time-series at fixed points
fdm/
solver.py ← FTCS explicit scheme, ghost-cell Neumann, explicit Robin
visualizer.py ← same 3 plot types for FDM-only output
app.py ← FDM CLI menu
```
### Neural Network (`model.py`)
`HeatPINN`: 5-layer fully connected, input `(x, t)` → output `T`.
**Output scaling** — the network predicts a dimensionless perturbation; the `forward()` applies:
```
T = T_AMB + (Q_VAL · L / K) · net(x, t)
```
This keeps `net` outputs in `[0, 1]` range and ensures gradients `∂T/∂x` are O(1) for the network to learn. Do not remove this scaling.
`heat_pinn_loss()` normalizes all three loss terms to O(1) using `T_char = Q_VAL·L/K` and `grad_char = (Q_VAL/K)²`. Changing physical parameters in `config.py` does not require re-tuning loss weights.
### Training (`engine.py`)
`prepare_data()` samples collocation points with **deliberate clustering**: extra points near `x=0` (steep Neumann gradient) and around `t=T_STEP` (flux step discontinuity). Increasing `N_f` / `N_bc` here is the first lever to pull if accuracy is low.
`train_model()` runs **Adam first, then L-BFGS fine-tuning**. L-BFGS uses a closure that captures loss components in `_last` dict (avoids calling `heat_pinn_loss` outside an active grad context).
`evaluate_model()` runs the FDM solver and downsamples its `(NX, NT)` output to the PINN prediction grid `(100, 100)` for L2 comparison.
### FDM Solver (`fdm/solver.py`)
Returns `(T_matrix[NX, NT], x_vals, t_vals)`. Uses:
- Ghost cell for Neumann: `T_ghost = T[1] + 2·dx·Q(t)/k`
- Explicit Robin at x=L: `T[N] = (T[N1] + dx·h/k·T_amb) / (1 + dx·h/k)` — uses `T_cur[-2]`, not `T_new[-2]`
- CFL check at startup (warns, does not crash)
### Loss Scaling Notes
If you change `Q_VAL`, `K`, `H_CONV`, or `L` in `config.py`, the normalization in `heat_pinn_loss()` adjusts automatically. If losses diverge, check that `T_char = Q_VAL·L/K` is not near zero.
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MIT License
Copyright (c) [year] [fullname]
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.
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# Projekt_NEO_PINN
# For the project to work as intended you need to download https://drive.google.com/file/d/1qZbRrY0va7xsfj1w-kk6C03Vo4LoD4ef/view?usp=drive_link and put the NEO_Curated.csv in data/ folder
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import sys
import engine
def print_header():
print("=" * 55)
print(" Heat Equation PINN — ∂T/∂t = α ∂²T/∂x²")
print(" Neumann BC (x=0) + Robin BC (x=L)")
print("=" * 55)
def _ask_float(prompt, default):
val = input(prompt).strip()
try:
return float(val)
except ValueError:
return default
def _ask_int(prompt, default):
val = input(prompt).strip()
return int(val) if val.isdigit() else default
def main_menu():
print("\nInitializing collocation points...")
data = engine.prepare_data()
print(f"Ready — device: {data['device']}\n")
while True:
print("\n" + "-" * 30)
print(" MAIN MENU")
print("-" * 30)
print("1. Train New Model")
print("2. Evaluate Model (L2 vs analytical)")
print("3. Visualize Temperature Field")
print("0. Exit")
print("-" * 30)
choice = input("Select an option (0-3): ").strip()
if choice == '1':
epochs = _ask_int("Epochs (default 5000): ", 5000)
engine.train_model(data, epochs=epochs)
elif choice == '2':
engine.evaluate_model(data)
elif choice == '3':
engine.generate_visualization(data)
elif choice == '0':
print("Exiting.")
sys.exit(0)
else:
print("Invalid choice.")
if __name__ == "__main__":
print_header()
main_menu()
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# Fisica
ALPHA = 0.01 # diffusività termica [m²/s]
K = 1.0 # conducibilità termica [W/m·K]
L = 1.0 # lunghezza barra [m]
T0 = 20.0 # temperatura iniziale uniforme [°C]
# Sorgente a x=0 (Neumann step)
Q_VAL = 150.0 # flusso di calore applicato [W/m²]
T_STEP = 0.2 # istante di attivazione flusso [s]
# Convezione a x=L (Robin)
H_CONV = 10.0 # coefficiente convettivo [W/m²·K]
T_AMB = 20.0 # temperatura ambiente [°C]
# Dominio temporale
T_END = 10.0 # fine simulazione [s]
# Griglia FDM
NX = 100 # nodi spaziali
NT = 5000 # passi temporali (verifica CFL automatica)
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import os
import random
import numpy as np
import torch
import torch.optim as optim
from torch.optim.lr_scheduler import ReduceLROnPlateau
import config
from model import HeatPINN, heat_pinn_loss
from visualizer import visualize_heat_field
BASE_DIR = os.path.dirname(os.path.abspath(__file__))
MODELS_DIR = os.path.join(BASE_DIR, 'models')
MODEL_SAVE_PATH = os.path.join(MODELS_DIR, 'best_heat_pinn_model.pth')
def set_seed(seed=42):
random.seed(seed)
np.random.seed(seed)
torch.manual_seed(seed)
if torch.cuda.is_available():
torch.cuda.manual_seed_all(seed)
def _get_device():
if torch.cuda.is_available():
try:
t = torch.zeros(2, 2).cuda()
torch.mm(t, t)
return torch.device('cuda')
except RuntimeError:
pass
if torch.backends.mps.is_available():
return torch.device('mps')
return torch.device('cpu')
def prepare_data(N_f=4000, N_ic=400, N_bc=400):
set_seed(42)
device = _get_device()
# Uniform collocation points
x_f = torch.rand(N_f, device=device) * config.L
t_f = torch.rand(N_f, device=device) * config.T_END
# Extra points near x=0 (steep Neumann gradient) and t=T_STEP (flux step)
n_extra = N_f // 4
x_near0 = torch.rand(n_extra, device=device) * config.L * 0.1 # x in [0, 0.1]
t_near0 = torch.rand(n_extra, device=device) * config.T_END
x_step = torch.rand(n_extra, device=device) * config.L
t_step = config.T_STEP + (torch.rand(n_extra, device=device) - 0.5) * 0.1 # t near T_STEP
t_step = t_step.clamp(0, config.T_END)
x_f = torch.cat([x_f, x_near0, x_step])
t_f = torch.cat([t_f, t_near0, t_step])
x_ic = torch.rand(N_ic, device=device) * config.L
t_bc = torch.rand(N_bc, device=device) * config.T_END
return {'device': device, 'x_f': x_f, 't_f': t_f, 'x_ic': x_ic, 't_bc': t_bc}
def train_model(data, epochs=5000, patience=100):
device = data['device']
model = HeatPINN().to(device)
optimizer = optim.Adam(model.parameters(), lr=1e-3)
scheduler = ReduceLROnPlateau(optimizer, mode='min', factor=0.5, patience=30, min_lr=1e-6)
os.makedirs(MODELS_DIR, exist_ok=True)
best_loss = float('inf')
patience_counter = 0
print(f"\n--- Heat PINN Training (Adam) on {device} ---")
for epoch in range(epochs):
model.train()
optimizer.zero_grad()
loss, L_pde, L_ic, L_bc = heat_pinn_loss(
model, data['x_f'], data['t_f'], data['x_ic'], data['t_bc']
)
loss.backward()
optimizer.step()
scheduler.step(loss.item())
if loss.item() < best_loss - 1e-7:
best_loss = loss.item()
patience_counter = 0
torch.save({'state_dict': model.state_dict()}, MODEL_SAVE_PATH)
else:
patience_counter += 1
if patience_counter >= patience:
print(f"Early stopping at epoch {epoch + 1}")
break
if (epoch + 1) % 100 == 0:
print(
f"Epoch [{epoch+1}/{epochs}] | Loss: {loss.item():.6f} "
f"| PDE: {L_pde.item():.6f} | IC: {L_ic.item():.6f} | BC: {L_bc.item():.6f}"
)
# L-BFGS fine-tuning phase (standard PINN practice for convergence to better minima)
print("\n--- L-BFGS fine-tuning ---")
ckpt = torch.load(MODEL_SAVE_PATH, map_location=device)
model.load_state_dict(ckpt['state_dict'])
lbfgs = optim.LBFGS(model.parameters(), lr=0.1, max_iter=50,
history_size=50, tolerance_grad=1e-7, line_search_fn='strong_wolfe')
_last = {}
for step in range(20):
def closure():
lbfgs.zero_grad()
loss, L_pde, L_ic, L_bc = heat_pinn_loss(
model, data['x_f'], data['t_f'], data['x_ic'], data['t_bc']
)
loss.backward()
_last['loss'] = loss.item()
_last['pde'] = L_pde.item()
_last['ic'] = L_ic.item()
_last['bc'] = L_bc.item()
return loss
lbfgs.step(closure)
if _last['loss'] < best_loss:
best_loss = _last['loss']
torch.save({'state_dict': model.state_dict()}, MODEL_SAVE_PATH)
if (step + 1) % 5 == 0:
print(f"L-BFGS step {step+1}/20 | Loss: {_last['loss']:.6f} "
f"| PDE: {_last['pde']:.6f} | IC: {_last['ic']:.6f} | BC: {_last['bc']:.6f}")
print("Training complete! Model saved.")
def _load_model(device):
if not os.path.exists(MODEL_SAVE_PATH):
print("Error: model not found. Train the model first.")
return None
ckpt = torch.load(MODEL_SAVE_PATH, map_location=device)
model = HeatPINN().to(device)
model.load_state_dict(ckpt['state_dict'])
model.eval()
return model
def _predict_grid(model, device, nx=100, nt=100):
x_vals = torch.linspace(0, config.L, nx, device=device)
t_vals = torch.linspace(0, config.T_END, nt, device=device)
xx, tt = torch.meshgrid(x_vals, t_vals, indexing='ij')
inp = torch.stack([xx.reshape(-1), tt.reshape(-1)], dim=1)
with torch.no_grad():
T_pred = model(inp).reshape(nx, nt).cpu().numpy()
return T_pred, x_vals.cpu().numpy(), t_vals.cpu().numpy()
def evaluate_model(data):
model = _load_model(data['device'])
if model is None:
return
T_pred, x_vals, t_vals = _predict_grid(model, data['device'])
# FDM reference
from fdm.solver import solve as fdm_solve
T_fdm, _, _ = fdm_solve()
# Downsample FDM time axis (NX=100, NT=5000) to match PINN grid (100x100)
nx, nt = T_pred.shape
t_indices = np.linspace(0, T_fdm.shape[1] - 1, nt, dtype=int)
T_fdm_ds = T_fdm[:, t_indices] # (100, 100)
l2_rel = np.sqrt(np.mean((T_pred - T_fdm_ds) ** 2)) / np.sqrt(np.mean(T_fdm_ds ** 2))
max_err = np.max(np.abs(T_pred - T_fdm_ds))
print(f"\n--- Evaluation vs FDM ---")
print(f"Relative L2 error vs FDM: {l2_rel:.6f}")
print(f"Max absolute error: {max_err:.6f} °C\n")
def generate_visualization(data):
model = _load_model(data['device'])
if model is None:
return
T_pred, x_vals, t_vals = _predict_grid(model, data['device'])
from fdm.solver import solve as fdm_solve
T_fdm, _, _ = fdm_solve()
visualize_heat_field(T_pred, x_vals, t_vals, T_fdm)
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import sys
import os
sys.path.insert(0, os.path.dirname(os.path.dirname(os.path.abspath(__file__))))
from fdm.solver import solve
from fdm.visualizer import visualize_fdm
def print_header():
print("=" * 38)
print(" Heat Equation — FDM Solver")
print(" ∂T/∂t = α ∂²T/∂x²")
print("=" * 38)
def main_menu():
print("\nInitializing solver...")
print("Ready.\n")
T, x_vals, t_vals = None, None, None
while True:
print("\n" + "-" * 30)
print(" MAIN MENU")
print("-" * 30)
print("1. Risolvi e salva risultati")
print("2. Heatmap T(x,t)")
print("3. Animazione T(x) nel tempo")
print("4. Grafico T(t) in punti fissi")
print("0. Esci")
print("-" * 30)
choice = input("Select an option (0-4): ").strip()
if choice == "1":
T, x_vals, t_vals = solve()
print(f"Soluzione completata. Shape T: {T.shape}")
print(f"T range: [{T.min():.2f}, {T.max():.2f}] °C")
elif choice in ("2", "3", "4"):
if T is None:
print("Eseguire prima l'opzione 1.")
else:
visualize_fdm(T, x_vals, t_vals)
print("Grafici salvati in animations/fdm/")
elif choice == "0":
print("Uscita.")
sys.exit(0)
else:
print("Scelta non valida.")
if __name__ == "__main__":
print_header()
main_menu()
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"""
FTCS (Forward-Time Centered-Space) explicit finite difference solver
for the 1D heat equation:
dT/dt = alpha * d²T/dx²
Boundary conditions:
- x=0 (Neumann): heat flux step Q(t) applied via ghost cell
- x=L (Robin): convective boundary condition
Returns T_matrix of shape (NX, NT).
"""
import sys
import os
import numpy as np
# Allow importing config from the project root
sys.path.insert(0, os.path.dirname(os.path.dirname(os.path.abspath(__file__))))
import config
def solve():
"""Run the FTCS solver and return (T_matrix, x_vals, t_vals).
Returns
-------
T_matrix : np.ndarray, shape (NX, NT)
Temperature at each spatial node (row) and time step (column).
T_matrix[i, n] = T(x_i, t_n).
x_vals : np.ndarray, shape (NX,)
Spatial node positions from 0 to L.
t_vals : np.ndarray, shape (NT,)
Time values from 0 to T_END.
"""
# -----------------------------------------------------------------
# Parameters from config
# -----------------------------------------------------------------
alpha = config.ALPHA
k = config.K
L = config.L
T0 = config.T0
Q_val = config.Q_VAL
t_step = config.T_STEP
h = config.H_CONV
T_amb = config.T_AMB
T_end = config.T_END
NX = config.NX
NT = config.NT
# -----------------------------------------------------------------
# Grid
# -----------------------------------------------------------------
x_vals = np.linspace(0.0, L, NX)
t_vals = np.linspace(0.0, T_end, NT)
dx = x_vals[1] - x_vals[0]
dt = t_vals[1] - t_vals[0]
# -----------------------------------------------------------------
# Stability check (CFL for explicit heat equation: r <= 0.5)
# -----------------------------------------------------------------
r = alpha * dt / dx**2
if dt > dx**2 / (2.0 * alpha):
print(
f"[FDM WARNING] Stability condition violated: "
f"dt={dt:.6g} > dx²/(2*alpha)={dx**2/(2.0*alpha):.6g} (r={r:.4f} > 0.5). "
"Solution may diverge."
)
# -----------------------------------------------------------------
# Allocate output matrix and set initial condition
# -----------------------------------------------------------------
T_matrix = np.zeros((NX, NT), dtype=np.float64)
T_matrix[:, 0] = T0 # uniform IC
# Working array for the current time level
T_cur = np.full(NX, T0, dtype=np.float64)
# -----------------------------------------------------------------
# Time integration
# -----------------------------------------------------------------
for n in range(NT - 1):
t_now = t_vals[n]
# --- Neumann BC at x=0: ghost cell ---
# Q(t) = Q_val if t >= t_step else 0
Q = Q_val if t_now >= t_step else 0.0
T_ghost = T_cur[1] + 2.0 * dx * Q / k # ghost node T[-1]
# --- Interior FTCS update (indices 1 .. NX-2) ---
T_new = T_cur.copy()
T_new[1:-1] = T_cur[1:-1] + r * (T_cur[2:] - 2.0 * T_cur[1:-1] + T_cur[:-2])
# --- Apply Neumann BC at i=0 using ghost cell ---
T_new[0] = T_cur[0] + r * (T_cur[1] - 2.0 * T_cur[0] + T_ghost)
# --- Apply Robin BC at x=L (explicit) ---
T_new[-1] = (T_cur[-2] + dx * h / k * T_amb) / (1.0 + dx * h / k)
T_cur = T_new
T_matrix[:, n + 1] = T_cur
return T_matrix, x_vals, t_vals
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import sys
import os
import numpy as np
import plotly.graph_objects as go
sys.path.insert(0, os.path.dirname(os.path.dirname(os.path.abspath(__file__))))
import config
BASE_DIR = os.path.dirname(os.path.dirname(os.path.abspath(__file__)))
FDM_ANIM_DIR = os.path.join(BASE_DIR, 'animations', 'fdm')
def _next_path(base_dir, prefix, ext):
i = 1
while True:
path = os.path.join(base_dir, f'{prefix}_{i:03d}{ext}')
if not os.path.exists(path):
return path
i += 1
def visualize_fdm(T_matrix, x_vals, t_vals):
"""Produce three HTML visualisations for the FDM solver output.
Parameters
----------
T_matrix : np.ndarray, shape (NX, NT)
Temperature field: T_matrix[i, n] = T(x_i, t_n).
x_vals : np.ndarray, shape (NX,)
Spatial node positions.
t_vals : np.ndarray, shape (NT,)
Time values.
"""
os.makedirs(FDM_ANIM_DIR, exist_ok=True)
# ------------------------------------------------------------------
# 1. Heatmap
# ------------------------------------------------------------------
zmax = float(np.max(np.abs(T_matrix - config.T0)))
# Use symmetric range centred on T0 if there is any variation,
# otherwise fall back to the raw range.
z_data = T_matrix.T # shape (NT, NX) — rows=time, cols=space
if zmax > 0:
z_center = float(np.mean(T_matrix))
z_abs = float(np.max(np.abs(T_matrix - z_center)))
zmin_sym = z_center - z_abs
zmax_sym = z_center + z_abs
else:
zmin_sym = float(np.min(T_matrix))
zmax_sym = float(np.max(T_matrix))
fig_heatmap = go.Figure(go.Heatmap(
z=z_data,
x=x_vals,
y=t_vals,
colorscale='RdBu_r',
zmin=zmin_sym,
zmax=zmax_sym,
colorbar=dict(title='T [°C]'),
))
fig_heatmap.update_layout(
title='FDM — Heat Equation T(x,t)',
xaxis_title='x [m]',
yaxis_title='t [s]',
height=500,
)
heatmap_path = _next_path(FDM_ANIM_DIR, 'heatmap', '.html')
fig_heatmap.write_html(heatmap_path)
print(f"Heatmap saved → {heatmap_path}")
# ------------------------------------------------------------------
# 2. Animated profile T(x) evolving in time
# ------------------------------------------------------------------
L = config.L
n_frames = len(t_vals)
# Subsample frames for a manageable animation (max ~200 frames)
max_frames = 200
step = max(1, n_frames // max_frames)
frame_indices = list(range(0, n_frames, step))
y_min = float(np.min(T_matrix)) - 1.0
y_max = float(np.max(T_matrix)) + 1.0
vline_shapes = [
dict(type='line', x0=0, x1=0, y0=y_min, y1=y_max,
line=dict(color='grey', dash='dash', width=1)),
dict(type='line', x0=L, x1=L, y0=y_min, y1=y_max,
line=dict(color='grey', dash='dash', width=1)),
]
frames = []
for idx in frame_indices:
frames.append(go.Frame(
data=[go.Scatter(
x=x_vals,
y=T_matrix[:, idx],
mode='lines',
line=dict(color='royalblue', width=2),
name='FDM',
)],
name=str(idx),
layout=go.Layout(
title_text=f'FDM | t = {t_vals[idx]:.3f} s',
),
))
fig_anim = go.Figure(
data=[go.Scatter(
x=x_vals,
y=T_matrix[:, frame_indices[0]],
mode='lines',
line=dict(color='royalblue', width=2),
name='FDM',
)],
layout=go.Layout(
title=f'FDM | t = {t_vals[frame_indices[0]]:.3f} s',
xaxis=dict(title='x [m]', range=[-0.02 * L, 1.02 * L]),
yaxis=dict(title='T [°C]', range=[y_min, y_max]),
shapes=vline_shapes,
updatemenus=[dict(
type='buttons',
showactive=False,
y=1.15,
x=0.5,
xanchor='center',
buttons=[
dict(
label='▶ Play',
method='animate',
args=[None, dict(
frame=dict(duration=40, redraw=False),
fromcurrent=True,
mode='immediate',
)],
),
dict(
label='⏸ Pause',
method='animate',
args=[[None], dict(
frame=dict(duration=0, redraw=False),
mode='immediate',
)],
),
],
)],
sliders=[dict(
steps=[
dict(
method='animate',
args=[[str(idx)], dict(
mode='immediate',
frame=dict(duration=0, redraw=False),
)],
label=f'{t_vals[idx]:.2f}',
)
for idx in frame_indices
],
transition=dict(duration=0),
x=0.05,
y=0,
len=0.9,
currentvalue=dict(prefix='t = ', font=dict(size=14)),
)],
),
frames=frames,
)
anim_path = _next_path(FDM_ANIM_DIR, 'animation', '.html')
fig_anim.write_html(anim_path)
print(f"Animation saved → {anim_path}")
# ------------------------------------------------------------------
# 3. Time evolution at fixed spatial points
# ------------------------------------------------------------------
fixed_fractions = [0.0, 0.25, 0.5, 0.75, 1.0]
colors = ['#1f77b4', '#ff7f0e', '#2ca02c', '#d62728', '#9467bd']
fig_ts = go.Figure()
for frac, color in zip(fixed_fractions, colors):
x_target = frac * L
idx_x = int(np.argmin(np.abs(x_vals - x_target)))
label = f'x = {x_vals[idx_x]:.2f} m'
fig_ts.add_trace(go.Scatter(
x=t_vals,
y=T_matrix[idx_x, :],
mode='lines',
name=label,
line=dict(color=color, width=2),
))
# "Heat ON" vertical dashed line at t = T_STEP
t_step = config.T_STEP
t_min_val = float(np.min(t_vals))
t_max_val = float(np.max(t_vals))
T_min_val = float(np.min(T_matrix)) - 1.0
T_max_val = float(np.max(T_matrix)) + 1.0
fig_ts.add_shape(
type='line',
x0=t_step, x1=t_step,
y0=T_min_val, y1=T_max_val,
line=dict(color='red', dash='dash', width=1.5),
)
fig_ts.add_annotation(
x=t_step,
y=T_max_val,
text='Heat ON',
showarrow=False,
yanchor='top',
font=dict(color='red', size=11),
)
fig_ts.update_layout(
title='FDM — Temperature evolution at fixed points',
xaxis=dict(title='t [s]', range=[t_min_val, t_max_val]),
yaxis=dict(title='T [°C]', range=[T_min_val, T_max_val]),
legend=dict(x=0.01, y=0.99),
height=480,
)
ts_path = _next_path(FDM_ANIM_DIR, 'time_series', '.html')
fig_ts.write_html(ts_path)
print(f"Time-series saved → {ts_path}")
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import torch
import torch.nn as nn
import config
class HeatPINN(nn.Module):
def __init__(self):
super().__init__()
self.net = nn.Sequential(
nn.Linear(2, 128), nn.Tanh(),
nn.Linear(128, 128), nn.Tanh(),
nn.Linear(128, 128), nn.Tanh(),
nn.Linear(128, 128), nn.Tanh(),
nn.Linear(128, 1),
)
def forward(self, x):
# Output scaled to physical range: T_AMB + (Q*L/K) * net
# net learns dimensionless perturbation in [0,1] range
T_scale = config.T_AMB + (config.Q_VAL * config.L / config.K) * self.net(x)
return T_scale
def heat_pinn_loss(model, x_f, t_f, x_ic, t_bc, w_pde=1.0, w_ic=1.0, w_bc=10.0):
# Characteristic scales for normalization
T_char = config.Q_VAL * config.L / config.K # ~50 °C — temperature scale
grad_char = (config.Q_VAL / config.K) ** 2 # ~2500 — gradient scale²
# PDE residual: dT/dt - alpha * d2T/dx2 = 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 = torch.autograd.grad(T_f.sum(), t_f, create_graph=True)[0]
dT_dx = torch.autograd.grad(T_f.sum(), x_f, create_graph=True)[0]
d2T_dx2 = torch.autograd.grad(dT_dx.sum(), x_f, create_graph=True)[0]
pde_scale = (T_char / config.T_END) ** 2 + 1e-8
L_pde = ((dT_dt - config.ALPHA * d2T_dx2) ** 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: Neumann — dT/dx + Q(t)/K = 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]
Q_t = torch.where(t_bc >= config.T_STEP,
torch.tensor(config.Q_VAL, device=t_bc.device, dtype=t_bc.dtype),
torch.tensor(0.0, device=t_bc.device, dtype=t_bc.dtype))
L_bc_left = ((dT_dx_left + Q_t / config.K) ** 2).mean() / grad_char
# 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() / grad_char
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
+5
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torch>=2.0.0
pandas>=2.0.0
numpy>=1.24.0
scikit-learn>=1.3.0
plotly>=5.15.0
+153
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import os
import numpy as np
import plotly.graph_objects as go
from plotly.subplots import make_subplots
import config
BASE_DIR = os.path.dirname(os.path.abspath(__file__))
ANIMATIONS_DIR = os.path.join(BASE_DIR, 'animations')
def visualize_heat_field(T_pred, x_vals, t_vals, T_fdm):
os.makedirs(ANIMATIONS_DIR, exist_ok=True)
# Downsample T_fdm from shape (NX, NT) to (NX, len(t_vals))
nt_pred = len(t_vals)
t_indices = np.linspace(0, T_fdm.shape[1] - 1, nt_pred, dtype=int)
T_fdm_ds = T_fdm[:, t_indices] # now shape (NX, nt_pred)
# --- Static heatmap: PINN vs FDM ---
fig_map = make_subplots(
rows=1, cols=2,
subplot_titles=["PINN Prediction T(x,t)", "FDM Reference T(x,t)"],
shared_yaxes=True,
)
colorscale = 'Hot_r'
zmin = float(min(np.min(T_pred), np.min(T_fdm_ds)))
zmax = float(max(np.max(T_pred), np.max(T_fdm_ds)))
fig_map.add_trace(go.Heatmap(
z=T_pred.T, x=x_vals, y=t_vals,
colorscale=colorscale, zmin=zmin, zmax=zmax,
colorbar=dict(x=0.46, title='T [°C]'),
), row=1, col=1)
fig_map.add_trace(go.Heatmap(
z=T_fdm_ds.T, x=x_vals, y=t_vals,
colorscale=colorscale, zmin=zmin, zmax=zmax,
colorbar=dict(x=1.01, title='T [°C]'),
), row=1, col=2)
fig_map.update_xaxes(title_text='x')
fig_map.update_yaxes(title_text='t', row=1, col=1)
fig_map.update_layout(title_text='Heat Equation PINN vs FDM', height=450)
map_path = _next_path('heatmap', '.html')
fig_map.write_html(map_path)
print(f"Heatmap saved → {map_path}")
# --- Animated profile T(x) evolving in time ---
n_frames = len(t_vals)
frames = []
for i in range(n_frames):
frames.append(go.Frame(
data=[
go.Scatter(x=x_vals, y=T_pred[:, i], mode='lines',
line=dict(color='royalblue', width=2), name='PINN'),
go.Scatter(x=x_vals, y=T_fdm_ds[:, i], mode='lines',
line=dict(color='firebrick', width=2, dash='dash'), name='FDM'),
],
name=str(i),
layout=go.Layout(title_text=f'Heat Equation PINN vs FDM | t = {t_vals[i]:.3f}'),
))
fig_anim = go.Figure(
data=frames[0].data,
layout=go.Layout(
title=f'Heat Equation PINN vs FDM | t = {t_vals[0]:.3f}',
xaxis=dict(title='x [m]', range=[-0.02, config.L + 0.02]),
yaxis=dict(title='T [°C]', range=[zmin - 1, zmax + 1]),
legend=dict(x=0.75, y=0.95),
updatemenus=[dict(
type='buttons', showactive=False, y=1.15, x=0.5, xanchor='center',
buttons=[
dict(label='▶ Play', method='animate',
args=[None, dict(frame=dict(duration=40, redraw=False),
fromcurrent=True, mode='immediate')]),
dict(label='⏸ Pause', method='animate',
args=[[None], dict(frame=dict(duration=0, redraw=False),
mode='immediate')]),
],
)],
sliders=[dict(
steps=[dict(method='animate', args=[[str(i)],
dict(mode='immediate', frame=dict(duration=0, redraw=False))],
label=f'{t_vals[i]:.2f}') for i in range(n_frames)],
transition=dict(duration=0), x=0.05, y=0, len=0.9,
currentvalue=dict(prefix='t = ', font=dict(size=14)),
)],
),
frames=frames,
)
anim_path = _next_path('heat_animation', '.html')
fig_anim.write_html(anim_path)
print(f"Animation saved → {anim_path}")
# --- Time-series comparison at fixed spatial points ---
# Spatial indices for x=0, x=L/2, x=L
nx = len(x_vals)
idx_x0 = 0
idx_xmid = nx // 2
idx_xL = nx - 1
points = [
(idx_x0, 'x=0', 'blue'),
(idx_xmid, 'x=L/2', 'green'),
(idx_xL, 'x=L', 'red'),
]
fig_ts = go.Figure()
for idx, label, color in points:
fig_ts.add_trace(go.Scatter(
x=t_vals, y=T_pred[idx, :],
mode='lines',
line=dict(color=color, width=2, dash='solid'),
name=f'PINN {label}',
))
fig_ts.add_trace(go.Scatter(
x=t_vals, y=T_fdm_ds[idx, :],
mode='lines',
line=dict(color=color, width=2, dash='dash'),
name=f'FDM {label}',
))
# Vertical dashed line at T_STEP ("Heat ON")
fig_ts.add_vline(
x=config.T_STEP,
line=dict(color='red', dash='dash', width=1.5),
annotation_text='Heat ON',
annotation_position='top right',
)
fig_ts.update_layout(
title='Heat Equation PINN vs FDM — Time Series at Fixed Points',
xaxis_title='t',
yaxis_title='T(x,t)',
legend=dict(x=0.01, y=0.99),
height=500,
)
comparison_path = _next_path('comparison', '.html')
fig_ts.write_html(comparison_path)
print(f"Time-series saved → {comparison_path}")
def _next_path(prefix, ext):
i = 1
while True:
path = os.path.join(ANIMATIONS_DIR, f'{prefix}_{i:03d}{ext}')
if not os.path.exists(path):
return path
i += 1