precice · MakisH · Jun 23, 2026 · Sep 29, 2025 · Oct 1, 2025 · Oct 14, 2025
diff --git a/changelog-entries/670.md b/changelog-entries/670.md
@@ -0,0 +1 @@
+New tutorial case: Partitioned Burgers' Equation in 1D solved with Finite Volumes and a Neural Network surrogate model !
diff --git a/partitioned-burgers-1d/README.md b/partitioned-burgers-1d/README.md
@@ -0,0 +1,141 @@
+---
+title: Partitioned Burgers' equation 1D
+permalink: tutorials-partitioned-burgers-1d.html
+keywords: Python, Neural Network, Surrogate, Burgers Equation, Finite Volume, CFD
+summary: This tutorial demonstrates the partitioned solution of the 1D Burgers' equation using preCICE and a neural network surrogate solver.
+---
+
+{% note %}
+Get the [case files of this tutorial](https://github.com/precice/tutorials/tree/develop/partitioned-burgers-1d), as continuously rendered here, or see the [latest released version](https://github.com/precice/tutorials/tree/master/partitioned-burgers-1d) (if there is already one). Read how in the [tutorials introduction](https://precice.org/tutorials.html).
+{% endnote %}
+
+## Setup
+
+We solve the 1D viscous Burgers' equation on the domain $[0,2]$:
+
+$$
+\frac{\partial u}{\partial t} = \nu \frac{\partial^2 u}{\partial x^2} - u \frac{\partial u}{\partial x},
+$$
+
+where $u(x,t)$ is the scalar velocity field and $\nu$ is the viscosity. In this tutorial by default $\nu$ is very small ($10^{-12}$), but can be changed in the solver.
+
+The domain is partitioned into participants at $x=1$:
+
+- **Dirichlet**: Solves the left half $[0,1]$ and receives Dirichlet boundary conditions at the interface.
+- **Neumann**: Solves the right half $[1,2]$ and receives Neumann boundary conditions at the interface.
+
+Both outer boundaries use zero-gradient conditions $\frac{\partial u}{\partial x} = 0$. The problem can be solved for different initial conditions of superimposed sine waves, which can be generated using the provided script `utils/generate_ic.py`.
+
+<p align="center">
+  <img src="images/tutorials-partitioned-burgers-1d-full-domain-diagram.png" alt="Domain Diagram" width="500"/>
+  <br><em>Diagram of the partitioned domain with an example initial condition.</em>
+</p>
+
+## Configuration
+
+preCICE configuration (image generated using the [precice-config-visualizer](https://precice.org/tooling-config-visualization.html)):
+
+<p align="center">
+  <img src="images/tutorials-partitioned-burgers-1d-precice-config.png" alt="preCICE configuration visualization" width="600"/>
+</p>
+
+## Available Solvers
+
+The conservative formulation of the Burgers' equation `solver-scipy` is implemented in a first-order finite volume code using Lax-Friedrichs fluxes and implicit Euler time stepping.
+
+This tutorial includes two versions for the Neumann participant:
+
+- A standard finite volume solver (`neumann-scipy`).
+- A pre-trained neural network surrogate that approximates the solver (`neumann-surrogate`).
+
+{% note %}
+The surrogate participant requires PyTorch and related dependencies, which requires several gigabytes of disk space (~7Gb).
+{% endnote %}
+
+## Running the simulation
+
+### Running the participants
+
+To run the partitioned simulation, open two separate terminals and start each participant individually:
+
+You can find the corresponding `run.sh` script for running the case in the folders corresponding to the participant you want to use:
+
+```bash
+cd dirichlet-scipy
+./run.sh
+```
+
+and
+
+```bash
+cd neumann-scipy
+./run.sh
+```
+
+or, to use the pretrained neural network surrogate participant:
+
+```bash
+cd neumann-surrogate
+./run.sh
+```
+
+### Initial condition
+
+The initial condition file `initial_condition.npz` is automatically generated by the run scripts if it does not exist.
+You can also manually generate it using the script in `utils/`:
+
+```bash
+python3 utils/generate_ic.py --epoch <seed>
+```
+
+This script requires the Python libraries `numpy` and `matplotlib`.
+
+---
+
+### Helper scripts
+
+There are helper scripts in the `utils/` directory that automate runs and visualization of both participants. They also accept an integer seed argument to specify the initial condition.
+
+```bash
+./utils/run-partitioned-scipy.sh
+```
+
+and
+
+```bash
+./utils/run-partitioned-surrogate.sh
+```
+
+### Monolithic solution (reference)
+
+You can run the whole domain using the monolithic solver for comparison:
+
+```bash
+cd solver-scipy
+./run.sh
+```
+
+## Visualization
+
+After both participants (and/or monolithic simulation) have finished, you can run the visualization script.
+`visualize_partitioned_domain.py` generates plots comparing the partitioned and monolithic solutions. You can specify which timestep to plot:
+
+```bash
+python3 visualize_partitioned_domain.py --neumann neumann-surrogate/surrogate.npz [timestep]
+```
+
+The script will produce the following output files in the `output/` directory:
+
+- `full-domain-timestep-slice.png`: Solution $u$ at a selected timestep
+
+<p align="left">
+  <img src="images/tutorials-partitioned-burgers-1d-full-domain-timestep-slice.png" alt="Full Domain Timestep Slice" width="400"/>
+</p>
+
+- `gradient-timestep-slice.png`: Gradient $du/dx$ at a selected timestep
+
+- `full-domain-evolution.png`: Time evolution of the solution
+
+<p align="left">
+  <img src="images/tutorials-partitioned-burgers-1d-full-domain-evolution.png" alt="Full Domain Evolution" width="400"/>
+</p>
diff --git a/partitioned-burgers-1d/clean-tutorial.sh b/partitioned-burgers-1d/clean-tutorial.sh
@@ -0,0 +1,16 @@
+#!/usr/bin/env sh
+set -e -u
+
+# shellcheck disable=SC1091
+. ../tools/cleaning-tools.sh
+
+clean_tutorial .
+clean_precice_logs .
+rm -fv ./*.log
+rm -fv ./*.vtu
+
+rm -f solver-scipy/full_domain.npz
+rm -f dirichlet-scipy/dirichlet.npz
+rm -f neumann-scipy/neumann.npz
+rm -rf output/
+rm -f initial_condition.npz
diff --git a/partitioned-burgers-1d/dirichlet-scipy/clean.sh b/partitioned-burgers-1d/dirichlet-scipy/clean.sh
@@ -0,0 +1,6 @@
+#!/usr/bin/env sh
+set -e -u
+
+rm -rf precice-profiling
+rm -f dirichlet-scipy.log precice-Dirichlet-convergence.log precice-Dirichlet-iterations.log
+rm -f dirichlet.npz
diff --git a/partitioned-burgers-1d/dirichlet-scipy/run.sh b/partitioned-burgers-1d/dirichlet-scipy/run.sh
@@ -0,0 +1,21 @@
+#!/usr/bin/env bash
+set -e -u
+
+if [ ! -v PRECICE_TUTORIALS_NO_VENV ]
+then
+    python3 -m venv .venv
+    . .venv/bin/activate
+    pip install -r ../solver-scipy/requirements.txt && pip freeze > pip-installed-packages.log
+fi
+
+if [ ! -f "../initial_condition.npz" ]; then
+	echo "Generating initial condition..."
+	python3 ../utils/generate_ic.py
+fi
+
+. ../../tools/log.sh
+exec > >(tee --append "$LOGFILE") 2>&1
+
+python3 ../solver-scipy/solver.py Dirichlet
+
+close_log
diff --git a/...oned-burgers-1d/images/tutorials-partitioned-burgers-1d-full-domain-diagram.png b/...oned-burgers-1d/images/tutorials-partitioned-burgers-1d-full-domain-diagram.png
diff --git a/...ed-burgers-1d/images/tutorials-partitioned-burgers-1d-full-domain-evolution.png b/...ed-burgers-1d/images/tutorials-partitioned-burgers-1d-full-domain-evolution.png
diff --git a/...rgers-1d/images/tutorials-partitioned-burgers-1d-full-domain-timestep-slice.png b/...rgers-1d/images/tutorials-partitioned-burgers-1d-full-domain-timestep-slice.png
diff --git a/...tioned-burgers-1d/images/tutorials-partitioned-burgers-1d-initial-condition.png b/...tioned-burgers-1d/images/tutorials-partitioned-burgers-1d-initial-condition.png
diff --git a/partitioned-burgers-1d/images/tutorials-partitioned-burgers-1d-precice-config.png b/partitioned-burgers-1d/images/tutorials-partitioned-burgers-1d-precice-config.png
diff --git a/partitioned-burgers-1d/neumann-scipy/clean.sh b/partitioned-burgers-1d/neumann-scipy/clean.sh
@@ -0,0 +1,6 @@
+#!/usr/bin/env sh
+set -e -u
+
+rm -rf precice-profiling
+rm -f neumann-scipy.log precice-Neumann-convergence.log precice-Neumann-iterations.log
+rm -f neumann.npz
diff --git a/partitioned-burgers-1d/neumann-scipy/run.sh b/partitioned-burgers-1d/neumann-scipy/run.sh
@@ -0,0 +1,21 @@
+#!/usr/bin/env bash
+set -e -u
+
+if [ ! -v PRECICE_TUTORIALS_NO_VENV ]
+then
+    python3 -m venv .venv
+    . .venv/bin/activate
+    pip install -r ../solver-scipy/requirements.txt && pip freeze > pip-installed-packages.log
+fi
+
+if [ ! -f "../initial_condition.npz" ]; then
+	echo "Generating initial condition..."
+	python3 ../utils/generate_ic.py
+fi
+
+. ../../tools/log.sh
+exec > >(tee --append "$LOGFILE") 2>&1
+
+python3 ../solver-scipy/solver.py Neumann
+
+close_log
diff --git a/partitioned-burgers-1d/neumann-surrogate/CNN_RES_UNROLL_1.pth b/partitioned-burgers-1d/neumann-surrogate/CNN_RES_UNROLL_1.pth
diff --git a/partitioned-burgers-1d/neumann-surrogate/CNN_RES_UNROLL_7.pth b/partitioned-burgers-1d/neumann-surrogate/CNN_RES_UNROLL_7.pth
diff --git a/partitioned-burgers-1d/neumann-surrogate/clean.sh b/partitioned-burgers-1d/neumann-surrogate/clean.sh
@@ -0,0 +1,6 @@
+#!/usr/bin/env sh
+set -e -u
+
+rm -rf precice-profiling
+rm -f neumann-surrogate.log precice-Neumann-convergence.log precice-Neumann-iterations.log
+rm -f surrogate.npz
diff --git a/partitioned-burgers-1d/neumann-surrogate/config.py b/partitioned-burgers-1d/neumann-surrogate/config.py
@@ -0,0 +1,15 @@
+import torch
+
+# Model architecture
+INPUT_SIZE = 128 + 2  # +2 for ghost cells
+HIDDEN_SIZE = 64  # num filters
+OUTPUT_SIZE = 128
+
+assert INPUT_SIZE >= OUTPUT_SIZE, "Input size must be greater or equal to output size."
+assert (INPUT_SIZE - OUTPUT_SIZE) % 2 == 0, "Input and output sizes must differ by an even number (for ghost cells)."
+
+NUM_RES_BLOCKS = 4
+KERNEL_SIZE = 5
+ACTIVATION = torch.nn.ReLU
+
+MODEL_NAME = "CNN_RES_UNROLL_7.pth"
diff --git a/partitioned-burgers-1d/neumann-surrogate/model.py b/partitioned-burgers-1d/neumann-surrogate/model.py
@@ -0,0 +1,117 @@
+import torch
+import torch.nn as nn
+import torch.nn.functional as F
+from torch.nn.utils import weight_norm
+
+
+def pad_with_ghost_cells(input_seq, bc_left, bc_right):
+    return torch.cat([bc_left, input_seq, bc_right], dim=1)
+
+
+class LinearExtrapolationPadding1D(nn.Module):
+    """Applies 'same' padding using linear extrapolation."""
+
+    def __init__(self, kernel_size: int, dilation: int = 1):
+        super().__init__()
+        self.pad_total = dilation * (kernel_size - 1)
+        self.pad_beg = self.pad_total // 2
+        self.pad_end = self.pad_total - self.pad_beg
+
+    def forward(self, x):
+        # Don't pad if not necessary
+        if self.pad_total == 0:
+            return x
+
+        ghost_cell_left = x[:, :, :1]
+        ghost_cell_right = x[:, :, -1:]
+
+        # Calculate the gradient at each boundary
+        grad_left = x[:, :, 1:2] - ghost_cell_left
+        grad_right = ghost_cell_right - x[:, :, -2:-1]
+
+        # Higher order finite difference gradient approximation
+        # grad_left = ( -11 * ghost_cell_left + 18 * x[:, :, 1:2] - 9 * x[:, :, 2:3] + 2 * x[:, :, 3:4]) / 6
+        # grad_right = (11 * ghost_cell_right - 18 * x[:, :, -2:-1] + 9 * x[:, :, -3:-2] - 2 * x[:, :, -4:-3]) / 6
+
+        # 3. Extrapolated padding tensors
+        left_ramp = torch.arange(self.pad_beg, 0, -1, device=x.device, dtype=x.dtype).view(1, 1, -1)
+        left_padding = ghost_cell_left - left_ramp * grad_left
+
+        right_ramp = torch.arange(1, self.pad_end + 1, device=x.device, dtype=x.dtype).view(1, 1, -1)
+        right_padding = ghost_cell_right + right_ramp * grad_right
+
+        return torch.cat([left_padding, x, right_padding], dim=2)
+
+
+class ResidualBlock1D(nn.Module):
+    """A residual block that uses custom 'same' padding with linear extrapolation and weight normalization."""
+
+    def __init__(self, channels, kernel_size=3, activation=nn.ReLU):
+        super(ResidualBlock1D, self).__init__()
+        self.activation = activation()
+        # Apply weight normalization
+        self.conv1 = weight_norm(nn.Conv1d(channels, channels, kernel_size, padding='valid', bias=True))
+        self.ghost_padding1 = LinearExtrapolationPadding1D(kernel_size)
+        self.conv2 = weight_norm(nn.Conv1d(channels, channels, kernel_size, padding='valid', bias=True))
+        self.ghost_padding2 = LinearExtrapolationPadding1D(kernel_size)
+
+    def forward(self, x):
+        identity = x
+
+        out = self.ghost_padding1(x)
+        out = self.conv1(out)
+        out = self.activation(out)
+
+        out = self.ghost_padding2(out)
+        out = self.conv2(out)
+
+        return self.activation(out) + identity
+
+
+class CNN_RES(nn.Module):
+    """
+    A CNN with residual blocks for 1D data.
+    Expects a pre-padded input with ghost_cells//2 number ghost cells on each side.
+    Applies a custom linear extrapolation padding for inner layers.
+    """
+
+    def __init__(self, hidden_channels, num_blocks=2, kernel_size=3, activation=nn.ReLU, ghost_cells=2):
+        super(CNN_RES, self).__init__()
+        self.activation = activation()
+        self.hidden_channels = hidden_channels
+        self.num_blocks = num_blocks
+        self.kernel_size = kernel_size
+        assert ghost_cells % 2 == 0, "ghost_cells must be even"
+        self.ghost_cells = ghost_cells
+
+        self.ghost_padding = LinearExtrapolationPadding1D(self.ghost_cells + self.kernel_size)
+
+        # Apply weight normalization to the input convolution
+        self.conv_in = weight_norm(nn.Conv1d(1, hidden_channels, kernel_size=1, bias=True))
+
+        layers = [ResidualBlock1D(hidden_channels, kernel_size, activation=activation) for _ in range(num_blocks)]
+        self.res_blocks = nn.Sequential(*layers)
+
+        self.conv_out = nn.Conv1d(hidden_channels, 1, kernel_size=1)
+
+    def forward(self, x):
+
+        if x.dim() == 2:
+            x = x.unsqueeze(1)  # Add channel dim: (B, 1, L)
+
+        if not self.ghost_cells == 0:
+            x_padded = self.ghost_padding(x)
+
+        else:
+            x_padded = x
+
+        total_pad_each_side = self.ghost_padding.pad_beg + self.ghost_cells // 2
+
+        out = self.activation(self.conv_in(x_padded))  # no extra padding here
+        out = self.res_blocks(out)
+        out = self.conv_out(out)  # no extra padding here
+
+        if not self.ghost_cells == 0:
+            out = out[:, :, total_pad_each_side:-total_pad_each_side]  # remove ghost cells, return only internal domain
+
+        return out.squeeze(1)
diff --git a/partitioned-burgers-1d/neumann-surrogate/requirements.txt b/partitioned-burgers-1d/neumann-surrogate/requirements.txt
@@ -0,0 +1,5 @@
+numpy==2.3.5
+pyprecice==3.3.1
+scipy==1.16.3
+matplotlib==3.10.8
+torch==2.9.1
diff --git a/partitioned-burgers-1d/neumann-surrogate/run.sh b/partitioned-burgers-1d/neumann-surrogate/run.sh
@@ -0,0 +1,21 @@
+#!/usr/bin/env bash
+set -e -u
+
+if [ ! -v PRECICE_TUTORIALS_NO_VENV ]
+then
+    python3 -m venv .venv
+    . .venv/bin/activate
+    pip install -r requirements.txt && pip freeze > pip-installed-packages.log
+fi
+
+if [ ! -f "../initial_condition.npz" ]; then
+	echo "Generating initial condition..."
+	python3 ../utils/generate_ic.py
+fi
+
+. ../../tools/log.sh
+exec > >(tee --append "$LOGFILE") 2>&1
+
+python3 solver.py
+
+close_log
Original file line number	Diff line number	Diff line change
		@@ -0,0 +1 @@
		New tutorial case: Partitioned Burgers' Equation in 1D solved with Finite Volumes and a Neural Network surrogate model !
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