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update NS demo - modified introduction #81

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921cc6c
update NS demo - modified introduction
May 22, 2025
cdc6ab8
update NavierStokes.ipynb
May 29, 2025
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39 changes: 16 additions & 23 deletions PARCtorch/demos/NavierStokes.ipynb
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Expand Up @@ -12,42 +12,36 @@
" <img src=\"../misc/iowa.png\" width=\"190\" alt=\"Image 3\" />\n",
" </div>\n",
"</div>\n",
"<p>A customizable framework to embed physics in Deep Learning. PARC's formulation is inspired by Advection-Diffusion-Reaction processes and uses an Inductive Bias approach to constrain the Neural Network.</p>\n",
"\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Why PARC?\n",
"<p>PARC brings together deep learning with first prinicples physics - its recurrent convolutional core is able to learn complex spatiotemporal patterns, while built-in biases (conservation laws & advection-diffusion operators) ensure every prediction is physically plausible. PARC is constructed in such a manner that is does not need to \"re-learn\" fundemental dynamics - allowing faster training with far less data.</p>\n",
"\n",
"<p>PINN (Physics-Informed Neural Networks) exists as an adjacent model to PARC. While PINN may preform decently on generics, it struggles with advection or chaotic/non-linear systems - net leading to higher computational cost. In such situations PARC is deemed the superior model with it being more scalable, efficient, and accurate than other physics-based models.</p>\n",
"\n",
"### Goal\n",
"<p>The goal of this notebook is to walk you through the use cases of PARC via the Navier-Stokes equation. At the end of this notebook you will be presented with visualization in accordance to the equations representing conservation of momentum for fluids and fully describing fluid motion.</p>\n",
"<p>This notebook is to demonstrate how to configure PARC to model the dynamcis of the Navier-Stokes equation.</p>\n",
"\n",
"The notebook will guide you through from start to finish in preparing, training, and modeling a physics-based equation. The notebook will cover the following:\n",
"Particularly, this notebook will guide thorugh the complete cycle of statistical modelling, more specifically: \n",
"- load and prepare data for Navier-Stokes\n",
"- train PARC to learn the dynamcis of the Navier-Stokes equation\n",
"- evalaute performance to ground truth simulation.\n",
"\n",
"- loading and preparinf data for Navier-Stokes\n",
"- Using PARCv2 Model to learn and predict time evolution of $u(x,t)$\n",
"- Evaluating the model's preformance and compare predicted resutls to ground truth\n",
"\n",
"### Internal General PARC PDE\n",
"<p>Below is the general form of the partial differential equation that PARCv2 is learning - and its inital boundaries. In the case of the Navier-Stokes equations - we can describe the certain vairables to represent the nessearcy points in which PARC tries to model after the equation.</p>\n",
"### PARC for Navier-Stokes\n",
"<p>PARC is designed to learn the general dynamical system that follows: </p>\n",
"\n",
"$$\n",
"\\frac{\\partial X}{\\partial t} = f(X,\\mu) + \\epsilon\n",
"\\frac{\\partial X}{\\partial t} = f(X,U, c) + \\epsilon\n",
"$$\n",
"\n",
"- $X$ is the fields of interest - Temperature, Pressure, Reynolds, Velocities (U & V)\n",
"- $μ$ is the microstructure\n",
"- Scalar Fields ($X$): Pressure, Density\n",
"- Velocity Fields ($U$): Velocity\n",
"- Scalar Value ($c$): Reynolds number\n",
"\n",
"\n",
"### Setting Up\n",
"<p>This document serves as a guide to training a PARC model for the Navier-Stokes equation. Here are the inital steps to take before you begin training your PARC model!<p>\n",
"<p>This document serves as a guide to train PARC model for the Navier-Stokes equation. Here are the inital steps to take before you begin training your PARC model!<p>\n",
"\n",
"Download & Prepare Data:\n",
"- Download the data from https://zenodo.org/records/13909869 and unzip it.\n",
Expand All @@ -73,18 +67,17 @@
},
{
"cell_type": "code",
"execution_count": null,
"execution_count": 15,
"metadata": {},
"outputs": [],
"source": [
"from pathlib import Path\n",
"from PARCtorch.data.normalization import compute_min_max\n",
"\n",
"# Define data directories\n",
"train_dir = Path(\"../data/navier_stokes/train\")\n",
"test_dir = Path(\"../data/navier_stokes/test\")\n",
"train_dir = Path(\"path/to/train/\")\n",
"test_dir = Path(\"path/to/test\")\n",
"min_max_file = train_dir.parent / \"ns_min_max.json\"\n",
"\n",
"compute_min_max([train_dir, test_dir], min_max_file)"
]
},
Expand Down Expand Up @@ -530,7 +523,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.13.2"
"version": "3.11.6"
}
},
"nbformat": 4,
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