Physics-Informed Diffusion Probabilistic Model

Overview

Pi-DPM leverages the Denoising Diffusion Probabilistic Model (DDPM) framework to learn the normal patterns of object trajectories, then detects anomalies as deviations from these patterns. Unlike standard diffusion models, Pi-DPM integrates physics-based constraints into the generation process, ensuring that synthetic trajectories remain physically plausible and adhere to known motion laws. This combination of data-driven learning and physics-informed priors improves the alignment of generated trajectories with real-world dynamics and provides a natural regularization against overfitting.

Key Features

• Trajectory Generation: Learn a diffusion model to generate new trajectories similar to those in the training data.
• Physics-Informed Constraints: Incorporate domain knowledge (e.g., smooth motion, dynamics equations) via an additional loss term to guide the model.
• Anomaly Detection: Compute anomaly scores for new trajectories based on reconstruction error under the diffusion model, flagging trajectories that deviate from normal patterns.

Requirements

The required packages with python environment is:

  python>=3.7
  torch>=1.7
  pandas
  numpy
  matplotlib
  pathlib
  shutil
  datetime
  colored
  math

Installation Instructions

1. Clone the repository:

Download the Pi-DPM repository to your local machine, either via git or as a ZIP download.

  git clone https://github.com/arunshar/Physics-Informed-Diffusion-Probabistic-Model.git
  cd Pi-DPM

2. Installation Dependencies:

Pi-DPM is built with Python (>=3.8) and PyTorch. Install the required packages using pip (it is recommended to use a virtual environment):

  pip install -r requirements.txt

Running Instructions

Once the environment is set up, you can use the provided scripts to train the model, detect anomalies on new trajectories, and generate synthetic trajectories. Below are the typical usage steps:

Training the Model

Once the environment is set up, you can use the provided scripts to train the model, detect anomalies on new trajectories, and generate synthetic trajectories. Below are the typical usage steps:

  python scripts/train.py --data data/train_dataset.csv --epochs 100 --batch_size 64 --out checkpoints/							

In this example:

--data specifies the path to the training dataset of normal trajectories.

--epochs and --batch_size control the training iterations and batch size.

--out is the directory to save model checkpoints and training logs.

Detecting Anomalies

Train Pi-DPM on your trajectory dataset by running the training script. This will learn the diffusion model on normal trajectory patterns:

  python scripts/detect.py --model checkpoints/pidpm_model.pth --data data/test_dataset.csv --threshold 0.1 --output results/anomalies.csv						

Here:

--model points to the trained Pi-DPM model checkpoint.

--data is the file or directory containing trajectories to evaluate.

The script will reconstruct or evaluate each trajectory and compute an anomaly score (e.g., based on reconstruction error). If a --threshold is provided, the script will label trajectories with a score above this threshold as anomalies.

--output (optional) can be used to save the anomaly detection results (e.g., anomaly scores or flags for each trajectory) to a CSV file.

Generating Synthetic Trajectories

Pi-DPM can also generate new, synthetic trajectories that mimic the normal behavior learned from the training data. This can be useful for data augmentation or simulating trajectories under the learned model:

python scripts/generate.py --model checkpoints/pidpm_model.pth --num_samples 50 --out results/synthetic_trajectories.csv

  python scripts/generate.py --model checkpoints/pidpm_model.pth --num_samples 50 --out results/synthetic_trajectories.csv

Project Structure

Physics-Informed-Diffusion-Probabistic-Model/
├── pidpm/                   # Core Python package for the Pi-DPM model
│   ├── __init__.py          # Init file for package
│   ├── diffusion.py         # Diffusion model implementation (forward & reverse process)
│   ├── physics.py           # Module for physics-informed constraints and losses
│   ├── models.py            # Neural network architectures for trajectory encoding/decoding
│   ├── utils.py             # Helper functions (data loading, metrics, etc.)
│   └── __init__.py          # Init file for package
├── scripts/                 # Scripts for training, inference, and generation
│   ├── train.py             # Script to train the Pi-DPM model on a dataset
│   ├── detect.py            # Script to compute anomaly scores for trajectories using a trained model
│   └── generate.py          # Script to generate synthetic trajectories from the model
├── data/                    # Directory for datasets (user-provided, not included in repository)
│   └── sample_dataset.csv   # Example placeholder for trajectory data
├── results/                 # Output directory for results (model checkpoints, anomaly outputs, synthetic data)
├── requirements.txt         # List of required Python packages for Pi-DPM
├── LICENSE                  # MIT License for this project
└── README.md                # Project documentation (this file)