<p align="center">
<img src=https://github.com/jung235/pydiffuser/assets/96967431/a9f54ef6-d1d4-4fcf-88bf-8c336dd671c0 width="30%">
<h1 align="center">Pydiffuser</h1>
</p>
[](https://pypi.org/project/pydiffuser/)
[](https://pypi.org/project/pydiffuser/)
[](https://zenodo.org/doi/10.5281/zenodo.10017027)
[](https://codecov.io/gh/jung235/pydiffuser)
[](https://github.com/jung235/pydiffuser/actions/workflows/ci.yml)
[](https://github.com/jung235/pydiffuser/blob/main/README.md)
[](https://github.com/jung235/pydiffuser)
Pydiffuser is a numerical simulation framework for nonequilibrium statistical physics based on [JAX](https://github.com/google/jax).
This package mainly aims:
- to share code to implement a numerical simulation on physical models written in various forms of [stochastic differential equations](https://en.wikipedia.org/wiki/Stochastic_differential_equation).
- to revisit recent research highlights in nonequilibrium statistical physics.
- to reduce the repeated code on time-series data analysis, e.g., statistical analysis of [single-particle trajectory](https://en.wikipedia.org/wiki/Single-particle_trajectory) for [SPT](https://en.wikipedia.org/wiki/Single-particle_tracking) experiments.
- to provide the skeleton of stochastic modeling for anyone interested in stochastic processes.
## Installation
### Requirements
Python 3.10+, [`jax>=0.4.18`](https://pypi.org/project/jax/), and [`jaxlib>=0.4.18`](https://pypi.org/project/jaxlib/).
### From [PyPI](https://pypi.org/project/pydiffuser/)
```console
$ pip install pydiffuser
```
If properly installed, you can run:
```console
$ pydiffuser --version
pydiffuser, version 0.0.3
```
## Quickstart
Pydiffuser provides various stochastic models that implement a numerical simulation based on the [Monte Carlo method](https://en.wikipedia.org/wiki/Monte_Carlo_method).
All Pydiffuser's models inherit an abstract class `pydiffuser.models.BaseDiffusion` and initiate the simulation after a method `generate` is called.
For the simplest case, you can produce a non-interacting [Brownian motion](https://en.wikipedia.org/wiki/Brownian_motion) at low Reynolds numbers as follows:
```python
from pydiffuser.models import BrownianMotion
from pydiffuser.tracer import Ensemble, Trajectory
model = BrownianMotion()
ensemble: Ensemble = model.generate()
tracer: Trajectory = ensemble[0] # the 0th particle
```
Relevant stochastic observables, such as [mean-squared displacement](https://en.wikipedia.org/wiki/Mean_squared_displacement) and normalized [velocity autocorrelation function](https://en.wikipedia.org/wiki/Autocorrelation), can be calculated through the [methods](#observables) of `Trajectory` and `Ensemble`.
```python
tamsd = tracer.get_mean_squared_displacement(lagtime=1, rolling=True)
eamsd = ensemble.get_mean_squared_displacement(lagtime=1, rolling=False)
eatamsd = ensemble.get_mean_squared_displacement(lagtime=1, rolling=True)
```
You can visualize the trajectory using [matplotlib](https://github.com/matplotlib/matplotlib):
<p align="center" width="100%">
<img width="25%" src=https://github.com/jung235/pydiffuser/assets/96967431/544f3d2f-1b51-46f6-8036-ee7f296fddad>
</p>
It is obtained by `matplotlib.pyplot.plot(tracer.position_x1, tracer.position_x2)`.
## CLI
List all stochastic models supported by Pydiffuser.
```console
$ pydiffuser model list
NAME MODEL CONFIG DIMENSION
abp ActiveBrownianParticle ActiveBrownianParticleConfig 2d
aoup ActiveOUParticle ActiveOUParticleConfig 1d, 2d, 3d
bm BrownianMotion BrownianMotionConfig 1d, 2d, 3d
levy LevyWalk LevyWalkConfig 1d, 2d, 3d
mips PhaseSeparation PhaseSeparationConfig 1d, 2d, 3d
rtp RunAndTumbleParticle RunAndTumbleParticleConfig 1d, 2d, 3d
smoluchowski SmoluchowskiEquation SmoluchowskiEquationConfig 1d, 2d
vicsek VicsekModel VicsekModelConfig 2d
```
## Features
### How fast is it?
When generating $N$ realizations consisting of $L$ footprints, we have:
```julia
═════════════════════════════════════════════════════════════════════════════════════════════════
Model Method Running time [s] for N x L =
10² x 10⁵ 10³ x 10⁴ 10⁴ x 10³
─────────────────────────────────────────────────────────────────────────────────────────────────
`loop` [*] 3.62 (0.19) 3.45 (0.23) 3.37 (0.21)
─────────────────────────────────────────────────────────────────────────────────────────────────
`abp` `generate` 1.95 (0.14) 1.74 (0.12) 1.59 (0.11)
`aoup` `generate` 1.61 (0.08) 1.61 (0.15) 1.55 (0.09)
`bm` `generate` 1.45 (0.11) 1.46 (0.13) 1.46 (0.14)
`smoluchowski` `generate` 1.71 (0.12) 1.67 (0.15) 1.64 (0.13)
─────────────────────────────────────────────────────────────────────────────────────────────────
`bm` `create` 1440.72 (158.16) 964.90 (83.06) 1195.41 (94.28)
═════════════════════════════════════════════════════════════════════════════════════════════════
```
<details>
<summary>[*]</summary>
```python
def loop(N: int, L: int) -> float:
"""Even the most straightforward loop requires over 3 [s] for all (N, L) conditions.
"""
t1 = time.time()
xes = []
for _ in range(N):
x = []
for _ in range(1, L):
x.append([])
xes.append(x)
t2 = time.time()
return t2 - t1
```
</details>
The represented running time is a mean $\mu$ (standard deviation $\sigma$) of five trials.
### Observables
*class* `pydiffuser.tracer.Trajectory` ∈ *class* `pydiffuser.tracer.Ensemble`
- `get_increments`
- `get_displacement_moment`
- `get_mean_squared_displacement`
- `get_cosine_moment`
- `get_velocity_autocorrelation`
- `get_real_time`
The above methods are defined in both `Trajectory` and `Ensemble` to enhance transparency.
Using `Trajectory`, the statistical analysis of [single-particle trajectory](https://en.wikipedia.org/wiki/Single-particle_trajectory) can be accelerated.
### Configuration
We introduce a configuration to deal with extensive parameter manipulation.
For instance, see [`config.json`](https://github.com/jung235/pydiffuser/blob/main/docs/features/configs/config.json), which contains all parameters demanded to instantiate `pydiffuser.ActiveBrownianParticle`.
Every JSON of the configurations listed in [CLI](#cli) can be obtained as follows:
```python
import pydiffuser as pyd
from pydiffuser.models import ActiveBrownianParticle, ActiveBrownianParticleConfig
config = ActiveBrownianParticleConfig()
config.to_json(json_path=<JSON_PATH>)
```
We suggest a research pipeline:
```python
┌────┐ ┌─────────────────────┐ ┌───────────────┐ ┌──────────┐ ┌────────────┐
│JSON├──>──┤`BaseDiffusionConfig`├──>──┤`BaseDiffusion`├──>──┤`Ensemble`├──>──┤NPY | PICKLE│
└────┘ [1] └─────────────────────┘ [2] └───────────────┘ [3] └──────────┘ [4] └────────────┘
```
It can be automized as follows:
```python
config = ActiveBrownianParticleConfig.from_json(json_path=<JSON_PATH>) # [1]
model = ActiveBrownianParticle.from_config(config=config) # [2]
ensemble = model.generate() # [3]
ensemble.to_npy(npy_path=<NPY_PATH>) # [4]
```
You can save and load any picklable object through `pydiffuser.save` and `pydiffuser.load`.
```python
MODEL_PATH = "model.pickle"
pyd.save(obj=model, pickle_path=MODEL_PATH) # Here, <PICKLE_PATH> = MODEL_PATH
model = pyd.load(pickle_path=MODEL_PATH)
```
## Related Works
[Hyperdiffusion of Poissonian run-and-tumble particles in two dimensions](https://arxiv.org/abs/2308.00554)
## License
[Apache License 2.0](https://github.com/jung235/pydiffuser/blob/main/LICENSE)
## Citation
```bibtex
@misc{jung2023pydiffuser,
title = {Pydiffuser: a simulation framework for nonequilibrium statistical physics},
author = {Jung, Yurim},
year = {2023},
note = {doi: 10.5281/zenodo.10017027},
}
```
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"keywords": "nonequilibrium statistical physics, langevin dynamics, stochastic process, computer simulation",
"author": "Yurim Jung",
"author_email": "jung65537@gmail.com",
"download_url": "https://files.pythonhosted.org/packages/81/40/312bafee8f8e8864c5ce3041955038663f21e4a8693b03fb5dfae73e04c9/pydiffuser-0.0.3.tar.gz",
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"description": "<p align=\"center\">\n <img src=https://github.com/jung235/pydiffuser/assets/96967431/a9f54ef6-d1d4-4fcf-88bf-8c336dd671c0 width=\"30%\">\n <h1 align=\"center\">Pydiffuser</h1>\n</p>\n\n[](https://pypi.org/project/pydiffuser/)\n[](https://pypi.org/project/pydiffuser/)\n[](https://zenodo.org/doi/10.5281/zenodo.10017027)\n[](https://codecov.io/gh/jung235/pydiffuser)\n[](https://github.com/jung235/pydiffuser/actions/workflows/ci.yml)\n[](https://github.com/jung235/pydiffuser/blob/main/README.md)\n[](https://github.com/jung235/pydiffuser)\n\nPydiffuser is a numerical simulation framework for nonequilibrium statistical physics based on [JAX](https://github.com/google/jax).\n\nThis package mainly aims:\n- to share code to implement a numerical simulation on physical models written in various forms of [stochastic differential equations](https://en.wikipedia.org/wiki/Stochastic_differential_equation).\n- to revisit recent research highlights in nonequilibrium statistical physics.\n- to reduce the repeated code on time-series data analysis, e.g., statistical analysis of [single-particle trajectory](https://en.wikipedia.org/wiki/Single-particle_trajectory) for [SPT](https://en.wikipedia.org/wiki/Single-particle_tracking) experiments.\n- to provide the skeleton of stochastic modeling for anyone interested in stochastic processes.\n\n## Installation\n\n### Requirements\n\nPython 3.10+, [`jax>=0.4.18`](https://pypi.org/project/jax/), and [`jaxlib>=0.4.18`](https://pypi.org/project/jaxlib/).\n\n### From [PyPI](https://pypi.org/project/pydiffuser/)\n\n```console\n$ pip install pydiffuser\n```\n\nIf properly installed, you can run:\n\n```console\n$ pydiffuser --version\npydiffuser, version 0.0.3\n```\n\n## Quickstart\n\nPydiffuser provides various stochastic models that implement a numerical simulation based on the [Monte Carlo method](https://en.wikipedia.org/wiki/Monte_Carlo_method).\nAll Pydiffuser's models inherit an abstract class `pydiffuser.models.BaseDiffusion` and initiate the simulation after a method `generate` is called.\nFor the simplest case, you can produce a non-interacting [Brownian motion](https://en.wikipedia.org/wiki/Brownian_motion) at low Reynolds numbers as follows:\n\n```python\nfrom pydiffuser.models import BrownianMotion\nfrom pydiffuser.tracer import Ensemble, Trajectory\n\n\nmodel = BrownianMotion()\nensemble: Ensemble = model.generate()\ntracer: Trajectory = ensemble[0] # the 0th particle\n```\n\nRelevant stochastic observables, such as [mean-squared displacement](https://en.wikipedia.org/wiki/Mean_squared_displacement) and normalized [velocity autocorrelation function](https://en.wikipedia.org/wiki/Autocorrelation), can be calculated through the [methods](#observables) of `Trajectory` and `Ensemble`.\n\n```python\ntamsd = tracer.get_mean_squared_displacement(lagtime=1, rolling=True)\neamsd = ensemble.get_mean_squared_displacement(lagtime=1, rolling=False)\neatamsd = ensemble.get_mean_squared_displacement(lagtime=1, rolling=True)\n```\n\nYou can visualize the trajectory using [matplotlib](https://github.com/matplotlib/matplotlib):\n\n<p align=\"center\" width=\"100%\">\n <img width=\"25%\" src=https://github.com/jung235/pydiffuser/assets/96967431/544f3d2f-1b51-46f6-8036-ee7f296fddad>\n</p>\n\nIt is obtained by `matplotlib.pyplot.plot(tracer.position_x1, tracer.position_x2)`.\n\n## CLI\n\nList all stochastic models supported by Pydiffuser.\n\n```console\n$ pydiffuser model list\nNAME MODEL CONFIG DIMENSION \nabp ActiveBrownianParticle ActiveBrownianParticleConfig 2d \naoup ActiveOUParticle ActiveOUParticleConfig 1d, 2d, 3d \nbm BrownianMotion BrownianMotionConfig 1d, 2d, 3d \nlevy LevyWalk LevyWalkConfig 1d, 2d, 3d \nmips PhaseSeparation PhaseSeparationConfig 1d, 2d, 3d \nrtp RunAndTumbleParticle RunAndTumbleParticleConfig 1d, 2d, 3d \nsmoluchowski SmoluchowskiEquation SmoluchowskiEquationConfig 1d, 2d \nvicsek VicsekModel VicsekModelConfig 2d \n```\n\n## Features\n\n### How fast is it?\n\nWhen generating $N$ realizations consisting of $L$ footprints, we have:\n\n```julia\n\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\nModel Method Running time [s] for N x L = \n 10\u00b2 x 10\u2075 10\u00b3 x 10\u2074 10\u2074 x 10\u00b3 \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n`loop` [*] 3.62 (0.19) 3.45 (0.23) 3.37 (0.21) \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n`abp` `generate` 1.95 (0.14) 1.74 (0.12) 1.59 (0.11) \n`aoup` `generate` 1.61 (0.08) 1.61 (0.15) 1.55 (0.09) \n`bm` `generate` 1.45 (0.11) 1.46 (0.13) 1.46 (0.14) \n`smoluchowski` `generate` 1.71 (0.12) 1.67 (0.15) 1.64 (0.13) \n\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\n`bm` `create` 1440.72 (158.16) 964.90 (83.06) 1195.41 (94.28) \n\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\u2550\n```\n\n<details>\n<summary>[*]</summary>\n\n```python\ndef loop(N: int, L: int) -> float:\n \"\"\"Even the most straightforward loop requires over 3 [s] for all (N, L) conditions.\n \"\"\"\n\n t1 = time.time()\n\n xes = []\n for _ in range(N):\n x = []\n for _ in range(1, L):\n x.append([])\n xes.append(x)\n\n t2 = time.time()\n return t2 - t1\n```\n</details>\n\nThe represented running time is a mean $\\mu$ (standard deviation $\\sigma$) of five trials.\n\n### Observables\n\n*class* `pydiffuser.tracer.Trajectory` \u2208 *class* `pydiffuser.tracer.Ensemble`\n\n- `get_increments`\n- `get_displacement_moment`\n- `get_mean_squared_displacement`\n- `get_cosine_moment`\n- `get_velocity_autocorrelation`\n- `get_real_time`\n\nThe above methods are defined in both `Trajectory` and `Ensemble` to enhance transparency.\nUsing `Trajectory`, the statistical analysis of [single-particle trajectory](https://en.wikipedia.org/wiki/Single-particle_trajectory) can be accelerated.\n\n### Configuration\n\nWe introduce a configuration to deal with extensive parameter manipulation.\nFor instance, see [`config.json`](https://github.com/jung235/pydiffuser/blob/main/docs/features/configs/config.json), which contains all parameters demanded to instantiate `pydiffuser.ActiveBrownianParticle`.\nEvery JSON of the configurations listed in [CLI](#cli) can be obtained as follows:\n\n```python\nimport pydiffuser as pyd\nfrom pydiffuser.models import ActiveBrownianParticle, ActiveBrownianParticleConfig\n\n\nconfig = ActiveBrownianParticleConfig()\nconfig.to_json(json_path=<JSON_PATH>)\n```\n\nWe suggest a research pipeline:\n\n```python\n\u250c\u2500\u2500\u2500\u2500\u2510 \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510 \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510 \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510 \u250c\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2510\n\u2502JSON\u251c\u2500\u2500>\u2500\u2500\u2524`BaseDiffusionConfig`\u251c\u2500\u2500>\u2500\u2500\u2524`BaseDiffusion`\u251c\u2500\u2500>\u2500\u2500\u2524`Ensemble`\u251c\u2500\u2500>\u2500\u2500\u2524NPY | PICKLE\u2502\n\u2514\u2500\u2500\u2500\u2500\u2518 [1] \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518 [2] \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518 [3] \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518 [4] \u2514\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2500\u2518\n```\n\nIt can be automized as follows:\n\n```python\nconfig = ActiveBrownianParticleConfig.from_json(json_path=<JSON_PATH>) # [1]\nmodel = ActiveBrownianParticle.from_config(config=config) # [2]\nensemble = model.generate() # [3]\nensemble.to_npy(npy_path=<NPY_PATH>) # [4]\n```\n\nYou can save and load any picklable object through `pydiffuser.save` and `pydiffuser.load`.\n\n```python\nMODEL_PATH = \"model.pickle\"\n\n\npyd.save(obj=model, pickle_path=MODEL_PATH) # Here, <PICKLE_PATH> = MODEL_PATH\nmodel = pyd.load(pickle_path=MODEL_PATH)\n```\n\n## Related Works\n\n[Hyperdiffusion of Poissonian run-and-tumble particles in two dimensions](https://arxiv.org/abs/2308.00554)\n\n## License\n\n[Apache License 2.0](https://github.com/jung235/pydiffuser/blob/main/LICENSE)\n\n## Citation\n\n```bibtex\n@misc{jung2023pydiffuser,\n title = {Pydiffuser: a simulation framework for nonequilibrium statistical physics},\n author = {Jung, Yurim},\n year = {2023},\n note = {doi: 10.5281/zenodo.10017027},\n}\n```\n",
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