| Name | separable-operator-networks JSON |
| Version |
0.0.2
JSON |
| download |
| home_page | None |
| Summary | Separable operator models for extreme-scale learning of parametric PDEs |
| upload_time | 2024-11-01 23:54:41 |
| maintainer | None |
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| author | None |
| requires_python | >=3.8 |
| license | Copyright (c) 2024 Hewlett Packard Development Enterprise LP 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. |
| keywords |
deeponet
pde
deep operator network
operator learning
partial differential equations
phyics-informed neural network
scientific machine learning
|
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# Separable Operator Networks (SepONet)
[](https://arxiv.org/abs/2407.11253)
[](https://pypi.org/project/separable-operator-networks)
This is the official repository for separable operator networks (SepONet) originally introduced in [this preprint](https://arxiv.org/abs/2407.11253) [1].
## Installation
This code uses JAX as a dependency. It is recommended to [install with GPU/TPU compatibility](https://jax.readthedocs.io/en/latest/installation.html) prior to installing this library. JAX CPU is provided as the default dependency.
Please install with pip:
```bash
pip install separable-operator-networks
```
Alternatively, you may specify the `[cuda12]` extra to install `jax[cuda12]` automatically:
```bash
pip install separable-operator-networks[cuda12]
```
## Description
Operator learning has become a powerful tool in machine learning for modeling complex physical systems governed by partial differential equations (PDEs). Although Deep Operator Networks (DeepONet) show promise, they require extensive data acquisition. Physics-informed DeepONets (PI-DeepONet) mitigate data scarcity but suffer from inefficient training processes. We introduce Separable Operator Networks (SepONet), a novel framework that significantly enhances the efficiency of physics-informed operator learning. SepONet uses independent trunk networks to learn basis functions separately for different coordinate axes, enabling faster and more memory-efficient training via forward-mode automatic differentiation. The SepONet architecture for a $d=2$ dimensional coordinate grid is depicted below. The architecture is inspired by the method of separation of variables and recent exploration of separable physics-informed neural networks [2] for single instance PDE solutions.
Our [preprint](https://arxiv.org/abs/2407.11253) provides a universal approximation theorem for SepONet proving that it generalizes to arbitrary operator learning problems. For a variety of 1D time-dependent PDEs, SepONet has similar accuracy scaling to PI-DeepONet, but with as much as 112x faster training time and 82x reduction in GPU memory usage. For 2D time-dependent PDEs, SepONet is capable of accurate predictions at scales where PI-DeepONet fails. The full test scaling results as a function of the number of collocation points and number of input functions is shown below. These results may be reproduced using our [scripts](https://github.com/HewlettPackard/separable-operator-networks/tree/main/scripts).
## Code Overview
A SepONet model can be imported using:
```python
import jax
import separable_operator_networks as sepop
d = ... # replace with problem dimension
branch_dim = ... # replace with input shape for branch network (MLP by default)
key = jax.random.key(0)
model = sepop.models.SepONet(d, branch_dim, key=key)
```
Other model classes such as `PINN`, `SPINN`, `DeepONet` are implemented in the `sepop.models` submodule. These models are implemented as subclasses of `eqx.Module` (see [equinox](https://github.com/patrick-kidger/equinox)), enabling `eqx.filter_vmap` and `eqx.filter_grad`, along with easily customizable training routines via [optax](https://github.com/google-deepmind/optax) (see `sepop.train.train_loop(...)` for a simple `optax` training loop). PDE instances, loss functions, and other helper functions can be imported from the corresponding examples in the `sepop.pde` submodule (such as `sepop.pde.advection`).
Test data can be generated using the Python scripts in `/scripts/generate_test_data`. Test cases can be ran using the scripts in `/scripts/main_scripts` and `/scripts/scale_tests`.
## Citation
```tex
@misc{yu2024separableoperatornetworks,
title={Separable Operator Networks},
author={Xinling Yu and Sean Hooten and Ziyue Liu and Yequan Zhao and Marco Fiorentino and Thomas Van Vaerenbergh and Zheng Zhang},
year={2024},
eprint={2407.11253},
archivePrefix={arXiv},
primaryClass={cs.LG},
url={https://arxiv.org/abs/2407.11253},
}
```
## Authors
Sean Hooten (sean dot hooten at hpe dot com)
Xinling Yu (xyu644 at ucsb dot edu)
## License
MIT (see LICENSE.md)
## References
[1] X. Yu, S. Hooten, Z. Liu, Y. Zhao, M. Fiorentino, T. Van Vaerenbergh, and Z. Zhang. Separable Operator Networks. arXiv preprint arXiv:2407.11253 (2024).
[2] J. Cho, S. Nam, H. Yang, S.-B. Yun, Y. Hong, E. Park. Separable PINN: Mitigating the Curse of Dimensionality in Physics-Informed Neural Networks. arXiv preprint arXiv: 2211.08761 (2023).
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"description": "# Separable Operator Networks (SepONet)\n[](https://arxiv.org/abs/2407.11253)\n[](https://pypi.org/project/separable-operator-networks)\n\nThis is the official repository for separable operator networks (SepONet) originally introduced in [this preprint](https://arxiv.org/abs/2407.11253) [1]. \n\n## Installation\nThis code uses JAX as a dependency. It is recommended to [install with GPU/TPU compatibility](https://jax.readthedocs.io/en/latest/installation.html) prior to installing this library. JAX CPU is provided as the default dependency.\n\nPlease install with pip:\n```bash\npip install separable-operator-networks\n```\nAlternatively, you may specify the `[cuda12]` extra to install `jax[cuda12]` automatically:\n```bash\npip install separable-operator-networks[cuda12]\n```\n\n## Description\n\nOperator learning has become a powerful tool in machine learning for modeling complex physical systems governed by partial differential equations (PDEs). Although Deep Operator Networks (DeepONet) show promise, they require extensive data acquisition. Physics-informed DeepONets (PI-DeepONet) mitigate data scarcity but suffer from inefficient training processes. We introduce Separable Operator Networks (SepONet), a novel framework that significantly enhances the efficiency of physics-informed operator learning. SepONet uses independent trunk networks to learn basis functions separately for different coordinate axes, enabling faster and more memory-efficient training via forward-mode automatic differentiation. The SepONet architecture for a $d=2$ dimensional coordinate grid is depicted below. The architecture is inspired by the method of separation of variables and recent exploration of separable physics-informed neural networks [2] for single instance PDE solutions.\n\nOur [preprint](https://arxiv.org/abs/2407.11253) provides a universal approximation theorem for SepONet proving that it generalizes to arbitrary operator learning problems. For a variety of 1D time-dependent PDEs, SepONet has similar accuracy scaling to PI-DeepONet, but with as much as 112x faster training time and 82x reduction in GPU memory usage. For 2D time-dependent PDEs, SepONet is capable of accurate predictions at scales where PI-DeepONet fails. The full test scaling results as a function of the number of collocation points and number of input functions is shown below. These results may be reproduced using our [scripts](https://github.com/HewlettPackard/separable-operator-networks/tree/main/scripts).\n\n\n\n\n\n## Code Overview\n\nA SepONet model can be imported using:\n```python\nimport jax\nimport separable_operator_networks as sepop\nd = ... # replace with problem dimension\nbranch_dim = ... # replace with input shape for branch network (MLP by default)\nkey = jax.random.key(0)\n\nmodel = sepop.models.SepONet(d, branch_dim, key=key)\n```\nOther model classes such as `PINN`, `SPINN`, `DeepONet` are implemented in the `sepop.models` submodule. These models are implemented as subclasses of `eqx.Module` (see [equinox](https://github.com/patrick-kidger/equinox)), enabling `eqx.filter_vmap` and `eqx.filter_grad`, along with easily customizable training routines via [optax](https://github.com/google-deepmind/optax) (see `sepop.train.train_loop(...)` for a simple `optax` training loop). PDE instances, loss functions, and other helper functions can be imported from the corresponding examples in the `sepop.pde` submodule (such as `sepop.pde.advection`).\n\nTest data can be generated using the Python scripts in `/scripts/generate_test_data`. Test cases can be ran using the scripts in `/scripts/main_scripts` and `/scripts/scale_tests`.\n\n## Citation\n\n```tex\n@misc{yu2024separableoperatornetworks,\ntitle={Separable Operator Networks}, \nauthor={Xinling Yu and Sean Hooten and Ziyue Liu and Yequan Zhao and Marco Fiorentino and Thomas Van Vaerenbergh and Zheng Zhang},\nyear={2024},\neprint={2407.11253},\narchivePrefix={arXiv},\nprimaryClass={cs.LG},\nurl={https://arxiv.org/abs/2407.11253}, \n}\n```\n\n## Authors\n\nSean Hooten (sean dot hooten at hpe dot com) \nXinling Yu (xyu644 at ucsb dot edu)\n\n## License\n\nMIT (see LICENSE.md)\n\n## References\n\n[1] X. Yu, S. Hooten, Z. Liu, Y. Zhao, M. Fiorentino, T. Van Vaerenbergh, and Z. Zhang. Separable Operator Networks. arXiv preprint arXiv:2407.11253 (2024). \n[2] J. Cho, S. Nam, H. Yang, S.-B. Yun, Y. Hong, E. Park. Separable PINN: Mitigating the Curse of Dimensionality in Physics-Informed Neural Networks. arXiv preprint arXiv: 2211.08761 (2023).",
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