Transformers for Modeling Physical Systems

<p>Data set associated with the publication&nbsp;<a href="https://arxiv.org/abs/2010.03957">Transformers for Modeling Physical Systems</a>. Transformers are widely used in natural language processing due to their ability to model longer-term dependencies in text. Although these models achieve state-of-the-art performance for many language related tasks, their applicability outside of the natural language processing field has been minimal. In this work, we propose the use of transformer models for the prediction of dynamical systems representative of physical phenomena.&nbsp;</p> <p>This data set includes data in HDF5 files&nbsp;for:</p> <p>Lorenz ODE:</p> <ul> <li><a href="https://zenodo.org/api/files/8580a888-775c-471a-95ef-5e6df6f085a2/lorenz_training_rk.tar.gz?versionId=c4bd1230-3b22-4d2e-83f0-357146a90423">lorenz_training_rk.tar.gz</a></li> <li><a href="https://zenodo.org/api/files/8580a888-775c-471a-95ef-5e6df6f085a2/lorenz_valid_rk.tar.gz?versionId=3cf95dac-a75d-42d8-85ab-615f7a2ad67f">lorenz_valid_rk.tar.gz</a></li> <li><a href="https://zenodo.org/api/files/8580a888-775c-471a-95ef-5e6df6f085a2/lorenz_test_rk.tar.gz?versionId=bbb4bd3d-33c9-4903-98ed-f7a926dc95db">lorenz_test_rk.tar.gz</a></li> </ul> <p>Flow Around a Cylinder:</p> <ul> <li><a href="https://zenodo.org/api/files/8580a888-775c-471a-95ef-5e6df6f085a2/cylinder_training.tar.gz?versionId=25bd1f3a-03b7-44d0-aa3f-afaffa6cd706">cylinder_training.tar.gz</a></li> <li><a href="https://zenodo.org/api/files/8580a888-775c-471a-95ef-5e6df6f085a2/cylinder_valid.tar.gz?versionId=58a6e98d-be41-4603-91cb-9522d848cf57">cylinder_valid.tar.gz</a></li> <li><a href="https://zenodo.org/api/files/8580a888-775c-471a-95ef-5e6df6f085a2/cylinder_test.tar.gz?versionId=a3c03293-0278-40ee-b181-2eb53a8d0b47">cylinder_test.tar.gz</a></li> </ul> <p>Gray-Scott Reaction-Diffusion:</p> <ul> <li><a href="https://zenodo.org/api/files/8580a888-775c-471a-95ef-5e6df6f085a2/grayscott_training.tar.gz">grayscott_training.tar.gz</a></li> <li><a href="https://zenodo.org/api/files/8580a888-775c-471a-95ef-5e6df6f085a2/grayscott_valid.tar.gz?versionId=3bb8aa25-c9c8-494e-a206-e8d1fdb8a88f">grayscott_valid.tar.gz</a></li> <li><a href="https://zenodo.org/api/files/8580a888-775c-471a-95ef-5e6df6f085a2/grayscott_test.tar.gz?versionId=d9cee8a6-b22f-44b9-ae1b-2433caf77e34">grayscott_test.tar.gz</a></li> </ul> <p>Rossler ODE:</p> <ul> <li><a href="https://zenodo.org/api/files/8580a888-775c-471a-95ef-5e6df6f085a2/rossler_training.tar.gz?versionId=d44be9cf-8fa7-4eb2-8b6e-8ac129822f51">rossler_training.tar.gz</a></li> <li><a href="https://zenodo.org/api/files/8580a888-775c-471a-95ef-5e6df6f085a2/rossler_valid.tar.gz?versionId=93c658e3-235a-4150-b233-ed514d6c7467">rossler_valid.tar.gz</a></li> </ul> <p>As well as several pretrained embedding models for the Google Collab notebooks on <a href="https://github.com/zabaras/transformer-physx/">Github</a>:</p> <ul> <li><a href="https://zenodo.org/api/files/8580a888-775c-471a-95ef-5e6df6f085a2/embedding_lorenz_pretrained.pth?versionId=cd30ff4e-34b3-4070-b346-718fb8526dac">embedding_lorenz_pretrained.pth</a></li> <li><a href="https://zenodo.org/api/files/8580a888-775c-471a-95ef-5e6df6f085a2/embedding_cylinder_pretrained.pth?versionId=69552efb-09e4-49d9-a224-ccc7cff91b86">embedding_cylinder_pretrained.pth</a></li> <li><a href="https://zenodo.org/api/files/8580a888-775c-471a-95ef-5e6df6f085a2/embedding_rossler_pretrained.pth?versionId=e7d1f4aa-3f31-45fe-91e4-8411e9cd634f">embedding_rossler_pretrained.pth</a></li> </ul> <p>See the Github repository for code base: <a href="https://github.com/zabaras/transformer-physx/">https://github.com/zabaras/transformer-physx/</a></p>