{"id":50663730,"url":"https://github.com/314arhaam/burger-pinn","last_synced_at":"2026-06-08T04:31:23.628Z","repository":{"id":201299238,"uuid":"425028672","full_name":"314arhaam/burger-pinn","owner":"314arhaam","description":"A Physics-Informed Neural Network for solving Burgers' equation.","archived":false,"fork":false,"pushed_at":"2024-03-06T19:52:52.000Z","size":1236,"stargazers_count":21,"open_issues_count":0,"forks_count":6,"subscribers_count":1,"default_branch":"main","last_synced_at":"2024-03-06T20:59:57.772Z","etag":null,"topics":["burgers-equation","deep-learning","machine-learning","neural-network","physics-informed-neural-networks"],"latest_commit_sha":null,"homepage":"","language":"Jupyter Notebook","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":"mit","status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/314arhaam.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":"LICENSE","code_of_conduct":null,"threat_model":null,"audit":null,"citation":null,"codeowners":null,"security":null,"support":null,"governance":null,"roadmap":null,"authors":null,"dei":null}},"created_at":"2021-11-05T17:16:18.000Z","updated_at":"2024-04-14T19:38:35.133Z","dependencies_parsed_at":"2024-04-14T19:38:34.057Z","dependency_job_id":"807dab50-9a01-4ce9-8344-42cfb455816c","html_url":"https://github.com/314arhaam/burger-pinn","commit_stats":null,"previous_names":["314arhaam/burger-pinn"],"tags_count":0,"template":false,"template_full_name":null,"purl":"pkg:github/314arhaam/burger-pinn","repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/314arhaam%2Fburger-pinn","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/314arhaam%2Fburger-pinn/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/314arhaam%2Fburger-pinn/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/314arhaam%2Fburger-pinn/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/314arhaam","download_url":"https://codeload.github.com/314arhaam/burger-pinn/tar.gz/refs/heads/main","sbom_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/314arhaam%2Fburger-pinn/sbom","scorecard":null,"host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":286080680,"owners_count":34048681,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2026-05-26T15:22:16.424Z","status":"online","status_checked_at":"2026-06-08T02:00:07.615Z","response_time":111,"last_error":null,"robots_txt_status":"success","robots_txt_updated_at":"2025-07-24T06:49:26.215Z","robots_txt_url":"https://github.com/robots.txt","online":true,"can_crawl_api":true,"host_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub","repositories_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories","repository_names_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repository_names","owners_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners"}},"keywords":["burgers-equation","deep-learning","machine-learning","neural-network","physics-informed-neural-networks"],"created_at":"2026-06-08T04:31:22.613Z","updated_at":"2026-06-08T04:31:23.623Z","avatar_url":"https://github.com/314arhaam.png","language":"Jupyter Notebook","funding_links":[],"categories":[],"sub_categories":[],"readme":"# 🍔 $\\textbf{Burger-PINN}$ ⚛️\nA Physics-Informed Neural Network to solve **Burgers' equation**.\n\nReference: [Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations](https://arxiv.org/abs/1711.10561)  \nAuthor's Github page: https://maziarraissi.github.io/PINNs/  \n\n**Check out my other PINN project: [heat-pinn](https://github.com/314arhaam/heat-pinn)**\n\n## Introduction\nThis work is an implementation of the reference paper above. In this work, a neural network is trained to solve Burgers' equation, a well-known PDE, for a given set of BCs and an IC.  \n\nTo train this model, certain number of points on the both boundaries and on the initial timestep were sampled, as input data, called **data points**, to compute MSE loss function, in addition to another set of points on the main domain of the problem, or **collocation points** to penalize the network in case the prediction on this set is not consistent with the governing PDE.\n\n### Problem details\nThe governing PDE is:\n\n### $\\partial_{t}{u}+u\\partial_{x}{u}-(\\frac{0.01}{\\pi})\\partial_{xx}{u} = 0$\n\nWhich is solved in the following spatial and temporal domain:\n\n### $D = \\\\{ (t, x)\\ |\\ 0\\le t \\le +1 \\land -1\\le x \\le +1 \\\\}$\n\nRegarding the following initial and boundary conditions:\n\n$$\n\\begin{equation}\n  \\begin{cases}\n    u(0, x) = -\\sin({\\pi x})\\\\\n    u(t, +1) = 0.0 \\\\\n    u(t, -1) = 0.0 \\\\  \n  \\end{cases}\n\\end{equation}\n$$\n\n\n## Results\n$u(t, x)$ profile (Figure 1. in reference or [author's Github page](https://maziarraissi.github.io/assets/img/Burgers_CT_inference.png))  \n![profile](https://github.com/314arhaam/burger-pinn/blob/main/graphics/u-profile.png)\n\n$u(t, x)$ in Cartesian coordinates for $t \\in \\\\{0.25,0.5,0.75\\\\}$ (Figure 1. in reference or [author's Github page](https://maziarraissi.github.io/assets/img/Burgers_CT_inference.png))  \n![plots](https://github.com/314arhaam/burger-pinn/blob/main/graphics/u-vs-x.png)\n\n$u(t, x)$ in Cartesian coordinates for more t values  \n\u003cp align=\"\"center\u003e\n  \u003cimg src=\"https://github.com/314arhaam/burger-pinn/blob/main/graphics/u-constant-time.png?raw=true\" alt=\"u-constant-time.png\" width=400 height=400 /\u003e\n\u003c/p\u003e\n\n# Note\nThis implementation is based on [Tensorflow 2.0](https://www.tensorflow.org/guide/effective_tf2) package and made possible by [Google Colabratory](https://colab.research.google.com) GPU.\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2F314arhaam%2Fburger-pinn","html_url":"https://awesome.ecosyste.ms/projects/github.com%2F314arhaam%2Fburger-pinn","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2F314arhaam%2Fburger-pinn/lists"}