{"id":16638278,"url":"https://github.com/sameerkash/sciml","last_synced_at":"2025-03-12T02:36:08.226Z","repository":{"id":228771909,"uuid":"773447067","full_name":"Sameerkash/sciml","owner":"Sameerkash","description":"Scientific Machine Learning using Julia","archived":false,"fork":false,"pushed_at":"2024-04-13T08:15:21.000Z","size":2273,"stargazers_count":0,"open_issues_count":0,"forks_count":0,"subscribers_count":1,"default_branch":"main","last_synced_at":"2024-04-13T21:59:57.973Z","etag":null,"topics":[],"latest_commit_sha":null,"homepage":null,"language":"Julia","has_issues":true,"has_wiki":null,"has_pages":null,"mirror_url":null,"source_name":null,"license":null,"status":null,"scm":"git","pull_requests_enabled":true,"icon_url":"https://github.com/Sameerkash.png","metadata":{"files":{"readme":"README.md","changelog":null,"contributing":null,"funding":null,"license":null,"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,"publiccode":null,"codemeta":null}},"created_at":"2024-03-17T17:27:12.000Z","updated_at":"2024-03-17T17:34:08.000Z","dependencies_parsed_at":"2024-04-13T09:40:15.307Z","dependency_job_id":null,"html_url":"https://github.com/Sameerkash/sciml","commit_stats":null,"previous_names":["sameerkash/sciml"],"tags_count":0,"template":false,"template_full_name":null,"repository_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Sameerkash%2Fsciml","tags_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Sameerkash%2Fsciml/tags","releases_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Sameerkash%2Fsciml/releases","manifests_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/repositories/Sameerkash%2Fsciml/manifests","owner_url":"https://repos.ecosyste.ms/api/v1/hosts/GitHub/owners/Sameerkash","download_url":"https://codeload.github.com/Sameerkash/sciml/tar.gz/refs/heads/main","host":{"name":"GitHub","url":"https://github.com","kind":"github","repositories_count":243145877,"owners_count":20243603,"icon_url":"https://github.com/github.png","version":null,"created_at":"2022-05-30T11:31:42.601Z","updated_at":"2022-07-04T15:15:14.044Z","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":[],"created_at":"2024-10-12T06:44:09.312Z","updated_at":"2025-03-12T02:36:08.202Z","avatar_url":"https://github.com/Sameerkash.png","language":"Julia","funding_links":[],"categories":[],"sub_categories":[],"readme":"# Scientific Machine learning Using Julia\n\nThis repoitory showcases the solution to Ordinary and Partial Differential Equations.\n\n## Ordinary Differential Equations\n\n### Oscilation of a pendulum\n\n**Equations**:\n\n```\ndθ(t)/dt = ω(t)\n\ndω(t)/dt = -3g/2l sin(θ(t)) + 3/ml^2M(t)\n```\n\n**Output**:\n![pendumlum](./outputs/pendulum.png)\n\n### SIR Model\n\nFor predicting suspetible, recovered and infected population in a pandemic\n\n**Equations**\n\n```\ndS(t)/dt = −βS(t)I(t)/N\n\ndI(t)/dt = βS(t)I(t)/N − γI(t)\n\ndR(t)/dt = γI(t),\n```\n\n**Output**:\n\n![SIR](./outputs/SIR_Output.gif), ![SIR](./outputs/SIR_MODEL.gif)\n\n###\n\nFor predicting suspetible, recovered and infected population in a pandemic\n\n## Partial Differential Equations\n\n### Schrodinger Equation\n\n**Equation**\n\n```\ni∂ψ(t, x)/∂t =∂^2ψ(t, x)/∂x^2 + V (x)ψ(t, x)\n```\n\n**Output**:\n\n![Schrodinger](./outputs/Schrodinger.gif),\n\n## Neural ODEs\n\n### SIR Model\n\nSolving the SIR model using a Neural Ordinary differential equation to predict infected, susceptible and recoevered population in a sample size of 1000\n\n**Equations**\n\n```\ndS(t)/dt = −βS(t)I(t)/N\n\ndI(t)/dt = βS(t)I(t)/N − γI(t)\n\ndR(t)/dt = γI(t),\n```\n\n![NEURAL_ODE](./outputs/SIR_NEURAL_ODE.png),\n\n## Neural PDE\n\n### 1 Dimensional Wave equation\n\n**Equations**\n\n```\n∂^2u(x, t)/∂t^2 = c^2 ∂^2u(x, t)/∂x^2\n\nu(0, t) = u(1, t) = 0 for all t \u003e 0\n\n(2) u(x, 0) = x(1 − x) for all 0 \u003c x \u003c 1\n\n(3) ∂u(x, 0) ∂t = 0 for all 0 \u003c x \u003c 1\n```\n\n![1D](./outputs/1d_wave_equation.png),\n\n## Universal Differential Equations\n\n### Lotka Voltera Predator Prey model\n\n**Equations**\n\n```\ndx/dt = αx − βxy,\ndy/dt = −δy + γxy\n\n```\n\n![1D](./outputs/lotka_voltera.png),\n","project_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fsameerkash%2Fsciml","html_url":"https://awesome.ecosyste.ms/projects/github.com%2Fsameerkash%2Fsciml","lists_url":"https://awesome.ecosyste.ms/api/v1/projects/github.com%2Fsameerkash%2Fsciml/lists"}