https://github.com/sameerkash/sciml
Scientific Machine Learning using Julia
https://github.com/sameerkash/sciml
Last synced: over 1 year ago
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Scientific Machine Learning using Julia
- Host: GitHub
- URL: https://github.com/sameerkash/sciml
- Owner: Sameerkash
- Created: 2024-03-17T17:27:12.000Z (over 2 years ago)
- Default Branch: main
- Last Pushed: 2024-04-13T08:15:21.000Z (about 2 years ago)
- Last Synced: 2024-04-13T21:59:57.973Z (about 2 years ago)
- Language: Julia
- Size: 2.17 MB
- Stars: 0
- Watchers: 1
- Forks: 0
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
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README
# Scientific Machine learning Using Julia
This repoitory showcases the solution to Ordinary and Partial Differential Equations.
## Ordinary Differential Equations
### Oscilation of a pendulum
**Equations**:
```
dθ(t)/dt = ω(t)
dω(t)/dt = -3g/2l sin(θ(t)) + 3/ml^2M(t)
```
**Output**:
### SIR Model
For predicting suspetible, recovered and infected population in a pandemic
**Equations**
```
dS(t)/dt = −βS(t)I(t)/N
dI(t)/dt = βS(t)I(t)/N − γI(t)
dR(t)/dt = γI(t),
```
**Output**:
, 
###
For predicting suspetible, recovered and infected population in a pandemic
## Partial Differential Equations
### Schrodinger Equation
**Equation**
```
i∂ψ(t, x)/∂t =∂^2ψ(t, x)/∂x^2 + V (x)ψ(t, x)
```
**Output**:
,
## Neural ODEs
### SIR Model
Solving the SIR model using a Neural Ordinary differential equation to predict infected, susceptible and recoevered population in a sample size of 1000
**Equations**
```
dS(t)/dt = −βS(t)I(t)/N
dI(t)/dt = βS(t)I(t)/N − γI(t)
dR(t)/dt = γI(t),
```
,
## Neural PDE
### 1 Dimensional Wave equation
**Equations**
```
∂^2u(x, t)/∂t^2 = c^2 ∂^2u(x, t)/∂x^2
u(0, t) = u(1, t) = 0 for all t > 0
(2) u(x, 0) = x(1 − x) for all 0 < x < 1
(3) ∂u(x, 0) ∂t = 0 for all 0 < x < 1
```
,
## Universal Differential Equations
### Lotka Voltera Predator Prey model
**Equations**
```
dx/dt = αx − βxy,
dy/dt = −δy + γxy
```
,