FlameCalc is a machine learning approach to a boundary problem of Calculus of Variation.
FlameCalc is built using PyTorch library, so please make sure the torch is installed on your device before installing flamecalc.
Calculus of variation is the field of mathematics that aims to find a function (or a curve) that extremizes a given functional. For example, a very simple and famous example of the calculus of variation is finding a path between two points on a 2-dimensional space. Such optimization problems are highly analogous to machine learning problems as the aim of both problem is to find a function that minimizes some value. Therefore, this package aims to solve such optimization problems using machine learning techniques.
$ pip install flamecalc
Suppose you want to find a shortest curve that connects two points on a 2-dimensional space.
Then, we can provide a functional such that
import torch
def f(y, dy, x):
return torch.sqrt(1 + dy**2)
Using the above functional, the length of the curve that connects two points will be an integration of the above functional.
Therefore, we use a flamecalc solver for this problem.
A = (1, 1) # Starting point
B = (2, 5) # End point
domain = torch.linspace(A[0], B[0], 100) # domain
model = CalVarSolver(f, A, B, domain) # Get solver
epoch = 2500 # Hyperparameter
result = model.optimize(lr=0.02, epoch=epoch) # Optimize
With this simple code, you can solve the calculus of variation problem given with boundary conditions.
The curve evolves to a straight line as the learning progresses.
