Get Started
Endia is a generalpurpose scientific computing library, featuring:
 Automatic differentiation: Compute derivatives of arbitrary order.
 Complex numbers: Use Endia for advanced scientific applications.
 Dual API: Choose between a PyTorchlike imperative or a JAXlike functional interface.
 JIT Compilation: Leverage MAX (opens in a new tab) to speed up training and inference.
⚠️ Warning: Endia is currently in an early development stage and not yet ready for production use. The API is subject to change without notice. Stay tuned for more exciting features to come (e.g. GPU support).
Installation

Install Mojo 24.5 (opens in a new tab) 🔥

Add the Endia Package (at the top level of your project):
curl o "endia.📦" https://raw.githubusercontent.com/endiaorg/Endia/main/endia.mojopkg
But what about all the other internal dependencies?  Good news, there are none. The core of Endia is built purely on top of Mojo and MAX!
A tiny tutorial
In this guide, we'll demonstrate how to compute the value, gradient, and the Hessian (i.e. the secondorder derivative) of a simple function. First by using Endia's Pytorchlike API and then by using a more Jaxlike functional API. In both examples, we initially define a function foo that takes an array and returns the sum of the squares of its elements.
The PyTorch way
When using Endia's imperative (PyTorchlike) interface, we compute the gradient of a function by calling the backward method on the function's output. This imperative style requires explicit management of the computational graph, including setting requires_grad=True
for the input arrays (i.e. leaf nodes) and using create_graph=True
in the backward method when computing higherorder derivatives.
from endia import Tensor, sum, arange
import endia.autograd.functional as F
# Define the function
def foo(x: Tensor) > Tensor:
return sum(x ** 2)
def main():
# Initialize variable  requires_grad=True needed!
x = arange(1.0, 4.0, requires_grad=True) # [1.0, 2.0, 3.0]
# Compute result, first and second order derivatives
y = foo(x)
y.backward(create_graph=True)
dy_dx = x.grad()
d2y_dx2 = F.grad(outs=sum(dy_dx), inputs=x)[0]
# Print results
print(y) # 14.0
print(dy_dx) # [2.0, 4.0, 6.0]
print(d2y_dx2) # [2.0, 2.0, 2.0]
The JAX way
When using Endia's functional (JAXlike) interface, the computational graph is handled implicitly. By calling the grad
or jacobian
function on foo, we create a Callable
which computes the full Jacobian matrix. This Callable
can be passed to the grad
or jacobian
function again to compute higherorder derivatives.
from endia import grad, jacobian
from endia.numpy import sum, arange, ndarray
def foo(x: ndarray) > ndarray:
return sum(x**2)
def main():
# create Callables for the first and second order derivatives
foo_jac = grad(foo)
foo_hes = jacobian(foo_jac)
x = arange(1.0, 4.0) # [1.0, 2.0, 3.0]
print(foo(x)) # 14.0
print(foo_jac(x)[ndarray]) # [2.0, 4.0, 6.0]
print(foo_hes(x)[ndarray]) # [[2.0, 0.0, 0.0], [0.0, 2.0, 0.0], [0.0, 0.0, 2.0]]
And there is so much more! Endia can handle complex valued functions, can perform both forward and reversemode automatic differentiation, it even has a builtin JIT compiler to make things go brrr. Explore the full list of features in the documentation (opens in a new tab).
Why another ML framework?
"Nothing in life is to be feared, it is only to be understood. Now is the time to understand more, so that we may fear less."  Marie Curie
Guided by this core belief, we embarked on a challenging journey to build something from first principles — a framework that is both powerful 🚀 and transparent 📐. Endia is crafted to be more than just a tool; it's a window into the algorithms you work with, stripping away layers of abstraction to reveal the underlying logic 🧠. In contrast to other popular Scientific Computing libraries which are built on piles of decadesold legacy Fortran and C++ code (like NumPy, for example), Endia is built on top of a uniquely minimalistic stack:
Contributing
Contributions to Endia are welcome! If you'd like to contribute, please follow the contribution guidelines in the CONTRIBUTING.md (opens in a new tab) file in the repository.
Citation
If you use Endia in your research or project, please cite it as follows:
@software{Fehrenbach_Endia_2024,
author = {Fehrenbach, Tillmann},
license = {Apache2.0 with LLVM Exceptions},
doi = {10.5281/zenodo.12810766},
month = {09},
title = {{Endia}},
url = {https://github.com/endiaorg/Endia},
version = {24.5.0},
year = {2024}
}
License
Endia is licensed under the Apache2.0 license with LLVM Exeptions (opens in a new tab).