SymPy VS NeuralPDE.jl

Thank you for your interest. There are some interesting examples in the SWE-bench-lite benchmark which are resolved by AutoCodeRover:

- From sympy: https://github.com/sympy/sympy/issues/13643. AutoCodeRover's patch for it: https://github.com/nus-apr/auto-code-rover/blob/main/results...

- Another one from scikit-learn: https://github.com/scikit-learn/scikit-learn/issues/13070. AutoCodeRover's patch (https://github.com/nus-apr/auto-code-rover/blob/main/results...) modified a few lines below (compared to the developer patch) and wrote a different comment.

There are more examples in the results directory (https://github.com/nus-apr/auto-code-rover/tree/main/results).

That's interesting. You should consider yourself lucky to have met Wolfram employees, as they are obviously vastly outnumbered by users of Mathematica.

I have not met any developers for either of these products but I know that SymPy has a huge list of contributors for a project of its size. See: https://github.com/sympy/sympy/blob/master/AUTHORS

You may not be hearing about SymPy users because SymPy is not a monolithic product. It is a library. If you know mathematicians big into using Python, they are probably aware of SymPy as it is the main attraction when it comes to symbolic computation in Python.

https://github.com/sympy/sympy/issues/9479 suggests that multivariate inequalities are still unsolved in SymPy, though it looks like https://github.com/sympy/sympy/pull/21687 was merged in August. This probably isn't yet implemented in C++ in SymForce yet?

bug report opened https://github.com/sympy/sympy/issues/25507

https://news.ycombinator.com/item?id=36463580

From https://news.ycombinator.com/item?id=36159017 :

> sympy.utilities.lambdify.lambdify() https://github.com/sympy/sympy/blob/a76b02fcd3a8b7f79b3a88df... :

>> """Convert a SymPy expression into a function that allows for fast numeric evaluation [with the CPython math module, mpmath, NumPy, SciPy, CuPy, JAX, TensorFlow, SymPy, numexpr,]*

From https://westurner.github.io/hnlog/#comment-19084622 :

> "latex2sympy parses LaTeX math expressions and converts it into the equivalent SymPy form" and is now merged into SymPy master and callable with sympy.parsing.latex.parse_latex(). It requires antlr-python-runtime to be installed. https://github.com/augustt198/latex2sympy https://github.com/sympy/sympy/pull/13706

ENH: 'generate a Jupyter notebook' (nbformat .ipynb JSON) function from this stem formula

https://en.wikipedia.org/wiki/Vectorization :

> Array programming, a style of computer programming where operations are applied to whole arrays instead of individual elements

> Automatic vectorization, a compiler optimization that transforms loops to vector operations

> Image tracing, the creation of vector from raster graphics

> Word embedding, mapping words to vectors, in natural language processing

> Vectorization (mathematics), a linear transformation which converts a matrix into a column vector

Vector (disambiguation) https://en.wikipedia.org/wiki/Vector

> Vector (mathematics and physics):

> Row and column vectors, single row or column matrices

> Vector space

> Vector field, a vector for each point

And then there are a number of CS usages of the word vector for 1D arrays.

Compute kernel: https://en.m.wikipedia.org/wiki/Compute_kernel

GPGPU > Vectorization, Stream Processing > Compute kernels: https://en.wikipedia.org/wiki/General-purpose_computing_on_g...

sympy.utilities.lambdify.lambdify() https://github.com/sympy/sympy/blob/a76b02fcd3a8b7f79b3a88df... :

> """Convert a SymPy expression into a function that allows for fast numeric evaluation [with the CPython math module, mpmath, NumPy, SciPy, CuPy, JAX, TensorFlow, SymPt, numexpr,]

pyorch lambdify PR, sympytorch: https://github.com/sympy/sympy/pull/20516#issuecomment-78428...

Sympytorch:

> Turn SymPy expressions into PyTorch Modules.

> SymPy floats (optionally) become trainable parameters. SymPy symbols are inputs to the Module.

sympy2jax https://github.com/MilesCranmer/sympy2jax :

> Turn SymPy expressions into parametrized, differentiable, vectorizable, JAX functions.

> All SymPy floats become trainable input parameters. SymPy symbols become columns of a passed matrix.

Look at sympy.isprime for a carefully-optimized pure-Python solution (though if gmpy2 is installed, which it usually is, it will use that instead after trying the easiest cases)

The documentation has a manifest associated with it: https://docs.sciml.ai/NeuralPDE/dev/#Reproducibility. Instantiating the manifest will give you all of the exact versions used for the documentation build (https://github.com/SciML/NeuralPDE.jl/blob/gh-pages/v5.7.0/assets/Manifest.toml). You just ]instantiate folder_of_manifest. Or you can use the Project.toml.

PDE solving libraries are MethodOfLines.jl and NeuralPDE.jl. NeuralPDE is very general but not very fast (it's a limitation of the method, PINNs are just slow). MethodOfLines is still somewhat under development but generates quite fast code.

GitHub - SciML/NeuralPDE.jl: Physics-Informed Neural Networks (PINN) and Deep BSDE Solvers of Differential Equations for Scientific Machine Learning (SciML) accelerated simulation

That doesn't mean there's no use case for PINNs, we wrote a giant review-ish kind of thing on NeuralPDE.jl to describe where PINNs might be useful. It's just... not the best for publishing. It's things like, (a) where you have not already optimized a classical method, (b) need something that's easy to generate solvers for different cases without too much worry about stability, (c) high dimensional PDEs, and (d) surrogates over parameters. (c) and (d) are the two "real" uses cases you can actually publish about, but they aren't quite good for (c) (see mesh-free methods from the old radial basis function literature in comparison) or (d) (there are much faster surrogate techniques). So we are continuing to work on them for (a) and (b) as an interesting option as part of a software suite, but that's not the kind of thing that's really publishable so I don't think we plan to ever submit that article anywhere.

Did this change at all with the advent of Physics Informed Neural Networks? The Julia language has some really impressive tools for that use case. https://github.com/SciML/NeuralPDE.jl

PDEs are difficult because you don't have a simple numerical definition over all PDEs because they can be defined by arbitrarily many functions. u' = Laplace u + f? Define f. u' = g(u) * Laplace u + f? Define f and g. Etc. To cover the space of PDEs you have to go symbolic at some point, and make the discretization methods dependent on the symbolic form. This is precisely what the ModelingToolkit.jl ecosystem is doing. One instantiation of a discretizer on this symbolic form is NeuralPDE.jl which takes a symbolic PDESystem and generates an OptimizationProblem for a neural network which represents the solution via a Physics-Informed Neural Network (PINN).

NeuralPDE.jl fully automates the approach (and extensions of it, which are required to make it solve practical problems) from symbolic descriptions of PDEs, so that might be a good starting point to both learn the practical applications and get something running in a few minutes. As part of MIT 18.337 Parallel Computing and Scientific Machine Learning I gave an early lecture on physics-informed neural networks (with a two part video) describing the approach, how it works and what its challenges are. You might find those resources enlightening.

What is great about ModelingToolkit.jl is how its used in practical ways for other packages. E.g. NeuralPDE.jl.

Compared to SymPy, I feel that it is less of a "how do I integrate this function" package and more about "how can I build this DSL" framework.

https://github.com/SciML/NeuralPDE.jl