Enhancement: add tests, pre-commit, and coverage support

[Saransh-cpp]

This is a placeholder issue for testing related developments of DeepXDE. Things I am planning to work on in the next couple of months -

• Add pre-commit support for better linting, formatting, and readability of the codebase
• Add integration tests (test all examples)
• Add basic testing infrastructure using pytest
• Add basic coverage infrastructure using pytest-cov
• Add Codecov integration for better coverage statistics on GitHub
• Add more and more tests to bring the coverage value up
• Add docs about testing and encourage developers to add a test with every new feature added to DeepXDE

[pescap]

Happy to help! This would greatly improve the package!

[Saransh-cpp]

Thanks @pescap! Apologies for abandoning this. I'll start some discussions here next week, along with finishing up the open PR.

[Saransh-cpp]

I think this can now be closed. The unchecked point aimed at adding automatic formatters, static code checkers, and linters using pre-commit and pre-commit.ci in DeepXDE's CI, but I would wait for everyone's opinion on that. I'll be happy to add them to the CI if they are needed!

[lululxvi]

Sounds good. I don't have experience on pre-commit and pre-commit.ci. So feel free to close.