Deepxde

DeepXDE now supports two backends: TensorFlow 1.x (`tensorflow.compat.v1` in TensorFlow 2.x) and TensorFlow 2.x. For how to select one, see [Working with different backends](https://deepxde.readthedocs.io/en/latest/user/installation.html#working-with-different-backends).

Areas of improvement
- Many modules are refactored to better support multiple backends.
- Support skopt>=0.9
- Documentation improvements

API changes
- Rename `dde.data.Func` to `dde.data.Function`

New APIs
- Add `Hypercube.random_boundary_points()`

This release is mainly about DeepONet.

API changes

- Rename `OpNN` to `DeepONet`
- Rename `OpDataSet` to `Triple`

New APIs

- Add `dde.__version__`
- Add `data.TripleCartesianProd`, `maps.DeepONetCartesianProd`, and `maps.FourierDeepONetCartesianProd`
- Add new metric: `mean_l2_relative_error`

Areas of improvement

- Bug fix: change 'sobol' to 'Sobol'

Areas of improvement

- Add Multi-scale Fourier Feature Neural Networks: `MsFFN` and `STMsFFN`
- `PDE` supports more sampling methods: LHS, Halton, Hammersley
- `DeepONet` supports input_transform and output_transform
- `PointSet` supports default value
- `Hypercube.boundary_normal()` returns averaged normal for vertices
- Speedup `Polygon.random_points()`

Areas of improvement

- `FNN` supports arguments `use_bias` and `kernel_constraint`, and layer normalization
- Change L-BFGS option `gtol` from 1e-5 to 1e-8
- Improve `saveplot`

New APIs

- Add a new Data `Constraint`
- Add metric `mean_squared_error`

We stop the support of Python 2.7 from this release.

Areas of improvement

- Vectorize geometry related methods
- `PDE` supports resample PDE residual points via callback `PDEResidualResampler`
- Implement `Polygon.boundary_normal()`

New APIs

- Add multifidelity DeepONet

API changes

- Geometry-related methods (`inside`, `on_boundary`, `on_initial`, `boundary_normal`, `periodic_point`) now use the 2d input of shape N by d, not a 1d vector.

Areas of improvement

- `PDE` supports excluded points
- Add `PointSetBC` for training using exact solution.
- Add `Hypersphere.boundary_normal()`
- Add `Triangle.inside()`

API changes

- `PDE` doesn't support numpy.array `X` as the third parameter. To define pde with extra coefficients, use `PDE(..., auxiliary_var_function=...)`, see an example at Lorenz_inverse_forced_Colab.ipynb.