update examples

README.md

@@ -2,7 +2,7 @@
 
 
 <p align="center">
-  	<img alt="Header image of pinnx." src="https://github.com/chaobrain/pinnx/blob/main/docs/_static/pinnx.png" width=50%>
+  	<img alt="Header image of pinnx." src="https://github.com/chaobrain/pinnx/blob/main/docs/_static/pinnx.png" width=40%>
 </p> 
 
 
@@ -11,8 +11,8 @@
 [![PyPI Version](https://badge.fury.io/py/pinnx.svg)](https://badge.fury.io/py/pinnx)
 [![License](https://img.shields.io/github/license/chaobrain/pinnx)](https://github.com/chaobrain/pinnx/blob/master/LICENSE)
 
-``PINNx`` is a library for scientific machine learning and physics-informed learning. 
-It is rewritten according to [DeepXDE](https://github.com/lululxvi/deepxde) but is enhanced by our 
+``PINNx`` is a library for scientific machine learning and physics-informed learning in JAX. 
+It is inspired from [DeepXDE](https://github.com/lululxvi/deepxde) but is enhanced by our 
 [Brain Dynamics Programming (BDP) ecosystem](https://ecosystem-for-brain-dynamics.readthedocs.io/). 
 For example, it leverages 
 
@@ -21,34 +21,14 @@ For example, it leverages
 - [braintools](https://braintools.readthedocs.io/) for checkpointing, loss functions, and other utilities.
 
 
-## Algorithms
-
-
-``PINNx`` implements the following algorithms, but with the flexibility and efficiency of JAX:
-
-- solving different PINN problems
-    - solving forward/inverse ordinary/partial differential equations (ODEs/PDEs) [[SIAM Rev.](https://doi.org/10.1137/19M1274067)]
-    - solving forward/inverse integro-differential equations (IDEs) [[SIAM Rev.](https://doi.org/10.1137/19M1274067)]
-    - fPINN: solving forward/inverse fractional PDEs (fPDEs) [[SIAM J. Sci. Comput.](https://doi.org/10.1137/18M1229845)]
-    - NN-arbitrary polynomial chaos (NN-aPC): solving forward/inverse stochastic PDEs (sPDEs) [[J. Comput. Phys.](https://doi.org/10.1016/j.jcp.2019.07.048)]
-    - PINN with hard constraints (hPINN): solving inverse design/topology optimization [[SIAM J. Sci. Comput.](https://doi.org/10.1137/21M1397908)]
-- improving PINN accuracy
-    - residual-based adaptive
-      sampling [[SIAM Rev.](https://doi.org/10.1137/19M1274067), [Comput. Methods Appl. Mech. Eng.](https://doi.org/10.1016/j.cma.2022.115671)]
-    - gradient-enhanced PINN (gPINN) [[Comput. Methods Appl. Mech. Eng.](https://doi.org/10.1016/j.cma.2022.114823)]
-    - PINN with multi-scale Fourier features [[Comput. Methods Appl. Mech. Eng.](https://doi.org/10.1016/j.cma.2021.113938)]
-- (physics-informed) deep operator network (DeepONet)
-    - DeepONet: learning operators [[Nat. Mach. Intell.](https://doi.org/10.1038/s42256-021-00302-5)]
-    - DeepONet extensions, e.g., POD-DeepONet [[Comput. Methods Appl. Mech. Eng.](https://doi.org/10.1016/j.cma.2022.114778)]
-    - MIONet: learning multiple-input operators [[SIAM J. Sci. Comput.](https://doi.org/10.1137/22M1477751)]
-    - Fourier-DeepONet [[Comput. Methods Appl. Mech. Eng.](https://doi.org/10.1016/j.cma.2023.116300)],
-      Fourier-MIONet [[arXiv](https://arxiv.org/abs/2303.04778)]
-    - physics-informed DeepONet [[Sci. Adv.](https://doi.org/10.1126/sciadv.abi8605)]
-    - multifidelity DeepONet [[Phys. Rev. Research](https://doi.org/10.1103/PhysRevResearch.4.023210)]
-    - DeepM&Mnet: solving multiphysics and multiscale problems [[J. Comput. Phys.](https://doi.org/10.1016/j.jcp.2021.110296), [J. Comput. Phys.](https://doi.org/10.1016/j.jcp.2021.110698)]
-    - Reliable extrapolation [[Comput. Methods Appl. Mech. Eng.](https://doi.org/10.1016/j.cma.2023.116064)]
-- multifidelity neural network (MFNN)
-    - learning from multifidelity data [[J. Comput. Phys.](https://doi.org/10.1016/j.jcp.2019.109020), [PNAS](https://doi.org/10.1073/pnas.1922210117)]
+## Quickstart
+
+
+```python
+
+```
+
+
 
 ## Installation
 

docs/about.rst

@@ -1,5 +1,5 @@
-More Information about PINNx
-=============================
+About ``PINNx``
+===============
 
 `PINNx <https://github.com/chaobrain/pinnx>`_ is a library for scientific machine learning and physics-informed learning.
 It is rewritten according to `DeepXDE <https://github.com/lululxvi/deepxde>`_ but is enhanced by our

docs/index.rst

@@ -49,16 +49,16 @@ User guide
 .. toctree::
     :maxdepth: 1
 
-    examples-unit.rst
-    examples-unitless.rst
+    about.rst
 
-About PINNx
-^^^^^^^^^^^
 
 .. toctree::
-    :maxdepth: 1
+    :maxdepth: 2
+
+    examples-unit.rst
+    examples-unitless.rst
+
 
-    about.rst
 
 
 See also the BDP ecosystem

docs/make.bat

@@ -0,0 +1,35 @@
+@ECHO OFF
+
+pushd %~dp0
+
+REM Command file for Sphinx documentation
+
+if "%SPHINXBUILD%" == "" (
+	set SPHINXBUILD=sphinx-build
+)
+set SOURCEDIR=.
+set BUILDDIR=_build
+
+if "%1" == "" goto help
+
+%SPHINXBUILD% >NUL 2>NUL
+if errorlevel 9009 (
+	echo.
+	echo.The 'sphinx-build' command was not found. Make sure you have Sphinx
+	echo.installed, then set the SPHINXBUILD environment variable to point
+	echo.to the full path of the 'sphinx-build' executable. Alternatively you
+	echo.may add the Sphinx directory to PATH.
+	echo.
+	echo.If you don't have Sphinx installed, grab it from
+	echo.http://sphinx-doc.org/
+	exit /b 1
+)
+
+%SPHINXBUILD% -M %1 %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O%
+goto end
+
+:help
+%SPHINXBUILD% -M help %SOURCEDIR% %BUILDDIR% %SPHINXOPTS% %O%
+
+:end
+popd

docs/unit-examples-forward.rst

@@ -0,0 +1,12 @@
+PINN Forward Examples
+=====================
+
+.. toctree::
+    :maxdepth: 1
+
+    unit-examples-forward/Burgers.ipynb
+    unit-examples-forward/Burgers_RAR.ipynb
+    unit-examples-forward/heat.ipynb
+    unit-examples-forward/heat_resample.ipynb
+    unit-examples-forward/Laplace_disk.ipynb
+

docs/examples-pinn-forward/heat.ipynb → docs/unit-examples-forward/heat.ipynb

@@ -8,9 +8,11 @@
     "\n",
     "## Problem setup\n",
     "We will solve a heat equation:\n",
+    "\n",
     "$$\n",
     "\\frac{\\partial u}{\\partial t}=\\alpha \\frac{\\partial^2u}{\\partial x^2}, \\qquad x \\in [0, 1], \\quad t \\in [0, 1]\n",
     "$$\n",
+    "\n",
     "where $alpha=0.4$ is the thermal diffusivity constant.\n",
     "\n",
     "With Dirichlet boundary conditions:\n",
@@ -20,6 +22,7 @@
     "$$\n",
     "\n",
     "and periodic(sinusoidal) inital condition:\n",
+    "\n",
     "$$\n",
     "u(x,0) = \\sin (\\frac{n\\pi x}{L}),\\qquad 0<x<L, \\quad n = 1,2,.....\n",
     "$$\n",

docs/examples-pinn-forward/heat_resample.ipynb → docs/unit-examples-forward/heat_resample.ipynb

@@ -8,9 +8,11 @@
     "\n",
     "## Problem setup\n",
     "We will solve a heat equation:\n",
+    "\n",
     "$$\n",
     "\\frac{\\partial u}{\\partial t}=\\alpha \\frac{\\partial^2u}{\\partial x^2}, \\qquad x \\in [0, 1], \\quad t \\in [0, 1]\n",
     "$$\n",
+    "\n",
     "where $alpha=0.4$ is the thermal diffusivity constant.\n",
     "\n",
     "With Dirichlet boundary conditions:\n",
@@ -20,6 +22,7 @@
     "$$\n",
     "\n",
     "and periodic(sinusoidal) inital condition:\n",
+    "\n",
     "$$\n",
     "u(x,0) = \\sin (\\frac{n\\pi x}{L}),\\qquad 0<x<L, \\quad n = 1,2,.....\n",
     "$$\n",