Update README (#4)

README.md

@@ -1,21 +1,56 @@
-# feos-torch
-Parallel evaluation of vapor pressures, liquid densities, and bubble/dew points including gradients using PyTorch.
+# FeOs-torch - Automatic differentiation of phase equilibria
 
-## Installation
-Install with (needs rust compiler)
+[![repository](https://img.shields.io/pypi/v/feos-torch)](https://pypi.org/project/feos-torch/)
 
-```
-pip install git+ssh://git@github.com/feos-org/feos-torch.git
-```
+`FeOs-torch` combines the [`FeOs`](https://github.com/feos-org/feos) thermodynamics engine with the machine learning/automatic differentiation framework [PyTorch](https://pytorch.org/). 
 
-## Basic usage
 ```python
 import torch
 from feos_torch import PcSaftPure
 
+# define PC-SAFT parameters
 # m, sigma, epsilon_k, mu, kappa_ab, epsilon_k_ab, na, nb
-params = torch.tensor([[1.5, 3.5, 150.0, 0, 0.03, 1500.0, 1, 1]] * 2, dtype=torch.float64, requires_grad=True)
-temperature = torch.tensor([250., 300.], dtype=torch.float64)
-pcsaft = PcSaftPure(params)
-vp = pcsaft.vapor_pressure(temperature)
+params = torch.tensor([1.5, 3.5, 250.0, 0, 0.03, 1500.0, 1, 1], dtype=torch.float64, requires_grad=True)
+pcsaft = PcSaftPure(params.repeat(5, 1))
+
+# evaluate vapor pressures (in Pa)
+temperature = torch.tensor([250., 300., 350., 400., 450.], dtype=torch.float64)
+_, vp = pcsaft.vapor_pressure(temperature)
+print(vp)
+
+# determine the derivatives of the first vapor pressure w.r.t. PC-SAFT parameters
+vp[0].backward()
+print(params.grad)
+```
+```terminal
+tensor([  20693.5960,  216164.6184, 1049770.6187, 3281855.9640, 7875531.7021],
+       dtype=torch.float64, grad_fn=<MulBackward0>)
+tensor([-6.7923e+04, -1.7737e+04, -7.0413e+02,  0.0000e+00, -5.7458e+05,
+        -6.9122e+01, -3.6892e+04, -3.6892e+04], dtype=torch.float64)
+
+```
+
+## Models
+
+The following models and properties are currently implemented in `FeOs-torch`
+
+|model|vapor pressure|liquid density|equilibrium liquid density|bubble point pressure|dew point pressure|
+|-|-|-|-|-|-|
+|PC-SAFT|✓|✓|✓|✓|✓|
+|gc-PC-SAFT||||✓|✓|
+
+## Cite us
+
+If you find `FeOs-torch` useful for your own research, consider citing our [publication](https://doi.org/10.1007/s10765-023-03290-3) from which this library resulted.
+
 ```
+@article{rehner2023mixtures,
+  author = {Rehner, Philipp and Bardow, André and Gross, Joachim},
+  title = {Modeling Mixtures with PCP-SAFT: Insights from Large-Scale Parametrization and Group-Contribution Method for Binary Interaction Parameters}
+  journal = {International Journal of Thermophysics},
+  volume = {44},
+  number = {12},
+  pages = {179},
+  year = {2023}
+}
+```