added references

paper/paper.bib

@@ -162,7 +162,7 @@ @article{Lin_2023
 	journal = {Journal of Computational Physics}
 }
 
-@article{10.1063/5.0032836,
+@article{fixed_node,
     author = {Schätzle, Z. and Hermann, J. and Noé, F.},
     title = "{Convergence to the fixed-node limit in deep variational Monte Carlo}",
     journal = {The Journal of Chemical Physics},
@@ -178,7 +178,7 @@ @article{10.1063/5.0032836
     eprint = {https://pubs.aip.org/aip/jcp/article-pdf/doi/10.1063/5.0032836/14009445/124108\_1\_online.pdf},
 }
 
-@article{PhysRevResearch.3.043126,
+@article{detfree_nn,
   title = {Determinant-free fermionic wave function using feed-forward neural networks},
   author = {Inui, Koji and Kato, Yasuyuki and Motome, Yukitoshi},
   journal = {Phys. Rev. Res.},

paper/paper.md

@@ -27,7 +27,7 @@ in a physically-motivated neural network. The use of `PyTorch` as a backend to p
 
 # Statement of need
 
-`QMCTorch` is a Python package using `PyTorch` [@pytorch] as a backend to perform Quantum Monte-Carlo (QMC) simulations, namely Variational Monte-Carlo,  of molecular systems. Many software such as `QMCPack`[@qmcpack], `QMC=Chem` [@qmcchem], `CHAMP` [@champ] provide high-quality implementation of advanced QMC methodologies in low-level languages (C++/Fortran).  Python implementations of QMC such as `PAUXY` [@pauxy] and `PyQMC` [@pyqmc] have also been proposed to facilitate the use and development of QMC techniques. Large efforts have been made to leverage recent development of deep learning techniques for QMC simulations with for example the creation of neural-network based wave-function ansatz [@paulinet; @ferminet] that have lead to very interesting results. `QMCTorch` allows to perform QMC simulations using physically motivated neural network architectures that closely follow the wave function ansatz used by QMC practitioners. Its architecture allows to rapidly explore new functional forms of some key elements of the wave function ansatz. Users do not need to derive analytical expressions for the gradients of the total energy w.r.t. the variational parameters, that are simply obtained via automatic diffentiation. This includes for example the parameters of the atomic orbitals that can be variationally optimized and the atomic coordinates that allows `QMCTorch` to perform geometry optimization of molecular structures. In addition, the GPU capabilities offered by `PyTorch` combined with the parallelization over multiple computing nodes obtained via `Horovod` [@horovod], allow to deploy the simulations on large heterogenous computing architectures. In summary, `QMCTorch` provides QMC practitionners a framework to rapidly protoytpe new ideas and to test them using modern computing ressources.
+`QMCTorch` is a Python package using `PyTorch` [@pytorch] as a backend to perform Quantum Monte-Carlo (QMC) simulations, namely Variational Monte-Carlo,  of molecular systems. Many software such as `QMCPack`[@qmcpack], `QMC=Chem` [@qmcchem], `CHAMP` [@champ] provide high-quality implementation of advanced QMC methodologies in low-level languages (C++/Fortran).  Python implementations of QMC such as `PAUXY` [@pauxy] and `PyQMC` [@pyqmc] have also been proposed to facilitate the use and development of QMC techniques. Large efforts have been made to leverage recent development of deep learning techniques for QMC simulations with for example the creation of neural-network based wave-function ansatz [@paulinet; @ferminet; @choo_fermionic_2020; @HAN2019108929; @ANN_QMC; @detfree_nn; @fixed_node; @Lin_2023; @ANN_WF] that have lead to very interesting results. `QMCTorch` allows to perform QMC simulations using physically motivated neural network architectures that closely follow the wave function ansatz used by QMC practitioners. Its architecture allows to rapidly explore new functional forms of some key elements of the wave function ansatz. Users do not need to derive analytical expressions for the gradients of the total energy w.r.t. the variational parameters, that are simply obtained via automatic diffentiation. This includes for example the parameters of the atomic orbitals that can be variationally optimized and the atomic coordinates that allows `QMCTorch` to perform geometry optimization of molecular structures. In addition, the GPU capabilities offered by `PyTorch` combined with the parallelization over multiple computing nodes obtained via `Horovod` [@horovod], allow to deploy the simulations on large heterogenous computing architectures. In summary, `QMCTorch` provides QMC practitionners a framework to rapidly protoytpe new ideas and to test them using modern computing ressources.
 
 
 # Wave Function Ansatz
@@ -37,7 +37,7 @@ The neural network used to encode the wave-function ansatz used in `QMCTorch` is
 
 **Jastrow Factor** The `Jastrow` layer computes the sum of three components: an electron-electron term $K_{ee}$; an electron-nuclei term $K_{en}$; and a three body electron-electron-nuclei term $K_{een}$. The sum is then exponentiated to give the Jastrow factor: $J(r_{ee}, r_{en}) = \exp\left( K_{ee}(r_{ee})+K_{en}(r_{en}) + K_{een}(r_{ee},r_{en})\right)$ where $r_{ee}$ and $r_{en}$ are the electron-electron and electron-nuclei distances. Several well-known Jastrow factor functional forms, as for example the electron-electron Pade-Jastrow: $K(r_{ee}) = \frac{\omega_0 r_{ee}}{1 + \omega r_{ee}}$, where $\omega$ is a variational parameter, are already implemented and available for use. Users can also define their own functional forms for the different kernel functions, $K$, and explore their effects on the resulting optimization.  
 
-**Backflow Transformation** The backflow transformation layer, `BF`, creates quasi-particles by mixing the electronic positions of the electrons: $\mathbf{q}_i = \mathbf{r}_i + \sum_{i\neq j} K_{BF}(r_{ij})(\mathbf{r}_i-\mathbf{r}_j)$ [@backflow]. Well-known transformations such as: $K_{BF} = \frac{\mu}{r_{ij}}$ where $\mu$ is a variational parameter, are already implemented and ready to use. Users can also easily specify the kernel of the backflow transformation, $K_{BF}$ to explore its impact on the wave function optimization.
+**Backflow Transformation** The backflow transformation layer, `BF`, creates quasi-particles by mixing the electronic positions of the electrons: $\mathbf{q}_i = \mathbf{r}_i + \sum_{i\neq j} K_{BF}(r_{ij})(\mathbf{r}_i-\mathbf{r}_j)$ [@backflow_1981; @backflow]. Well-known transformations such as: $K_{BF} = \frac{\mu}{r_{ij}}$ where $\mu$ is a variational parameter, are already implemented and ready to use. Users can also easily specify the kernel of the backflow transformation, $K_{BF}$ to explore its impact on the wave function optimization.
 
 **Atomic Orbitals** The Atomic Orbital layer `AO` computes the values of the different atomic orbitals of the system at all the positions $q_e$. Both Slater type orbitals (STOs) and Gaussian type orbitals (GTOs) are supported. The initial parameters of the AOs are extracted from popular quantum chemistry codes, `pyscf` [@pyscf] and `ADF` [@adf].  During the optimization, the parameters of the AOs (exponents, coefficients) are variational parameters that can be optimized to minimize the total energy. Since GTOs can introduce a significant amount of noise in the QMC simulations, `QMCTorch` offers the possibility to fit GTOs to single exponent STOs.