Update README.md

README.md

@@ -11,14 +11,18 @@ References: For Domain Decomposition based PINN framework
 
 2. A.D.Jagtap, E. Kharazmi, G.E.Karniadakis, Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems, Computer Methods in Applied Mechanics and Engineering, 365, 113028 (2020). (https://doi.org/10.1016/j.cma.2020.113028)
 
+3. K. Shukla, A.D. Jagtap, G.E. Karniadakis, Parallel Physics-Informed Neural Networks via Domain Decomposition, arXiv preprint arXiv:2104.10013, 2021.
 
 References: For adaptive activation functions
 
-3. A.D.Jagtap, K.Kawaguchi, G.E.Karniadakis, Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 20200334, 2020. (http://dx.doi.org/10.1098/rspa.2020.0334).
+1. A.D.Jagtap, K.Kawaguchi, G.E.Karniadakis, Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 20200334, 2020. (http://dx.doi.org/10.1098/rspa.2020.0334).
 
-4. A.D. Jagtap, K.Kawaguchi, G.E.Karniadakis, Adaptive activation functions accelerate convergence in deep and physics-informed neural networks, Journal of Computational Physics, 404 (2020) 109136. (https://doi.org/10.1016/j.jcp.2019.109136)
+2. A.D. Jagtap, K.Kawaguchi, G.E.Karniadakis, Adaptive activation functions accelerate convergence in deep and physics-informed neural networks, Journal of Computational Physics, 404 (2020) 109136. (https://doi.org/10.1016/j.jcp.2019.109136)
 
+3. A.D. Jagtap, Y. Shin, K. Kawaguchi, G.E. Karniadakis, Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions,
+arXiv preprint, arXiv:2105.09513, 2021.
 
-Recommended software versions: TensorFlow 1.14, Python 3.6
+
+Recommended software versions: TensorFlow 1.14, Python 3.6, Latex (for plotting figures)
 
 For any queries regarding the XPINN code, feel free to contact me : [email protected], [email protected]