Computational Mathematics Group 
Computational Mathematics Group 


Panos Stinis specializes in scientific computing with application interests in model reduction of complex systems, multiscale modeling, uncertainty quantification, and machine learning. 

Stinis studied aeronautical engineering at the Technical University of Athens, Greece. He earned his PhD in applied mathematics in 2003, from Columbia University in New York, in the area of model reduction. He began his career at Lawrence Berkeley National Laboratory and the Stanford Center for Turbulence Research, where he worked on applying model reduction methods to hyperbolic systems and in developing techniques for locating and tracking singularities of partial differential equations. In 2008, he became a faculty member at the Mathematics Department at the University of Minnesota, where he worked on renormalization, mesh refinement, particle filtering and optimization.

He moved to PNNL in 2014, where he is currently leading the Computational Mathematics group.  He serves as the co-director of the Physics-Informed Learning Machines (PhILMs) multi-institution collaboration and leads the Digital Twin Component Development thrust of the Energy Storing Materials Initiative.

Disciplines and Skills

  • Model reduction  

  • Multiscale modeling 

  • Uncertainty quantification 

  • Machine learning 


PhD in Applied Mathematics, Columbia University, 2003 

Diploma in Aeronautical Engineering, National Technical University of Athens, 1996 



Meuris B., S. Qadeer, and P. Stinis. 2023. "Machine-learning-based spectral methods for partial differential equations." Scientific Reports 13, no. 1:Art. No. 1739. PNNL-SA-168281. doi:10.1038/s41598-022-26602-3


He Q., Y. Fu, P. Stinis, and A.M. Tartakovsky. 2022. "Enhanced physics-constrained deep neural networks for modeling vanadium redox flow battery." Journal of Power Sources 542. PNNL-SA-170353. doi:10.1016/j.jpowsour.2022.231807

He Q., P. Stinis, and A.M. Tartakovsky. 2022. "Physics-constrained deep neural network method for estimating parameters in the redox flow battery." Journal of Power Sources 528. PNNL-SA-163269. doi:10.1016/j.jpowsour.2022.231147

Li J., and P. Stinis. 2022. "Model reduction for a power grid model." Journal of Computational Dynamics 9, no. 1:1-26. PNNL-SA-150116. doi:10.3934/jcd.2021019

Qadeer S., G.D. Santis, P. Stinis, and S.S. Xantheas. 2022. "Vibrational Levels of a Generalized Morse Potential." The Journal of Chemical Physics 157, no. 14:Art. No. 144104. PNNL-SA-174299. doi:10.1063/5.0103433

Tipireddy R., P. Perdikaris, P. Stinis, and A.M. Tartakovsky. 2022. "Multistep and continuous physics-informed neural network methods for learning governing equations and constitutive relations." Journal of Machine Learning for Modeling and Computing 3, no. 2:23-46. PNNL-SA-177559. doi:10.1615/JMachLearnModelComput.2022041787


He Q, P Stinis and A Tartakovsky. 2021. “Physics-constrained deep neural network method for estimating parameters in a redox flow battery.” arXiv:2106.11451.

Lee K, N Trask and P Stinis. 2021. “Machine learning structure preserving brackets for forecasting irreversible Processes.” arXiv:2106.12619.

Price J, B Meuris, M Shapiro and P Stinis. 2021. “Optimal renormalization of multi-scale systems.” Proceedings of the National Academy of Sciences, 118(37). DOI: 10.1073/pnas.2102266118.

Roth J, D Barajas-Solano, P Stinis, J Weare and M Anitescu. 2021. “A Kinetic Monte Carlo Approach for Simulating Cascading Transmission Line Failure.” Multiscale Modeling and Simulation, 19(1), pp. 208-241. DOI:10.1137/19M1306865.

Tipireddy R, P Stinis and A Tartakovsky. 2021. “Time-dependent stochastic basis adaptation for uncertainty quantification.” arXiv:2103.03316.


Stinis P. 2020. “Enforcing constraints for time series prediction in supervised, unsupervised and reinforcement learning.” Proceedings of the AAAI 2020 Spring Symposium on Combining Artificial Intelligence and Machine Learning with Physical Sciences, CEUR Workshop Proceedings, Vol. 2587.

Stinis P, H Lei, J Li and H Wan. 2020. “Improving solution accuracy and convergence for stochastic physics parameterizations with colored noise.” MonthlyWeather Review, 148(6). DOI:10.1175/MWRD-19-0178.1.

Vogl CJ, H Wan, S Zhang, C Woodward, and P Stinis. 2020. “Improving time-step convergence in an atmosphere model with simplified physics: using mathematical rigor to avoid nonphysical behavior in a parameterization.” Journal of Advances in Modeling Earth Systems, 12(10). DOI:10.1029/2019MS001974.

Wan H, C Woodward, S Zhang, CJ Vogl, P Stinis, D Gardner, and PJ Rasch. 2020. “Improving timestep convergence in an atmosphere model with simplified physics: the impacts of closure assumption and process coupling.” Journal of Advances in Modeling Earth Systems, 12(1). DOI:10.1029/2019MS001982.


Lei H, J Li, P Gao, P Stinis and N Baker. 2019. “A data-driven framework for sparsity-enhanced surrogates with arbitrary mutually dependent randomness.” Computer Methods in Applied Mechanics and Engineering, 350, pp. 199-227. DOI:10.1016/j.cma.2019.03.014.

Li J and P Stinis. 2019. “Model reduction for a power grid model.” arXiv:1912.12163.

Li J and P Stinis. 2019. “Mori-Zwanzig reduced models for uncertainty quantification.” Journal of Computational Dynamics 6(1), pp. 39-68. DOI:10.3934/jcd.2019002.

Price J and P Stinis. 2019. “Renormalized reduced order models with memory for long time prediction.” Multiscale Modeling and Simulation, 17(1), pp. 68-91. DOI:10.1137/17M1151389.

Stinis P, T Hagge, AM Tartakovsky and E Yeung. 2019. “Enforcing constraints for interpolation and extrapolation in Generative Adversarial Networks.” Journal of Computational Physics, 397. DOI:10.1016/


Hodas N and P Stinis. 2018. “Doing the impossible: Why neural networks can be trained at all.” Frontiers in Psychology. DOI: 10.3389/fpsyg.2018.01185.

Price J and P. Stinis. 2018. “Renormalization and blow-up for the 3D Euler equations.” arXiv:1805.08766.

Tipireddy R, P Stinis and A Tartakovsky. 2018. “Stochastic basis adaptation and spatial domain decomposition for PDEs with random coefficients.” SIAM Journal of Uncertainty Quantification, Vol. 6, No. 1, pp. 273-301. DOI: 101137/16M1097134.

Ye F, P Stinis and H Qian. 2018. “Dynamic Looping of a Free-Draining Polymer.” SIAM Journal of Applied Mathematics, Vol. 78, No. 1, pp. 104-123. DOI: 10.1137/17M1127260.


Hagge T, E Yeung, P Stinis and A Tartakovsky. 2017. “Solving differential equations with unknown constitutive relations as recurrent neural networks.” arXiv:1710.02242.

Tipireddy R, P Stinis and A Tartakovsky. 2017. “Basis adaptation and domain decomposition for steady partial differential equations with random coefficients.” Journal of Computational Physics, 351, pp. 203-215. DOI: 10.1016/


Li J and P. Stinis. 2016. “A unified framework for mesh refinement in random and physical space.” Journal of Computational Physics, Vol. 323 pp. 243-264. DOI: 10.1016/


Li J and P Stinis. 2015. “Mesh refinement for uncertainty quantification through model reduction.” Journal of Computational Physics, 280, pp. 164-183. DOI: 10.1016/

Li J and P Stinis. 2015. “Efficient failure probability calculation through mesh refinement.” arXiv:1509.06668.

Stinis P. 2015. “Renormalized Mori-Zwanzig reduced models for systems without scale separation.” Proceedings of the Royal Society A Vol. 471 No. 2176. DOI: 10.1098/rspa.2014.0446.


Stinis P. 2014. “Model reduction and mesh refinement.” arXiv:1402.6402v1.


Stinis P. 2013. “Renormalized reduced models for singular PDEs.” Communications in Applied Mathematics and Computational Science, Vol. 8, No. 1, pp. 39-66. DOI: 10.2140/camcos.2013.8.39.


Maroulas V and P Stinis. 2012. “Improved particle filters for multi-target tracking.” Journal of Computational Physics, 231, pp. 602-611. DOI: 10.106/

Stinis P. 2012. “Mori-Zwanzig reduced models for uncertainty quantification II: Initial condition uncertainty.” arXiv:1212.6360v1.

Stinis P. 2012. “Mori-Zwanzig reduced models for uncertainty quantification I: Parametric uncertainty.” arXiv:1211.4285v1.

Stinis P. 2012. “Numerical computation of solutions of the critical nonlinear Schrödinger equation after the singularity.” Multiscale Modeling and Simulation 10, pp. 48-60. DOI: 10.1137/110831222.

Stinis P. 2012. “Stochastic global optimization as a filtering problem.” Journal of Computational Physics 231, pp. 2002-2014. DOI: 10.1016/


Stinis P. 2011. “Conditional path sampling of stochastic differential equations by drift relaxation.” Communications in Applied Mathematics and Computational Science, Vol. 6, No 1, pp. 63-78. DOI: 10.2140/camcos.2011.6.63.


Stinis P. 2009. “A phase transition approach to detecting singularities of PDEs.” Communications in Applied Mathematics and Computational Science, Vol. 4, No. 1, 217-239. DOI: 10.2140/camcos.2009.4.217.


Givon D, P Stinis and J Weare. 2009. “Dimensional reduction for particle filters of systems with time-scale separation.” IEEE Transactions on Signal Processing, Vol.57 No.2, pp. 424-435. DOI: 10.1109/TSP.2008.2008252.

Stinis P. 2008. “Dimensional reduction approach to shock capturing.” Technical Report - Center for Turbulence Research, Stanford. 


Hald OH, P Stinis. 2007. “Optimal prediction and the rate of decay for solutions of the Euler equations in two and three dimensions.” Proceedings of the National Academy of Sciences 104, no 16, pp. 6527-6532. DOI:10.1073/pnas.0700084104 (Published with a Commentary, same issue of PNAS, pp. 6495-6499, and featured on the cover).

Stinis P. 2007. “Higher order Mori-Zwanzig models for the Euler equations.” Multiscale Modeling and Simulation 6, no 3, pp. 741-760. DOI: 10.1137/06066504X.

Stinis P. 2007. “Dimensional reduction as a tool for mesh refinement and tracking singularities of PDEs.” Technical Report LBNL-62851. arXiv: 0706.2895v1.


Chorin AJ, P Stinis. 2006. “Problem reduction, renormalization and memory.” Communications in Applied Mathematics and Computational Science 1, pp. 1-27. DOI:10.2140/camcos.2006.1.1.

Stinis P. 2006. “A comparative study of two stochastic mode reduction methods.” Physica D, 213, pp. 197-213. DOI: 10.1016/j.physd.2005.11.010.

Stinis P, AJ Chorin. 2006. “Numerical scaling analysis of the small-scale structure in turbulence.” Technical Report LBNL-59490. arXiv: math/0509027v1.


Stinis P. 2005. “A maximum likelihood algorithm for the estimation and renormalization of exponential densities.” Journal of Computational Physics, 208, pp. 691-703. DOI: 10.1016/


Stinis P. 2004. “Stochastic optimal prediction for the Kuramoto-Sivashinsky equation.” Multiscale Modeling and Simulation 2, no 4, pp. 580-612. DOI: 10.1137/030600424.


Stinis P. 2003. “A hybrid method for the inviscid Burgers equation.” Discrete and Continuous Dynamical Systems 9, pp. 793-799. DOI:10.3934/dcds.2003.9.793.

Stinis P. 2003. “Stochastic Optimal Prediction for the Kuramoto-Sivashinsky Equation.” PhD Thesis, Columbia University, New York.