Bar-Sinai, Y., Hoyer, S., Hickey, J., and Brenner, M.P. (2019). Learning data-driven discretizations for partial differential equations. Proceedings of the National Academy of Sciences, 116(31), 15344–15349. Cybenko, G. (1989). Approximation by superpositions of a sigmoidal function. Mathematics of control, signals and systems, 2(4), 303–314. Dao, T.S., Vyasarayani, C.P., and McPhee, J. (2012). Simplification and order reduction of lithium-ion battery model based on porous-electrode theory. Journal of Power Sources, 198, 329 – 337. doi: https://doi.org/10.1016/j.jpowsour.2011.09.034. Doyle, M., Fuller, T.F., and Newman, J. (1993). Modeling of galvanostatic charge and discharge of the lithium/polymer/insertion cell. Journal of the Electrochemical society, 140(6), 1526. Dunn, B., Kamath, H., and Tarascon, J.M. (2011). Electrical energy storage for the grid: a battery of choices. Science, 334(6058), 928–935. Forman, J.C., Bashash, S., Stein, J.L., and Fathy, H.K. (2011). Reduction of an electrochemistry-based li-ion battery model via quasi-linearization and pade approximation. Journal of The Electrochemical Society, 158(2), A93. doi:10.1149/1.3519059. Hamilton, A., Tran, T., Mckay, M., Quiring, B., and Vassilevski, P. (2019). Dnn approximation of nonlinear finite element equations. Technical report, Lawrence Livermore National Lab.(LLNL), Livermore, CA (United States). Marquis, S.G., Sulzer, V., Timms, R., Please, C.P., and Chapman, S.J. (2019). An asymptotic derivation of a single particle model with electrolyte. Journal of The Electrochemical Society, 166(15), A3693–A3706. Mishra, P.P., Garg, M., Mendoza, S., Liu, J., Rahn, C.D., and Fathy, H.K. (2016). How does model reduction affect lithium-ion battery state of charge estimation errors? theory and experiments. Journal of The Electrochemical Society, 164(2), A237–A251. doi: 10.1149/2.0751702jes. Raissi, M., Perdikaris, P., and Karniadakis, G.E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics, 378, 686–707. Speltino, C., Di Domenico, D., Fiengo, G., and Stefanopoulou, A. (2009). Comparison of reduced order lithium-ion battery models for control applications. In Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference, 3276–3281. doi: 10.1109/CDC.2009.5400816. Sulzer, V., Marquis, S.G., Timms, R., Robinson, M., and Chapman, S.J. (2020). Python battery mathematical modelling (pybamm). ECSarXiv. February, 7. Tripathy, R.K. and Bilionis, I. (2018). Deep uq: Learning deep neural network surrogate models for high dimensional uncertainty quantification. Journal of computational physics, 375, 565–588. Zhu, Y. and Zabaras, N. (2018). Bayesian deep convolutional encoder–decoder networks for surrogate modeling and uncertainty quantification. Journal of Computational Physics, 366, 415–447. Zou, C., Manzie, C., and Neˇsi ́c, D. (2016). A framework for simplification of pde-based lithium-ion battery models. IEEE Transactions on Control Systems Technology, 24(5), 1594–1609. doi:10.1109/TCST.2015.2502899.