Maximum-likelihood estimators in physics-informed neural networks for high-dimensional inverse problems

Gusmão, Gabriel S.; Medford, Andrew J.

doi:10.1016/j.compchemeng.2023.108547

Title: Maximum-likelihood estimators in physics-informed neural networks for high-dimensional inverse problems

Journal Article · 01 February 2024 · Computers and Chemical Engineering

DOI: https://doi.org/10.1016/j.compchemeng.2023.108547 · OSTI ID:2246670

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Sponsoring Organization:: USDOE

OSTI ID:: 2246670

Journal Information:: Computers and Chemical Engineering, Journal Name: Computers and Chemical Engineering Vol. 181 Journal Issue: C; ISSN 0098-1354

Publisher:: ElsevierCopyright Statement

Country of Publication:: United Kingdom

Language:: English

References (54)

Single-Event MicroKinetics: Catalyst design for complex reaction networks Thybaut, J. W.; Marin, G. B. Journal of Catalysis, Vol. 308 https://doi.org/10.1016/j.jcat.2013.08.013	journal	December 2013
LSODE and LSODI, two new initial value ordinary differnetial equation solvers Hindmarsh, Alan C. ACM SIGNUM Newsletter, Vol. 15, Issue 4 https://doi.org/10.1145/1218052.1218054	journal	December 1980
Automatic Selection of Methods for Solving Stiff and Nonstiff Systems of Ordinary Differential Equations Petzold, Linda SIAM Journal on Scientific and Statistical Computing, Vol. 4, Issue 1 https://doi.org/10.1137/0904010	journal	March 1983
Approximation of function and its derivatives using radial basis function networks Mai-Duy, Nam; Tran-Cong, Thanh Applied Mathematical Modelling, Vol. 27, Issue 3 https://doi.org/10.1016/S0307-904X(02)00101-4	journal	March 2003
Physics-Informed Neural Networks with Hard Constraints for Inverse Design Lu, Lu; Pestourie, Raphaël; Yao, Wenjie SIAM Journal on Scientific Computing, Vol. 43, Issue 6 https://doi.org/10.1137/21M1397908	journal	January 2021
Universal approximation of an unknown mapping and its derivatives using multilayer feedforward networks Hornik, Kurt; Stinchcombe, Maxwell; White, Halbert Neural Networks, Vol. 3, Issue 5 https://doi.org/10.1016/0893-6080(90)90005-6	journal	January 1990
Physics informed neural networks for simulating radiative transfer Mishra, Siddhartha; Molinaro, Roberto Journal of Quantitative Spectroscopy and Radiative Transfer, Vol. 270 https://doi.org/10.1016/j.jqsrt.2021.107705	journal	August 2021
Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems Yu, Jeremy; Lu, Lu; Meng, Xuhui Computer Methods in Applied Mechanics and Engineering, Vol. 393 https://doi.org/10.1016/j.cma.2022.114823	journal	April 2022
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations Raissi, M.; Perdikaris, P.; Karniadakis, G. E. Journal of Computational Physics, Vol. 378 https://doi.org/10.1016/j.jcp.2018.10.045	journal	February 2019
Nonlinear parameter estimation: A case study comparison Biegler, L. T.; Damiano, J. J.; Blau, G. E. AIChE Journal, Vol. 32, Issue 1 https://doi.org/10.1002/aic.690320105	journal	January 1986
The Y-Procedure methodology for the interpretation of transient kinetic data: Analysis of irreversible adsorption Redekop, Evgeniy A.; Yablonsky, Gregory S.; Constales, Denis Chemical Engineering Science, Vol. 66, Issue 24 https://doi.org/10.1016/j.ces.2011.08.055	journal	December 2011
Approximation by superpositions of a sigmoidal function Cybenko, G. Mathematics of Control, Signals, and Systems, Vol. 2, Issue 4 https://doi.org/10.1007/BF02551274	journal	December 1989
Multilayer feedforward networks with a nonpolynomial activation function can approximate any function Leshno, Moshe; Lin, Vladimir Ya.; Pinkus, Allan Neural Networks, Vol. 6, Issue 6 https://doi.org/10.1016/S0893-6080(05)80131-5	journal	January 1993
Solving high-dimensional partial differential equations using deep learning Han, Jiequn; Jentzen, Arnulf; E., Weinan Proceedings of the National Academy of Sciences, Vol. 115, Issue 34 https://doi.org/10.1073/pnas.1718942115	journal	August 2018
Sequential-Optimization-Based Framework for Robust Modeling and Design of Heterogeneous Catalytic Systems Rangarajan, Srinivas; Maravelias, Christos T.; Mavrikakis, Manos The Journal of Physical Chemistry C, Vol. 121, Issue 46 https://doi.org/10.1021/acs.jpcc.7b08089	journal	November 2017
Preconditioning Wathen, A. J. Acta Numerica, Vol. 24 https://doi.org/10.1017/S0962492915000021	journal	April 2015
PolyODENet: Deriving mass-action rate equations from incomplete transient kinetics data Wu, Qin; Avanesian, Talin; Qu, Xiaohui The Journal of Chemical Physics, Vol. 157, Issue 16 https://doi.org/10.1063/5.0110313	journal	October 2022
Autonomous Discovery of Unknown Reaction Pathways from Data by Chemical Reaction Neural Network Ji, Weiqi; Deng, Sili The Journal of Physical Chemistry A, Vol. 125, Issue 4 https://doi.org/10.1021/acs.jpca.0c09316	journal	January 2021
Autonomous kinetic modeling of biomass pyrolysis using chemical reaction neural networks Ji, Weiqi; Richter, Franz; Gollner, Michael J. Combustion and Flame, Vol. 240 https://doi.org/10.1016/j.combustflame.2022.111992	journal	June 2022
Physics-informed graph neural Galerkin networks: A unified framework for solving PDE-governed forward and inverse problems Gao, Han; Zahr, Matthew J.; Wang, Jian-Xun Computer Methods in Applied Mechanics and Engineering, Vol. 390 https://doi.org/10.1016/j.cma.2021.114502	journal	February 2022
Advanced solution methods for microkinetic models of catalytic reactions: A methanol synthesis case study Rubert-Nason, Patricia; Mavrikakis, Manos; Maravelias, Christos T. AIChE Journal, Vol. 60, Issue 4 https://doi.org/10.1002/aic.14322	journal	December 2013
fPINNs: Fractional Physics-Informed Neural Networks Pang, Guofei; Lu, Lu; Karniadakis, George Em SIAM Journal on Scientific Computing, Vol. 41, Issue 4 https://doi.org/10.1137/18M1229845	journal	January 2019
The ALAMO approach to machine learning Wilson, Zachary T.; Sahinidis, Nikolaos V. Computers & Chemical Engineering, Vol. 106 https://doi.org/10.1016/j.compchemeng.2017.02.010	journal	November 2017
On the history of maximum likelihood in relation to inverse probability and least squares Hald, Anders Statistical Science, Vol. 14, Issue 2 https://doi.org/10.1214/ss/1009212248	journal	May 1999
The numerical solution of linear ordinary differential equations by feedforward neural networks Meade, A. J.; Fernandez, A. A. Mathematical and Computer Modelling, Vol. 19, Issue 12 https://doi.org/10.1016/0895-7177(94)90095-7	journal	June 1994
Physics-informed neural networks (PINNs) for fluid mechanics: a review Cai, Shengze; Mao, Zhiping; Wang, Zhicheng Acta Mechanica Sinica, Vol. 37, Issue 12 https://doi.org/10.1007/s10409-021-01148-1	journal	December 2021
Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for PDEs Mishra, Siddhartha; Molinaro, Roberto IMA Journal of Numerical Analysis, Vol. 42, Issue 2 https://doi.org/10.1093/imanum/drab032	journal	June 2021
Elucidating complex catalytic mechanisms based on transient pulse-response kinetic data Redekop, Evgeniy A.; Yablonsky, Gregory S.; Constales, Denis Chemical Engineering Science, Vol. 110 https://doi.org/10.1016/j.ces.2013.11.050	journal	May 2014
Multi-Fidelity Physics-Constrained Neural Network and Its Application in Materials Modeling Liu, Dehao; Wang, Yan Journal of Mechanical Design, Vol. 141, Issue 12 https://doi.org/10.1115/1.4044400	journal	September 2019
A well-conditioned estimator for large-dimensional covariance matrices Ledoit, Olivier; Wolf, Michael Journal of Multivariate Analysis, Vol. 88, Issue 2 https://doi.org/10.1016/S0047-259X(03)00096-4	journal	February 2004
Noise in temporal analysis of products (TAP) pulse responses Roelant, R.; Constales, D.; Yablonsky, G. Catalysis Today, Vol. 121, Issue 3-4 https://doi.org/10.1016/j.cattod.2006.05.087	journal	March 2007
Physics-informed machine learning Karniadakis, George Em; Kevrekidis, Ioannis G.; Lu, Lu Nature Reviews Physics, Vol. 3, Issue 6 https://doi.org/10.1038/s42254-021-00314-5	journal	May 2021
Kinetics of chemical processes: From molecular to industrial scale Marin, Guy B.; Galvita, Vladimir V.; Yablonsky, Gregory S. Journal of Catalysis https://doi.org/10.1016/j.jcat.2021.09.014	journal	September 2021
Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems Jagtap, Ameya D.; Kharazmi, Ehsan; Karniadakis, George Em Computer Methods in Applied Mechanics and Engineering, Vol. 365 https://doi.org/10.1016/j.cma.2020.113028	journal	June 2020
Efficient machine learning based surrogate models for surface kinetics by approximating the rates of the rate-determining steps Döppel, Felix A.; Votsmeier, Martin Chemical Engineering Science, Vol. 262 https://doi.org/10.1016/j.ces.2022.117964	journal	November 2022
Approximation capabilities of multilayer feedforward networks Hornik, Kurt Neural Networks, Vol. 4, Issue 2 https://doi.org/10.1016/0893-6080(91)90009-T	journal	January 1991
Artificial neural networks for solving ordinary and partial differential equations Lagaris, I. E.; Likas, A.; Fotiadis, D. I. IEEE Transactions on Neural Networks, Vol. 9, Issue 5 https://doi.org/10.1109/72.712178	journal	January 1998
Dynamic methods for catalytic kinetics Berger, Rob J.; Kapteijn, Freek; Moulijn, Jacob A. Applied Catalysis A: General, Vol. 342, Issue 1-2 https://doi.org/10.1016/j.apcata.2008.03.020	journal	June 2008
Solution of nonlinear ordinary differential equations by feedforward neural networks Meade, A. J.; Fernandez, A. A. Mathematical and Computer Modelling, Vol. 20, Issue 9 https://doi.org/10.1016/0895-7177(94)00160-X	journal	November 1994
Thermodynamically consistent physics-informed neural networks for hyperbolic systems Patel, Ravi G.; Manickam, Indu; Trask, Nathaniel A. Journal of Computational Physics, Vol. 449 https://doi.org/10.1016/j.jcp.2021.110754	journal	January 2022
Thermodynamic Theory of Affinity. By Th. De Donder and Pierre Van Rysselberghe MacDougall, F. H. The Journal of Physical Chemistry, Vol. 41, Issue 5 https://doi.org/10.1021/j150383a036	journal	May 1937
Discovering governing equations from data by sparse identification of nonlinear dynamical systems Brunton, Steven L.; Proctor, Joshua L.; Kutz, J. Nathan Proceedings of the National Academy of Sciences, Vol. 113, Issue 15 https://doi.org/10.1073/pnas.1517384113	journal	March 2016
B-PINNs: Bayesian physics-informed neural networks for forward and inverse PDE problems with noisy data Yang, Liu; Meng, Xuhui; Karniadakis, George Em Journal of Computational Physics, Vol. 425 https://doi.org/10.1016/j.jcp.2020.109913	journal	January 2021
The application of flash desorption spectroscopy to chemical reactions on surfaces: Temperature programmed reaction spectroscopy Madix, Robert J. Critical Reviews in Solid State and Materials Sciences, Vol. 7, Issue 2 https://doi.org/10.1080/10408437808243436	journal	September 1978
Tutorial on maximum likelihood estimation Myung, In Jae Journal of Mathematical Psychology, Vol. 47, Issue 1, p. 90-100 https://doi.org/10.1016/S0022-2496(02)00028-7	journal	February 2003
Estimation of the disturbance structure from data using semidefinite programming and optimal weighting Rajamani, Murali R.; Rawlings, James B. Automatica, Vol. 45, Issue 1 https://doi.org/10.1016/j.automatica.2008.05.032	journal	January 2009
Fast Direct Methods for Gaussian Processes Ambikasaran, Sivaram; Foreman-Mackey, Daniel; Greengard, Leslie IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 38, Issue 2 https://doi.org/10.1109/TPAMI.2015.2448083	journal	February 2016
Solution and Parameter Identification of a Fixed-Bed Reactor Model for Catalytic CO2 Methanation Using Physics-Informed Neural Networks Ngo, Son Ich; Lim, Young-Il Catalysts, Vol. 11, Issue 11 https://doi.org/10.3390/catal11111304	journal	October 2021
Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker--Planck Equation and Physics-Informed Neural Networks Chen, Xiaoli; Yang, Liu; Duan, Jinqiao SIAM Journal on Scientific Computing, Vol. 43, Issue 3 https://doi.org/10.1137/20M1360153	journal	January 2021
The C-matrix: Augmentation and reduction in the analysis of chemical composition and structure Constales, D.; Yablonsky, G. S.; Marin, G. B. Chemical Engineering Science, Vol. 110 https://doi.org/10.1016/j.ces.2013.09.043	journal	May 2014
Generalized reactor neural ODE for dynamic reaction process modeling with physical interpretability Yin, Jun; Li, Jiali; Karimi, Iftekhar A. Chemical Engineering Journal, Vol. 452 https://doi.org/10.1016/j.cej.2022.139487	journal	January 2023
Physics-Informed Neural Networks for Heat Transfer Problems Cai, Shengze; Wang, Zhicheng; Wang, Sifan Journal of Heat Transfer, Vol. 143, Issue 6 https://doi.org/10.1115/1.4050542	journal	April 2021
PPINN: Parareal physics-informed neural network for time-dependent PDEs Meng, Xuhui; Li, Zhen; Zhang, Dongkun Computer Methods in Applied Mechanics and Engineering, Vol. 370 https://doi.org/10.1016/j.cma.2020.113250	journal	October 2020
A Fast Algorithm for the Minimum Covariance Determinant Estimator Rousseeuw, Peter J.; Driessen, Katrien Van Technometrics, Vol. 41, Issue 3 https://doi.org/10.1080/00401706.1999.10485670	journal	August 1999

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