@article{Karniadakis:NatRevPhys:2021,
  author =        {Karniadakis, George Em and Kevrekidis, Ioannis G. and
                   Lu, Lu and Perdikaris, Paris and Wang, Sifan and
                   Yang, Liu},
  journal =       {Nature Reviews Physics},
  month =         {Jun},
  number =        {6},
  pages =         {422-440},
  title =         {Physics-informed machine learning},
  volume =        {3},
  year =          {2021},
  abstract =      {Despite great progress in simulating multiphysics
                   problems using the numerical discretization of
                   partial differential equations (PDEs), one still
                   cannot seamlessly incorporate noisy data into
                   existing algorithms, mesh generation remains complex,
                   and high-dimensional problems governed by
                   parameterized PDEs cannot be tackled. Moreover,
                   solving inverse problems with hidden physics is often
                   prohibitively expensive and requires different
                   formulations and elaborate computer codes. Machine
                   learning has emerged as a promising alternative, but
                   training deep neural networks requires big data, not
                   always available for scientific problems. Instead,
                   such networks can be trained from additional
                   information obtained by enforcing the physical laws
                   (for example, at random points in the continuous
                   space-time domain). Such physics-informed learning
                   integrates (noisy) data and mathematical models, and
                   implements them through neural networks or other
                   kernel-based regression networks. Moreover, it may be
                   possible to design specialized network architectures
                   that automatically satisfy some of the physical
                   invariants for better accuracy, faster training and
                   improved generalization. Here, we review some of the
                   prevailing trends in embedding physics into machine
                   learning, present some of the current capabilities
                   and limitations and discuss diverse applications of
                   physics-informed learning both for forward and
                   inverse problems, including discovering hidden
                   physics and tackling high-dimensional problems.},
  doiurl =        {10.1038/s42254-021-00314-5},
  issn =          {2522-5820},
  url =           {https://doi.org/10.1038/s42254-021-00314-5},
}

@article{Fortov:PhysUspekhi:2009,
  author =        {Fortov, V. E.},
  journal =       {Physics Uspekhi},
  number =        {6},
  pages =         {615-647},
  title =         {Extreme states of matter on Earth and in space},
  volume =        {52},
  year =          {2009},
  url =           {https://dx.doi.org/10.3367/UFNe.0179.200906h.0653},
}

@phdthesis{baker1992modeling,
  author =        {Baker, Ernest Lowell},
  school =        {Washington State University},
  title =         {Modeling and optimization of shaped charge liner
                   collapse and jet formation},
  year =          {1992},
}

@inproceedings{baker1996numerical,
  author =        {Baker, EL and Schimel, B and Grantham, WJ},
  booktitle =     {AIP Conference Proceedings},
  number =        {1},
  organization =  {American Institute of Physics},
  pages =         {409--412},
  title =         {Numerical optimization of Ignition and Growth
                   reactive flow modeling for PAX2A},
  volume =        {370},
  year =          {1996},
}

@inproceedings{murphy1996reactive,
  author =        {Murphy, MJ and Simpson, RL and Urtiew, PA and
                   Souers, PC and Garcia, F and Garza, RG},
  booktitle =     {AIP Conference Proceedings},
  number =        {1},
  organization =  {American Institute of Physics},
  pages =         {417--420},
  title =         {Reactive flow model development for PBXW-126 using
                   modern nonlinear optimization methods},
  volume =        {370},
  year =          {1996},
}

@techreport{murphy1996utility,
  author =        {Murphy, Michael J},
  institution =   {Lawrence Livermore National Lab., CA (United States)},
  title =         {Utility of coupling nonlinear optimization methods
                   with numerical modeling software},
  year =          {1996},
}

@article{schimel1997method,
  author =        {Schimel, Boyd D and Baker, Ernest L and
                   Grantham, Walter J},
  journal =       {Journal of Energetic Materials},
  number =        {4},
  pages =         {289--311},
  publisher =     {Taylor \& Francis},
  title =         {A method for parameter optimization of reactive flow
                   continuum models by sequential quadratic programming},
  volume =        {15},
  year =          {1997},
}

@techreport{gardner1999optimization,
  author =        {Gardner, David R and Vaughan, COURTENAY T},
  institution =   {Sandia National Labs., Albuquerque, NM (US); Sandia
                   National Labs~…},
  title =         {The Optimization of a Shaped-Charge Design Using
                   Parallel Computers},
  year =          {1999},
}

@article{amarchinta2010simulation,
  author =        {Amarchinta, Hemanth K and Grandhi, Ramana V and
                   Clauer, Allan H and Langer, Kristina and
                   Stargel, David S},
  journal =       {Journal of Materials Processing Technology},
  number =        {14},
  pages =         {1997--2006},
  publisher =     {Elsevier},
  title =         {Simulation of residual stress induced by a laser
                   peening process through inverse optimization of
                   material models},
  volume =        {210},
  year =          {2010},
}

@article{baranda2010reactive,
  author =        {Baranda Ribeiro, Jose and Mendes, Ricardo and
                   Silva, Crist{\'o}v{\~a}o},
  journal =       {Propellants, Explosives, Pyrotechnics},
  number =        {3},
  pages =         {292--299},
  publisher =     {Wiley Online Library},
  title =         {Reactive Flow Model Parameter Estimation Using
                   Genetic Algorithms},
  volume =        {35},
  year =          {2010},
}

@article{walls2013optimization,
  author =        {Walls, Kenneth and Littlefield, David and
                   Dorgan, Robert and Lambert, David},
  journal =       {Procedia Engineering},
  pages =         {279--288},
  publisher =     {Elsevier},
  title =         {An Optimization Framework for Calibration of Material
                   Models},
  volume =        {58},
  year =          {2013},
}

@article{gambino2018numerical,
  author =        {Gambino, James R and Tarver, Craig M and
                   Springer, H Keo},
  journal =       {Journal of Applied Physics},
  number =        {19},
  pages =         {195901},
  publisher =     {AIP Publishing LLC},
  title =         {Numerical parameter optimizations of the ignition and
                   growth model for a HMX plastic bonded explosive},
  volume =        {124},
  year =          {2018},
}

@article{JWL,
  author =        {Kapila, A. K. and Schwendeman, D. W. and Bdzil, J. B. and
                   Henshaw, W. D.},
  journal =       {Combustion Theory and Modelling},
  number =        {5},
  pages =         {781--822},
  publisher =     {Taylor \& Francis},
  title =         {A study of detonation diffraction in the
                   ignition-and-growth model},
  volume =        {11},
  year =          {2007},
  language =      {english},
}

@article{ahrens1968material,
  author =        {Ahrens, Thomas J and Gust, WH and Royce, EB},
  journal =       {Journal of Applied Physics},
  number =        {10},
  pages =         {4610--4616},
  publisher =     {American Institute of Physics},
  title =         {Material strength effect in the shock compression of
                   alumina},
  volume =        {39},
  year =          {1968},
}

@article{barker1972laser,
  author =        {Barker, LM and Hollenbach, RE},
  journal =       {Journal of Applied Physics},
  number =        {11},
  pages =         {4669--4675},
  publisher =     {American Institute of Physics},
  title =         {Laser interferometer for measuring high velocities of
                   any reflecting surface},
  volume =        {43},
  year =          {1972},
}

@article{parshikov2002,
  author =        {Anatoly N. Parshikov and Stanislav A. Medin},
  journal =       {Journal of Computational Physics},
  number =        {1},
  pages =         {358 - 382},
  title =         {Smoothed Particle Hydrodynamics Using Interparticle
                   Contact Algorithms},
  volume =        {180},
  year =          {2002},
  doiurl =        {10.1006/jcph.2002.7099},
  issn =          {0021-9991},
}

@article{egorova2019,
  author =        {Egorova, M. S. and Dyachkov, S. A. and
                   Parshikov, A. N. and Zhakhovsky, V. V.},
  journal =       {Computer Physics Communications},
  pages =         {112--125},
  publisher =     {Elsevier},
  title =         {Parallel SPH modeling using dynamic domain
                   decomposition and load balancing displacement of
                   Voronoi subdomains},
  volume =        {234},
  year =          {2019},
}

@article{1983:Cook,
  author =        {Johnson, G. R. and Cook, W. H.},
  journal =       {Proceedings of the seventh international simposium on
                   ballistics, Hague, Netherlands},
  pages =         {541--547},
  title =         {A constitutive model and data for metals subjected to
                   largestrains, high strain rates and high
                   temperatures},
  year =          {1983},
  language =      {english},
}

@article{1985:Cook,
  author =        {Johnson, G. R. and Cook, W. H.},
  journal =       {Engineering Fracture Mechanics},
  number =        {1},
  pages =         {31--48},
  title =         {Fracture characteristics of three metals subjected to
                   various strains, strain rates, temperatures and
                   pressures},
  volume =        {21},
  year =          {1985},
  doiurl =        {10.1016/0013-7944(85)90052-9},
  language =      {english},
}

@article{casem2012shock,
  author =        {Casem, Daniel T and Dandekar, Dattatraya P},
  journal =       {Journal of Applied Physics},
  number =        {6},
  pages =         {063508},
  publisher =     {American Institute of Physics},
  title =         {Shock and mechanical response of 2139-T8 aluminum},
  volume =        {111},
  year =          {2012},
}

@misc{SciPy,
  note =          {SciPy \href{https://scipy.org} {https://scipy.org}},
}

@article{1964:Powell,
  author =        {Powell, M. J. D.},
  journal =       {The Computer Journal},
  number =        {2},
  pages =         {155--162},
  title =         {An efficient method for finding the minimum of a
                   function of several variables without calculating
                   derivatives},
  volume =        {7},
  year =          {1964},
  doiurl =        {10.1093/comjnl/7.2.155},
}

@article{1965:NelderMead,
  author =        {Nelder, J. A. and Mead, R.},
  journal =       {The Computer Journal},
  number =        {4},
  pages =         {308--313},
  title =         {A Simplex Method for Function Minimization},
  volume =        {7},
  year =          {1965},
  doiurl =        {10.1093/comjnl/7.4.308},
}

@article{1913:vonMises,
  author =        {von Mises, R.},
  journal =       {Mathematisch-Physikalische Klasse},
  pages =         {582--592},
  title =         {Mechanik der festen K\"{o}rper im
                   plastisch-deformablen Zustand},
  volume =        {1},
  year =          {1913},
}

@article{1999:JAP:Johnson_Holmquist,
  author =        {Johnson, Gordon R and Holmquist, Tim J},
  journal =       {Journal of Applied Physics},
  number =        {12},
  pages =         {8060--8073},
  publisher =     {AIP},
  title =         {Response of boron carbide subjected to large strains,
                   high strain rates, and high pressures},
  volume =        {85},
  year =          {1999},
}

@article{johnson_holmquist:2003,
  author =        {Johnson, Gordon R and Holmquist, Timothy J and
                   Beissel, Stephen R},
  journal =       {Journal of applied physics},
  number =        {3},
  pages =         {1639--1646},
  publisher =     {AIP},
  title =         {Response of aluminum nitride (including a phase
                   change) to large strains, high strain rates, and high
                   pressures},
  volume =        {94},
  year =          {2003},
}

@article{2005:JAP:Johnson_Holmquist,
  author =        {Holmquist, Timothy J and Johnson, Gordon R},
  journal =       {Journal of applied physics},
  number =        {9},
  pages =         {093502},
  publisher =     {AIP},
  title =         {Characterization and evaluation of silicon carbide
                   for high-velocity impact},
  volume =        {97},
  year =          {2005},
}

@article{dyachkov2018explicit,
  author =        {Dyachkov, SA and Parshikov, AN and Egorova, MS and
                   Grigoryev, S Yu and Zhakhovsky, VV and Medin, SA},
  journal =       {Journal of Applied Physics},
  number =        {8},
  pages =         {085902},
  publisher =     {AIP Publishing},
  title =         {Explicit failure model for boron carbide ceramics
                   under shock loading},
  volume =        {124},
  year =          {2017},
}

@article{2006:JAP:Vogler,
  author =        {Vogler, TJ and Reinhart, WD and Chhabildas, LC and
                   Dandekar, DP},
  journal =       {Journal of applied physics},
  number =        {2},
  pages =         {023512},
  publisher =     {AIP},
  title =         {Hugoniot and strength behavior of silicon carbide},
  volume =        {99},
  year =          {2006},
}

@book{antoun2003spall,
  author =        {Antoun, Tarabay},
  publisher =     {Springer Science \& Business Media},
  title =         {Spall fracture},
  year =          {2003},
}

@article{chen2006spall,
  author =        {Chen, X and Asay, JR and Dwivedi, SK and Field, DP},
  journal =       {Journal of applied physics},
  number =        {2},
  pages =         {023528},
  publisher =     {AIP},
  title =         {Spall behavior of aluminum with varying
                   microstructures},
  volume =        {99},
  year =          {2006},
}

@inproceedings{holtkamp2004survey,
  author =        {Holtkamp, DB and Clark, DA and Ferm, EN and
                   Gallegos, RA and Hammon, D and Hemsing, WF and
                   Hogan, GE and Holmes, VH and King, NSP and
                   Liljestrand, R and others},
  booktitle =     {AIP Conference Proceedings},
  number =        {1},
  organization =  {AIP},
  pages =         {477--482},
  title =         {A Survey of High Explosive-Induced Damage and Spall
                   in Selected Metals Using Proton Radiography},
  volume =        {706},
  year =          {2004},
}

@article{de2007experimental,
  author =        {De Ress{\'e}guier, T and Signor, Lo{\"\i}c and
                   Dragon, A and Boustie, M and Roy, G and Llorca, F},
  journal =       {Journal of applied physics},
  number =        {1},
  pages =         {013506},
  publisher =     {AIP},
  title =         {Experimental investigation of liquid spall in laser
                   shock-loaded tin},
  volume =        {101},
  year =          {2007},
}

@article{de2010dynamic,
  author =        {De Resseguier, T and Signor, L and Dragon, A and
                   Roy, G},
  journal =       {International Journal of Fracture},
  number =        {1-2},
  pages =         {109--119},
  publisher =     {Springer},
  title =         {Dynamic fragmentation of laser shock-melted tin:
                   experiment and modelling},
  volume =        {163},
  year =          {2010},
}

@article{signor2010investigation,
  author =        {Signor, Lo{\"\i}c and de Ress{\'e}guier, Thibaut and
                   Dragon, Andr{\'e} and Roy, Gilles and Fanget, Alain and
                   Faessel, Matthieu},
  journal =       {International Journal of Impact Engineering},
  number =        {8},
  pages =         {887--900},
  publisher =     {Elsevier},
  title =         {Investigation of fragments size resulting from
                   dynamic fragmentation in melted state of laser
                   shock-loaded tin},
  volume =        {37},
  year =          {2010},
}

@article{grady1988spall,
  author =        {Grady, DE},
  journal =       {Journal of the Mechanics and Physics of Solids},
  number =        {3},
  pages =         {353--384},
  publisher =     {Elsevier},
  title =         {The spall strength of condensed matter},
  volume =        {36},
  year =          {1988},
}

@article{dongare2009atomic,
  author =        {Dongare, Avinash M and Rajendran, Arunachalam M and
                   LaMattina, Bruce and Zikry, Mohammed A and
                   Brenner, Donald W},
  journal =       {Physical Review B},
  number =        {10},
  pages =         {104108},
  publisher =     {APS},
  title =         {Atomic scale simulations of ductile failure
                   micromechanisms in nanocrystalline Cu at high strain
                   rates},
  volume =        {80},
  year =          {2009},
}

@article{dongare2010atomic,
  author =        {Dongare, Avinash M and Rajendran, Arunachalam M and
                   LaMattina, Bruce and Zikry, Mohammed A and
                   Brenner, Donald W},
  journal =       {Journal of Applied Physics},
  number =        {11},
  pages =         {113518},
  publisher =     {AIP},
  title =         {Atomic scale studies of spall behavior in
                   nanocrystalline Cu},
  volume =        {108},
  year =          {2010},
}

@article{luo2009shock,
  author =        {Luo, Sheng-Nian and An, Qi and Germann, Timothy C and
                   Han, Li-Bo},
  journal =       {Journal of Applied Physics},
  number =        {1},
  pages =         {013502},
  publisher =     {AIP},
  title =         {Shock-induced spall in solid and liquid Cu at extreme
                   strain rates},
  volume =        {106},
  year =          {2009},
}

@article{luo2009spall,
  author =        {Luo, Sheng-Nian and Germann, Timothy C and
                   Tonks, Davis L},
  journal =       {Journal of Applied Physics},
  number =        {12},
  pages =         {123518},
  publisher =     {AIP},
  title =         {Spall damage of copper under supported and decaying
                   shock loading},
  volume =        {106},
  year =          {2009},
}

@article{kuksin2010theory,
  author =        {Kuksin, A Yu and Norman, GE and Pisarev, VV and
                   Stegailov, VV and Yanilkin, AV},
  journal =       {Physical Review B},
  number =        {17},
  pages =         {174101},
  publisher =     {APS},
  title =         {Theory and molecular dynamics modeling of spall
                   fracture in liquids},
  volume =        {82},
  year =          {2010},
}

@article{xiang2013spalling,
  author =        {Xiang, Meizhen and Hu, Haibo and Chen, Jun},
  journal =       {Journal of Applied Physics},
  number =        {14},
  pages =         {144312},
  publisher =     {AIP},
  title =         {Spalling and melting in nanocrystalline Pb under
                   shock loading: Molecular dynamics studies},
  volume =        {113},
  year =          {2013},
}

@article{cai2017spall,
  author =        {Cai, Y and Wu, HA and Luo, SN},
  journal =       {Journal of Applied Physics},
  number =        {10},
  pages =         {105901},
  publisher =     {AIP Publishing},
  title =         {Spall strength of liquid copper and accuracy of the
                   acoustic method},
  volume =        {121},
  year =          {2017},
}