Photo of Samuel Grauer

232 Research East Building
Penn State

Samuel Grauer’s Home Page

Jump to: Biography | Students | Publications | Code | Gallery | Links


I am an assistant professor in the Department of Mechanical Engineering at Penn State. My research group studies inverse problems related to optical diagnostics. This work involves data assimilation for flow reconstruction, limited-data non-destructive testing and evaluation, and large-scale non-linear uncertainty quantification.

In particular, my group has ongoing projects that involve the following diagnostics:

We develop image reconstruction and data assimilation methods to interpret measurements from these sensors. Additional information about the measured system is typically required, either in the form of the governing equations (comprehensive, filtered, or otherwise reduced) or a generic penalty (e.g., an L2 or L1 smoothness prior). Most of our codes utilize scientific machine learning or a related differentiable programming technique, and we perform Bayesian inference for uncertainty quantification. Our group employs these methods to study: A consistent theme of our research is developing “high-fidelity, differentiable observation operators” and realistic noise models, which are needed to push the limits of reconstruction algorithms vis-á-vis accuracy and resolution. Observation operators map a system state to measurements thereof; hence, accurate operators are needed for accurate reconstructions, differentiable operators are required when using a variational reconstruction algorithm, and a veridical noise model is a necessary precursor to robust estimates of uncertainty.

I received a PhD from the University of Waterloo in September 2018 and a BSc in Mechanical Engineering from the University of Manitoba in 2014. From 2018 to 2020, I was a postdoc in the Ben T. Zinn Combustion Lab at Georgia Tech.

Curriculum Vitae – You can find a copy of my CV here.


Underlined degrees were earned in my group.

Grauer Lab at Penn State

*Co-supervised with Yuan Xuan

Prospective Students

If you are an aspiring PhD student who is gifted in the areas of programming, applied physics, and/or statistics, who has a penchant for tinkering with laser beams and high-speed cameras, and who possesses an unquenchable thirst for knowledge and an interest in problems that lie at the junction of physics, measurement, and uncertainty... then please do send me an email.


Underlined authors were supervised by me and indicates that authors made an equal contribution.

Book Chapters

  1. SJ Grauer, TA Sipkens, PJ Hadwin, and KJ Daun, “Statistical inversion, uncertainty quantification, and the optimal design of optical experiments,” in Optical Diagnostics for Reacting and Non-Reacting Flows: Theory and Practice, A Steinberg and S Roy, eds, 1st ed (AIAA, 2023), 1137–1202. doi:10.2514/5.9781624106330.1137.1202
  2. BR Halls, TR Meyer, SJ Grauer, and L Ma, “Tutorial: Tomographic imaging in combustion-related flows,” in Optical Diagnostics for Reacting and Non-Reacting Flows: Theory and Practice, A Steinberg and S Roy, eds, 1st ed (AIAA, 2023), 1089–1136. doi:10.2514/5.9781624106330.1089.1136
  3. H McCann, P Wright, K Daun, SJ Grauer, C Liu, and S Wagner, “Chemical species tomography,” in Industrial Tomography: Systems and Applications, M Wang, ed, 2nd ed (Woodhead Publishing, 2022), 155–206. doi:10.1016/B978-0-12-823015-2.00004-2

Journal Papers

  1. JL Suazo Betancourt, SJ Grauer, J Bak, AM Steinberg, and MLR Walker, “Bayesian plasma model selection for Thomson scattering,” Rev Sci Instrum 95, 043004, 2024. doi:10.1063/5.0158749
  2. Y Bin, X Hu, J Li, SJ Grauer, and XIA Yang, “Constrained re-calibration of two-equation Reynolds-averaged Navier–Stokes models,” Theor Appl Mech Lett 14(2), 100503, 2024. doi:10.1016/j.taml.2024.100503
  3. FJ Bauer, PAB Braeuer, MWR Wilke, S Will, and SJ Grauer, “2D in situ determination of soot optical band gaps in flames using hyperspectral absorption tomography,” Combust Flame 258, 112730, 2023. doi:10.1016/j.combustflame.2023.112730
  4. K Zhou, J Li, J Hong, and SJ Grauer, “Stochastic particle advection velocimetry (SPAV): theory, simulations, and proof-of-concept experiments,” Meas Sci Technol 34(6), 065302, 2023. doi:10.1088/1361-6501/acc049
  5. JP Molnar, L Venkatakrishnan, BE Schmidt, TA Sipkens, and SJ Grauer, “Estimating density, velocity, and pressure fields in supersonic flows using physics-informed BOS,” Exp Fluids 64, 14, 2023. doi:10.1007/s00348-022-03554-y
  6. TA Sipkens, JC Corbin, SJ Grauer, and GJ Smallwood, “Tutorial: Guide to error propagation for particle counting measurements,” J Aerosol Sci 167, 106091, 2023. doi:10.1016/j.jaerosci.2022.106091
  7. SJ Grauer, K Mohri, T Yu, H Liu, and W Cai, “Volumetric emission tomography for combustion processes,” Prog Energy Combust Sci 94, 101024, 2023. doi:10.1016/j.pecs.2022.101024
  8. SJ Grauer, KM Rice, JM Donbar, NJ Bisek, JJ France, BA Ochs, and AM Steinberg, “Optimization of tunable diode laser arrays for inlet mass capture measurement,” AIAA J 60(10), 5854–5867, 2022. doi:10.2514/1.J061774
  9. JP Molnar and SJ Grauer, “Flow field tomography with uncertainty quantification using a Bayesian physics-informed neural network,” Meas Sci Technol 33(6), 065305, 2022. doi:10.1088/1361-6501/ac5437
  10. M Gomez, SJ Grauer, J Ludwigsen, AM Steinberg, SF Son, S Roy, and TR Meyer, “Megahertz-rate background-oriented schlieren tomography in post-detonation blasts,” Appl Opt 61(10), 2444–2458, 2022. doi:10.1364/AO.449654
  11. TA Sipkens, SJ Grauer, AM Steinberg, SN Rogak, and P Kirchen, “Megahertz-rate background-oriented schlieren tomography in post-detonation blasts,” Appl Opt 61(10), 2444–2458, 2022. doi:10.1088/1361-6501/ac3f83
  12. NP Brown, SJ Grauer, JA Deibel, MLR Walker, and AM Steinberg, “Bayesian framework for THz-TDS plasma diagnostics,” Opt Express 29(4), 4887–4901, 2021. doi:10.1364/OE.417396
  13. SJ Grauer and AM Steinberg, “Linear absorption tomography with velocimetry (LATV) for multiparameter measurements in high-speed flows,” Opt Express 28(22), 32676–32692, 2020. doi:10.1364/OE.408588
  14. RB Miguel, J Emmert, SJ Grauer, J Thornock, and KJ Daun, “Optimal filter selection for quantitative gas mixture imaging,” J Quant Spectrosc Radiat Transfer 254, 107208, 2020. doi:10.1016/j.jqsrt.2020.107208
  15. SJ Grauer and AM Steinberg, “Fast and robust volumetric refractive index measurement by unified background-oriented schlieren tomography,” Exp Fluids 61(3), 80, 2020. doi:10.1007/s00348-020-2912-1
  16. J Emmert, SJ Grauer, S Wagner, and KJ Daun, “Efficient Bayesian inference of absorbance spectra from transmitted intensity spectra,” Opt Express 27(19), 26893–26909, 2019. doi:10.1364/OE.27.026893
  17. SJ Grauer, J Emmert, ST Sanders, S Wagner, and KJ Daun, “Multiparameter gas sensing with linear hyperspectral absorption tomography,” Meas Sci Technol 30(10), 105401, 2019. doi:10.1088/1361-6501/ab274b
  18. SJ Grauer, A Unterberger, A Rittler, KJ Daun, AM Kempf, and K Mohri, “Instantaneous 3D flame imaging by background-oriented schlieren tomography,” Combust Flame 196, 284–299, 2018. doi:10.1016/j.combustflame.2018.06.022
  19. TA Sipkens, PJ Hadwin, SJ Grauer, and KJ Daun, “Predicting the heat of vaporization of iron at high temperatures using time-resolved laser-induced incandescence and Bayesian model selection,” J Appl Phys 123(9), 095103, 2018. doi:10.1063/1.5016341
  20. SJ Grauer, BC Conrad, RB Miguel, and KJ Daun, “Gaussian model for emission rate measurement of a heated plume using hyperspectral data,” J Quant Spectrosc Radiat Transfer 206, 125–134, 2018. doi:10.1016/j.jqsrt.2017.11.005
  21. TA Sipkens, PJ Hadwin, SJ Grauer, and KJ Daun, “General error model for analysis of laser-induced incandescence signals,” Appl Opt 56(30), 8436–8445, 2017. doi:10.1364/AO.56.008436
  22. SJ Grauer, PJ Hadwin, TA Sipkens, KJ Daun, “Measurement-based meshing, basis selection, and prior assignment in chemical species tomography,” Opt Express 25(21), 25135–2514, 2017. doi:10.1364/OE.25.025135
  23. SJ Grauer, RW Tsang, and KJ Daun, “Broadband chemical species tomography: Measurement theory and a proof-of-concept emission detection experiment,” J Quant Spectrosc Radiat Transfer 198, 145–154, 2017. doi:10.1016/j.jqsrt.2017.04.030
  24. SJ Grauer, PJ Hadwin, and KJ Daun, “Improving chemical species tomography of turbulent flows using covariance estimation,” Appl Opt 56(13), 3900–3912, 2017. doi:10.1364/AO.56.003900
  25. SJ Grauer, PJ Hadwin, and KJ Daun, “Bayesian approach to the design of chemical species tomography experiments,” Appl Opt 55(21), 5772–5782, 2016. doi:10.1364/AO.55.005772
  26. KJ Daun, SJ Grauer, and PJ Hadwin, “Chemical species tomography of turbulent flows: Discrete ill-posed and rank deficient problems and the use of prior information,” J Quant Spectrosc Radiat Transfer 172, 58–74, 2016. doi:10.1016/j.jqsrt.2015.09.011
  27. SJ Grauer, EJFR Caron, NL Chester, MA Wells, and KJ Daun, “Investigation of melting in the Al–Si coating of a boron steel sheet by differential scanning calorimetry,” J Mater Process Technol 216, 89–94, 2015. doi:10.1016/j.jmatprotec.2014.09.001


  1. K Zhou and SJ Grauer, “Flow reconstruction and particle characterization from inertial Lagrangian tracks,” arXiv preprint, 2311.09076, 2023. doi:10.48550/arXiv.2311.09076


Coming soon.


Bowling, Spring 2024

Photo of Grauer Lab


Personal research profiles

Affiliated research links