David Sondak
About Me
I am a Research and Development Software Engineer in the Physics Theory and Modeling group at Dassault Systèmes Simulia Corp. Prior to this, I was a Lecturer in Computational Science in the Institute for Applied Computational Science (IACS) at Harvard University where I conducted research and taught classes. My research is at the intersection of applied mathematics, physics, and machine learning with an emphasis on fluid mechanics and multiscale phenomena. At IACS, I taught classes on basic software principles (CS207), high performance computing (CS205, AC290r), and fluid mechanics (ES123). I also led a version of the capstone course (AC297r) which requires students to work closely with industrial and academic partners to solve real-world problems.
Research Projects
Multiscale Physical Systems
Multiscale phenomena are common in everyday life and engineering systems. Fluid systems in particular exhibit multiple spatial and temporal scales. The quintessential example of a multiscale phenomenon in fluid mechanics is turbulence --- the disordered, seemingly random, motion of a fast-moving fluid. Much of my research in this area has focused on developing turbulence models for a variety of fluid systems including Rayleigh-Bénard convection and magnetohydrodynamics. I have also found exact coherent structures in Rayleigh-Bénard convection that optimize heat transport and provide an upper bound on the actual turbulent heat transport. Ongoing research aims to find the signature of these optimal solutions in actual turbulent flows. The emerging field of machine learning is a good candidate to search for such solutions. An aim of my future research is to apply and extend these models to complex physical systems including geophysical flows (e.g. magnetoconvection).
Relevant publications
- Coherent Solutions and Transition to Turbulence in Two-Dimensional Rayleigh-Bénard Convection, P. Kooloth, D.Sondak, L.M.Smith, Physical Review Fluids, 6(1), 2021, doi: https://doi.org/10.1103/PhysRevFluids.6.013501; Editors' Suggestion
- High Rayleigh number variational multiscale large eddy simulations of Rayleigh-Bénard Convection, D.Sondak, T.M.Smith, R.P.Pawlowski, S.Conde, J.N.Shadid, Mechanics Research Communications, 2020, https://doi.org/10.1016/j.mechrescom.2020.103614
- The effect of Prandtl number on optimal scaling laws in Rayleigh-Bénard convection, D.Sondak, F.Waleffe, L.M.Smith, Journal of Fluid Mechanics, 784, 565-595, 2015
- A new class of finite element variational multiscale turbulence models for incompressible magnetohydrodynamics, D.Sondak, J.N.Shadid, A.A.Oberai, R.P.Pawlowski, E.C.Cyr, T.M.Smith, Journal of Computational Physics, 295, 596-616, 2015
- A residual-based eddy viscosity model for the large eddy simulation of turbulent flows, A.A. Oberai, J. Liu, D. Sondak, T.J.R. Hughes, Computer Methods in Applied Mechanics and Engineering, 282, 54-70, 2014
- LES models for incompressible magnetohydrodynamics derived from the variational multiscale formulation, D. Sondak and A.A. Oberai, Physics of Plasmas, 19(10), 102308, 2012.
- Application of the variational Germano identity to the variational multiscale formulation, A.A. Oberai and D. Sondak, International Journal for Numerical Methods in Biomedical Engineering, 27(2), 335-344, 2011.
Data-Driven Modeling and Machine Learning
At the heart of research in multiscale phenomena and fluid mechanics is the desire to find reliable, reduced models that can be used to make predictions of scientific and engineering interest. New statistical algorithms emerging from the machine learning community provide a new perspective on developing turbulence models. Developing new machine learning models provides an avenue to perform computations with data and understand the effects of uncertainties in models and their prediction. My primary focus in this area has been on how to build physics into data-driven algorithms. This approach has the benefit of leading to more reliable predictions in parameter regimes for which data is unavailable and better-performing algorithms.
Relevant publications
- Finding Multiple Solutions of ODEs with Neural Networks, M.Di Giovanni, D.Sondak, P.Protopapas, M.Brambilla, Association for the Advancement of Artificial Intelligence Symposium on Machine Learning with Physics Sciences, 2020
- Neural Network Models for the Anisotropic Reynolds Stress Tensor in Turbulent Channel Flow, R.Fang, D.Sondak, P.Protopapas, S.Succi, Journal of Turbulence, 1-19, 2019, doi: 10.1080/14685248.2019.1706742
- Physical Symmetries Embedded in Neural Networks, M. Mattheakis, P. Protopapas, D.Sondak, M. Di Giovanni, E. Kaxiras, arXiv:1904.08991, 2019
- An Inadequacy Formulation for an Uncertain Flamelet Model, D.Sondak, T.Oliver, C.Simmons, R.D.Moser, 19th AIAA Non-Deterministic Approaches Conference, 2017
Other Projects and Collaborations
I genuinly enjoy collaborating with researchers from outside my traditional field of expertise. It is a fun challenge to bring my domain knowledge to bear on interesting research areas to see what new things can be uncovered together.
Relevant publications
- Can phoretic particles swim in two dimensions?, D.Sondak, C.Hawley, S.Heng, R.Vinsonhaler, E.Lauga, J.-L. Thiffeault, Physical Review E, 94, 062606, 2016
- Remediation of time-delay effects in tokamak axisymmetric control loops by optimal tuning and robust predictor augmentation, D.Sondak, R.Arastoo, E. Schuster, M.L.Walker, Fusion Engineering and Design, 86(6), 1112–1115, 2011.
- Optimal Tuning of Tokamak Plasma Equilibrium Controllers in the Presence of Time Delays, E. Schuster, D. Sondak, R. Arastoo, M. L. Walker and D. A. Humphreys, Proceedings of the 3rd IEEE Multi-conference on Systems and Control, Saint Petersburg, Russia, July 8-10, 2009.
Teaching
Harvard
CS107/AC207: Systems Development for Computational Science --- Fall 2017, 2018, 2019, 2020
ES123: Introduction to Fluid Mechanics and Transport Processes --- Spring 2020
CS205: Computing Foundations of Computational Science --- Spring 2018, 2020
AC290: Extreme Computing --- Spring 2019
AC297r: Computational Science and Engineering Capstone --- Spring 2019
University of Wisconsin - Madison
MATH 322: Applied Mathematical Analysis 2 --- Fall 2014, 2015
MATH 320: Linear Algebra and Differential Equations --- Fall 2013, Spring 2015
MATH 222: Calculus and Analytic Geometry 2 --- Spring 2014
Publications
In Preparation
- Physical Symmetries Embedded in Neural Networks, M. Mattheakis, P. Protopapas, D.Sondak, M. Di Giovanni, E. Kaxiras, arXiv:1904.08991, 2019
- Convergence properties of neural networks for solving differential equations, M.DiGiovanni, D.Sondak, P.Protopapas, M.Mattheakis
- Solving differential equations using neural network solution bundles, C.Flamant, P.Protopapas, D.Sondak
- Unsupervised learning of solution to differential equations with generative adversarial networks, D.Randle, P.Protopapas, D.Sondak
- Uncertainty quantification of neural network-based Reynolds averaged Navier Stokes models, X.Zhou, D.Sondak, C.Garraffo, P.Protopapas
Journal Papers
- Learning a reduced basis of dynamical systems using an autoencoder, D.Sondak, P.Protopapas, Phys. Rev. E 104, 034202, 2021, doi: https://doi.org/10.1103/PhysRevE.104.034202
- Port-Hamiltonian Neural Networks for Learning Explicit Time-Dependent Dynamical Systems, S.Desai, M.Mattheakis, D.Sondak, P.Protopapas, S.Roberts, arXiv:2107.08024
- Convolutional Neural Network Models and Interpretability for the Anisotropic Reynolds Stress Tensor in Turbulent One-dimensional Flows, H.Ocáriz Borde, D.Sondak, P.Protopapas, arXiv:2106.15757
- Coherent Solutions and Transition to Turbulence in Two-Dimensional Rayleigh-Bénard Convection, P. Kooloth, D.Sondak, L.M.Smith, Physical Review Fluids, 6(1), 2021, doi: https://doi.org/10.1103/PhysRevFluids.6.013501; Editors' Suggestion
- High Rayleigh number variational multiscale large eddy simulations of Rayleigh-Bénard Convection, D.Sondak, T.M.Smith, S.Conde, R.Pawlowski, J.N.Shadid, Mechanics Research Communications, (2020), https://doi.org/10.1016/j.mechrescom.2020.103614
- NeuroDiffEq: A Python package for solving differential equations with neural networks, F.Chen, D.Sondak, P.Protopapas, M.Mattheakis, S.Liu, D.Agarwal, M.DiGiovanni, Journal of Open Source Software, 5(46), 1931, 2020
- Neural Network Models for the Anisotropic Reynolds Stress Tensor in Turbulent Channel Flow, R.Fang, D.Sondak, P.Protopapas, S.Succi, Journal of Turbulence, 1-19, 2019, doi: 10.1080/14685248.2019.1706742
- Can phoretic particles swim in two dimensions?, D.Sondak, C.Hawley, S.Heng, R.Vinsonhaler, E.Lauga, J.-L. Thiffeault, Physical Review E, 94, 062606, 2016
- The effect of Prandtl number on optimal scaling laws in Rayleigh-Bénard convection, D.Sondak, F.Waleffe, L.M.Smith, Journal of Fluid Mechanics, 784, 565-595, 2015
- A new class of finite element variational multiscale turbulence models for incompressible magnetohydrodynamics, D.Sondak, J.N.Shadid, A.A.Oberai, R.P.Pawlowski, E.C.Cyr, T.M.Smith, Journal of Computational Physics, 295, 596-616, 2015
- A residual-based eddy viscosity model for the large eddy simulation of turbulent flows, A.A. Oberai, J. Liu, D. Sondak, T.J.R. Hughes, Computer Methods in Applied Mechanics and Engineering, 282, 54-70, 2014
- LES models for incompressible magnetohydrodynamics derived from the variational multiscale formulation, D. Sondak and A.A. Oberai, Physics of Plasmas, 19(10), 102308, 2012.
- Remediation of time-delay effects in tokamak axisymmetric control loops by optimal tuning and robust predictor augmentation, D.Sondak, R.Arastoo, E. Schuster, M.L.Walker, Fusion Engineering and Design, 86(6), 1112–1115, 2011.
- Application of the variational Germano identity to the variational multiscale formulation, A.A. Oberai and D. Sondak, International Journal for Numerical Methods in Biomedical Engineering, 27(2), 335-344, 2011.
- Optimal Tuning of Tokamak Plasma Equilibrium Controllers in the Presence of Time Delays, E. Schuster, D. Sondak, R. Arastoo, M. L. Walker and D. A. Humphreys, Proceedings of the 3rd IEEE Multi-conference on Systems and Control, Saint Petersburg, Russia, July 8-10, 2009.
Peer-reviewed Conference Proceedings
- Finding Multiple Solutions of ODEs with Neural Networks, M.Di Giovanni, D.Sondak, P.Protopapas, M.Brambilla, Association for the Advancement of Artificial Intelligence Symposium on Machine Learning with Physics Sciences, 2020
- An Inadequacy Formulation for an Uncertain Flamelet Model, D.Sondak, T.Oliver, C.Simmons, R.D.Moser, 19th AIAA Non-Deterministic Approaches Conference, 2017