Harbir Antil

Articles in Review

  1. H. Antil, R. Lohner and R. Price
    Data Assimilation with Deep Neural Nets Informed by Nudging.
    Submitted 2021.

  2. H. Antil, S. Dolgov and A. Onwunta
    TTRISK: Tensor Train Decomposition Algorithm for Risk Averse Optimization.
    Submitted 2021. arxiv

  3. H. Antil, C.G. Gal and M. Warma
    A Unified Framework for Optimal Control of Fractional in Time Subdiffusive Semilinear PDEs.
    Submitted 2021. arxiv

  4. H. Antil and H. Diaz
    Boundary Control of Time-Harmonic Eddy Current Equations.
    Submitted 2021.

  5. H. Antil, T.S Brown, R. Loehner, F. Togashi, and D. Verma
    Deep Neural Nets with Fixed Bias Configuration.
    Submitted 2021. arxiv

  6. H. Antil, S. Kubota, K. Shirakawa, and N. Yamazaki
    Temperature Control of PDE Constrained Optimization Problems Governed by Kobayashi-Warren-Carter Type Models of Grain Boundary Motions.
    Submitted 2021. arxiv

  7. H. Antil, A.N. Ceretani, and C.N. Rautenberg.
    The Spatially Variant Fractional Laplacian.
    Submitted 2021. arxiv

  8. T Shi, H. Antil, and D.P. Kouri.
    Spectral, Tensor and Domain Decomposition Methods for Fractional PDEs.
    Submitted 2021.

  9. H. Antil, S. Bartels, and A. Schikorra.
    Approximation of Fractional Harmonic Maps.
    Submitted 2021. arxiv

  10. M. Panagoda, T. Berry, and H. Antil.
    Convergence Analysis of the Rank Restricted Soft SVD Algorithm.
    Submitted 2021. arxiv

  11. H. Antil, Hugo Diaz-Norambuena, and T.N.T. Quyen.
    Optimal Control of Parameterized Maxwell's System: Reduced Basis, Convergence Analysis, and A Posteriori Error Estimates.
    Submitted 2021.

  12. H. Antil, H.C. Elman, A. Onwunta, D. Verma.
    Novel Deep Neural Networks for Solving Bayesian Statistical Inverse Problems.
    Submitted 2021. arxiv

  13. H. Antil, R. Arndt, C.N. Rautenberg and D. Verma.
    Non-Diffusive Variational Problems with Distributional and Weak Gradient Constraints.
    Submitted 2021.

  14. H. Antil, D.P. Kouri, and D. Ridzal.
    An Augmented Lagrangian Equality-constrained SQP Method for Optimization with General Constraints.
    Submitted 2021. Preprint

  15. S. Hardesty, H. Antil, D.P. Kouri and D. Ridzal.
    The Strip Method for Shape Derivatives.
    Submitted 2020. preprint

  16. R. Vaughn, T. Berry, H. Antil
    Diffusion Maps for Embedded Manifolds with Boundary with Applications to PDEs.
    Submitted 2020. arxiv

  17. H. Antil, U. Biccari, R. Ponce, M. Warma, and S. Zamorano
    Controllability properties from the exterior under positivity constraints for a 1--D fractional heat equation.
    Submitted 2019. arxiv

  18. H. Antil, C. Lizama, R. Ponce, and M. Warma
    Convergence of solutions of discrete semi-linear space-time fractional evolution equations.
    Submitted 2019. arxiv

  19. Z. Zou , S. Mukherjee, H. Antil, and W. Aquino
    Adaptive particle-based approximations of the Gibbs posterior for inverse problems.
    Submitted 2019. arxiv

Book

  1. H. Antil, Drew Kouri, Martin Lacasse, and Denis Ridzal.
    Frontiers in PDE-constrained Optimization.
    The IMA Volumes in Mathematics and its Applications, Springer 2018. Link

    Book Review. SIAM Review. Volume 61, Issue 4, pp. 903. Year, 2019. Link

Published Articles

2021
  1. H. Antil, T.S. Brown, R. Khatri, A. Onwunta, D. Verma, and M. Warma
    Optimal Control, Numerics, and Applications of Fractional PDEs.
    Accepted in Handbook of Numerical Analysis. arxiv

  2. R. Loehner and H. Antil.
    High-Fidelity Simulation of Pathogen Propagation, Transmission, and Mitigation.
    SIAM News, Volume 54, Number 6. July/August 2021. Link

  3. H. Antil, T.S. Brown, D. Verma and M. Warma.
    Optimal Control of Fractional PDEs with State and Control Constraints.
    Accepted in Pure and Applied Functional Analysis, 2021.

  4. R. Lohner, H. Antil, A. Srinivasan, S. Idelsohn, and E. Onate.
    High Fidelity Simulation of Pathogen Propagation, Transmission and Mitigation in the Built Environment.
    Accepted in Archives of Computational Methods in Engineering. 2021.

  5. T.S. Brown, H. Antil, R. Lohner, F. Togashi, and D. Verma.
    Novel DNNs for Stiff ODEs with Applications to Chemically Reacting Flows.
    Accepted in Computational Fluid Dynamics Simulations and Analysis (CFDML) 2021. arxiv

  6. H. Antil, P. Dondl, and L. Striet.
    Approximation of Integral Fractional Laplacian and Fractional PDEs via sinc-Basis.
    Accepted in SIAM Journal of Scientific Computing 2021. arXiv

  7. H. Antil, T. Berry, and J. Harlim.
    Fractional Diffusion Maps.
    Accepted in Applied and Computational Harmonic Analysis 2021. arxiv

  8. H. Antil, C.N. Rautenberg, and A. Schikorra.
    On a Fractional Version of a Murat Compactness Result and Applications.
    Accepted in SIAM Journal on Mathematical Analysis, 2021. arxiv

  9. C. Glusa, H. Antil, M. D'Elia, B van Bloemen Waanders, and C.J. Weiss
    A fast solver for the fractional Helmholtz equation.
    Accepted in SIAM Journal of Scientific Computing 2021. preprint

  10. H. Antil, D.P. Kouri, and J. Pfefferer.
    Risk-Averse Control of Fractional Diffusion with Uncertain Exponent.
    Accepted in SIAM Journal of Control and Optimization 2021.

  11. H. Dinh, H. Antil, Y. Chen, E. Cherkaev, and A. Narayan
    Model reduction for fractional elliptic problems using the Kato's formula.
    Accepted in Mathematical Control & Related Fields 2021. arxiv

  12. H. Antil, A. Draganescu and K. Green.
    A Note on Multigrid Preconditioning for Fractional PDE-Constrained Optimization Problems.
    Accepted in Results in Applied Mathematics, 2021. arxiv

2020
  1. H. Antil.
    Role of Fractional Operators in Inverse Problems.
    Mathematisches Forschungsinstitut Oberwolfach (2020). Report No. 39/2020. DOI: 10.4171/OWR/2020/39

  2. H. Antil.
    Fractional Operators: Analysis, Control, and Applications.
    Mathematisches Forschungsinstitut Oberwolfach (2020). Report No. 37/2020. DOI: 10.4171/OWR/2020/37

  3. R. Loehner, H. Antil, H.R. Tamaddon-Jahromi, N.K. Chakshu, P. Nithiarasu.
    Deep Learning or Interpolation for Inverse Modeling of Heat and Fluid Flow Problems.
    Accepted in International Journal of Numerical Methods for Heat and Fluid Flow. 2020.

  4. R. Loehner and H. Antil.
    High Fidelity Modeling of Aerosol Pathogen Propagation in Built Enviornments with Moving Pedestrians.
    Accepted in International Journal for Numerical Methods in Biomedical Engineering, 2020. arXiv

  5. R. Lohner, H. Antil, S. Idelsohn, and E. Onate.
    Detailed Simulation of Viral Propagation In The Built Environment.
    Computational Mechanics. 2020. DOI: https://doi.org/10.1007/s00466-020-01881-7. arxiv

  6. H. Antil, R. Khatri, R. Loehner, and D. Verma.
    Fractional Deep Neural Network via Constrained Optimization.
    Accepted in Machine Learning: Science and Technology 2020. arxiv

  7. H. Antil, S. Kubota, K. Shirakawa, and N. Yamazaki
    Optimal Control Problems Governed by 1-D Kobayashi-Warren-Carter Type Systems.
    Accepted in Mathematical Control & Related Fields, 2020. arxiv

  8. H. Antil, D. Verma, and M. Warma
    Optimal Control of Fractional Elliptic PDEs with State Constraints and Characterization of the dual of Fractional Order Sobolev Spaces.
    Accepted in Journal of Optimization Theory and Applications (JOTA) 2020. arxiv

  9. H. Antil, Z. (Wendy) Di, and R. Khatri
    Bilevel optimization, deep learning and fractional Laplacian with applications in tomography.
    Inverse Problems, 36 - 064001 (22pp), (2020). arxiv

  10. R. Lohner and H. Antil
    Revisiting Calderon's Problem.
    International Journal of Numerical Methods for Heat and Fluid Flow. 2020.
    DOI: https://doi.org/10.1108/HFF-12-2019-0931. arxiv

  11. H. Antil, D. Verma, and M. Warma.
    External optimal control of fractional parabolic PDEs.
    ESAIM: Control, Optimisation and Calculus of Variations (CoCV), Volume: 26, Article Number: 20, Pages: 33, Year: 2020. arxiv

  12. C.J. Weiss, B.G. van Bloemen Waanders, and H. Antil.
    Fractional Operators Applied to Geophysical Electromagnetics.
    Geophysical Journal International, 220(2), 1242-1259, 2020. arxiv

  13. H. Antil and M. Warma.
    Optimal control of fractional semilinear PDEs.
    ESAIM: Control, Optimisation and Calculus of Variations (ESAIM: COCV), Volume: 26, Article Number : 5, Pages: 30. 2020. arxiv

2019
  1. H. Antil, Y. Chen, and A. Narayan.
    Reduced basis methods for fractional Laplace equations via extension.
    SIAM J. of Sci. Computing 41(6), pp. A3552-A3575, 2019. arxiv

  2. H. Antil, T. Brown, and F.J. Sayas.
    A problem in control of elastodynamics with piezoelectric effects.
    DOI: https://doi.org/10.1093/imanum/drz047. IMA Journal of Numerical Analysis, 2019. arxiv

  3. H. Antil and C.N. Rautenberg.
    Sobolev spaces with non-Muckenhoupt weights, fractional elliptic operators, and applications.
    SIAM Journal on Mathematical Analysis 51(3), 2479-2503, 2019. arxiv

  4. H. Antil, R. Khatri, and M. Warma.
    External optimal control of nonlocal PDEs.
    Inverse Problems 35(8) 2019. arxiv

  5. H. Antil and M. Warma.
    Optimal control of the coefficient for regional fractional p-Laplace equation: Approximation and convergence.
    Mathematical Control & Related Fields, 9(1), pp 1-38, 2019. arxiv
    Among the 10 most downloaded article in this journal. Years 2018-19.

  6. A. Hazra, V. Maggioni, P. Houser, H. Antil and M. Noonan.
    A monte carlo-based multi-objective optimization approach to merge different precipitation estimates for land surface modeling.
    Journal of Hydrology 570, 454--462, 2019.

2018
  1. H. Antil, K. Shirakawa, and N. Yamazaki.
    A class of parabolic systems associated with optimal control of grain boundary motions.
    Advances in Mathematical Sciences and Applications 27 (2), 299--336, 2018. arxiv

  2. H. Antil, J. Pfefferer, and S. Rogovs.
    Fractional operators with inhomogeneous boundary bonditions: analysis, control, and discretization.
    Communications in Mathematical Sciences (CMS) 16 (5), 1395--1426, 2018. arxiv

  3. H. Antil, R. H. Nochetto, and P. Venegas.
    Controlling the Kelvin force: Basic Strategies and Applications to Magnetic Drug Targeting.
    Optimization and Engineering, 19 (3), 559--589, 2018. arxiv

  4. H. Antil, D. Chen, and S. E. Field.
    A Note on QR-Based Model Reduction: Algorithm, Software, and Gravitational Wave Applications.
    Computing in Science and Engineering 19 (3), 2018. arxiv

  5. H. Antil, E. Otarola, and A. J. Salgado.
    Optimization with respect to order in a fractional diffusion model: analysis, approximation and algorithmic aspects
    Journal of Scientific Computing, 77 (1), 204--224, 2018. Published version

  6. H. Antil and M. Warma.
    Optimal control of the coefficient for fractional p-Laplace equation: Approximation and convergence.
    RIMS Kokyuroku, 2090, 102--116, 2018.

  7. H. Antil and D. Leykekhman.
    A brief introduction to PDE constrained optimization.
    The IMA Volumes in Mathematics and its Applications, 3--40, Springer (2018).

  8. H. Antil, and C. N. Rautenberg.
    Fractional elliptic quasi-variational inequalities: theory and numerics.
    Interface and Free Boundaries 20 (1), 1--24, 2018. arxiv

  9. H. Antil, R. H. Nochetto, and P. Venegas.
    Optimizing the Kelvin Force in a Moving Target Subdomain.
    Math. Models Methods Appl. Sci. (M3AS) 28 (1), 195--130, 2018. arxiv

  10. H. Antil, and S. W. Walker.
    Optimal Control of a Degenerate PDE for Surface Shape.
    DOI: 10.1007/s00245-017-9407-3. Appl. Math. Optim. 78 (2), 297--328, 2018 link

2017
  1. H. Antil, E. Otarola, and A. J. Salgado.
    Some applications of weighted norm inequalities to the analysis of optimal control problems.
    DOI: https://doi.org/10.1093/imanum/drx018. IMA Journal of Numerical Analysis, 38 (1), 852--883, 2017. arxiv

  2. H. Antil, and E. Otarola.
    An a posteriori error analysis for an optimal control problem involving the fractional Laplacian.
    DOI: https://doi.org/10.1093/imanum/drx005. IMA Journal of Numerical Analysis 38 (1), 198--226, (2017). arxiv

  3. H. Antil and J. Pfefferer.
    A short Matlab implementation of fractional Poisson equation with nonzero boundary conditions.
    Technical Report 2017. Technical Report and Code

  4. H. Antil and S. Bartels.
    Spectral approximation of fractional PDEs in image processing and phase field modeling.
    DOI: https://doi.org/10.1515/cmam-2017-0039. Computational Methods in Applied Mathematics 17 (4) (2017) arxiv

  5. H. Antil, J. Pfefferer, and M. Warma.
    A note on semilinear fractional elliptic equation: analysis and discretization.
    DOI: https://doi.org/10.1051/m2an/2017023. Math. Model. Numer. Anal. (ESAIM: M2AN) 51 (6) (2017). arxiv

  6. H. Antil, and C. N. Rautenberg.
    A Numerical Method for Fractional Elliptic Quasi-Variational Inequalities
    Mathematisches Forschungsinstitut Oberwolfach, Report, 2017. link

  7. H. Antil, M. Heinkenschloss, and S. Hardesty.
    Shape Optimization of Shell Structure Acoustics.
    SIAM J. Control Optim. 55 (3), 1347--1376, 2017.

  8. H. Antil, M. Heinkenschloss, and S. Hardesty.
    Supplementary Materials: Shape Optimization of Shell Structure Acoustics.
    Department of Computational and Applied Mathematics, Rice University (2017). Technical Report

  9. H. Antil, M. Hintermueller, R. H. Nochetto, T. M. Surowiec and D. Wegner.
    Finite Horizon Model Predictive Control of Electrowetting on Dielectric with Pinning.
    Interface and Free Boundaries 19 (1), 1-30, 2017.

  10. K. Carlberg, M. Barone, and H. Antil.
    Galerkin v. discrete-optimal projection in nonlinear model reduction.
    Journal of Computational Physics, 330, 693-734, 2017. arxiv

2016
  1. H. Antil, E. Otarola, and A. J. Salgado.
    A fractional space-time optimal control problem: analysis and discretization.
    SIAM Journal of Control and Optimization, 54(3), 1295-1328, 2016. arxiv

  2. H. Antil, and A. J. Salgado.
    Approximation of elliptic equations with BMO coefficients.
    IMA Journal of Numerical Analysis, 36(1), 222-237, 2016. arxiv

2015
  1. H. Antil, R. H. Nochetto, and P. Sodré.
    The Stokes problem with Navier slip boundary condition: Minimal fractional Sobolev regularity of the domain.
    Technical Report. arxiv

  2. H. Antil, and E. Otarola.
    A FEM for an optimal control problem of fractional powers of elliptic operators.
    SIAM Journal of Control and Optimization, 53(6), 3432-3456, 2015. arxiv

  3. H. Antil, R. H. Nochetto, and P. Sodré.
    Optimal Control of a Free Boundary Problem with Surface Tension Effects: A Priori Error Analysis.
    SIAM J. Numer. Anal. 53, no. 5, 2279-2306, (2015). arxiv

2014
  1. H. Antil, R. H. Nochetto, and P. Sodré.
    Optimal Control of a Free Boundary Problem: Analysis with Second Order Sufficient Conditions.
    SIAM Journal of Control and Optimization (2014), 52(5):2771--2799. arxiv

  2. H. Antil, M. Heinkenschloss, and D. C. Sorensen.
    Application of Discrete Empirical Interpolation Method to Reduced Order Modeling of Nonlinear and Parametric Systems.
    A. Quarteroni and G. Rozzas (eds.), Reduced Order Methods for Modeling and Computational Reduction, Model. Simul.& Appl. Vol. 9, 2014, pp. 101-136, Springer Italia, Milan.
2013
  1. H. Antil, S. Field, F. Herrmann, R. H. Nochetto, and M. Tiglio.
    Two-step Greedy Algorithm for Reduced Order Quadratures.
    Journal of Scientific Computing, 57:604--637, 2013. arxiv
    Reduced Order Quadrature (ROQ) is now part of software package FINESSE used at LIGO. link
    Relevant article: D. Brown, R. Smith, A. Freise (2015) link
2012
  1. H. Antil.
    Optimal Control of a Free Boundary Problem with Surface Tension Effects (2012).
    Mathematisches Forschungsinstitut Oberwolfach, Report No. 57/2012, DOI: 10.4171/OWR/2012/57. link
  2. H. Antil, M. Heinkenschloss, R.H.W. Hoppe, C. Linsenmann, and A. Wixforth.
    Reduced Order Modeling Based Shape Optimization of Surface Acoustic Wave Driven Microfluidic Biochips.
    Mathematics and Computers in Simulation (2012). link
2011
  1. H. Antil, R.H.W. Hoppe, C. Linsenmann, and A. Wixforth.
    Multiscale Aspects in Modeling and Simulation of Surface Acoustic Wave Driven Microfluidic Biochips .
    E-Book Series: Progress in Computational Physics (PiCP) (2011), Volume 2, Bentham Science Publishers. link
  2. H. Antil, M. Heinkenschloss, and R.H.W. Hoppe.
    Domain decomposition and balanced truncation model reduction for shape optimization of the Stokes system.
    Optimization Methods and Software (2011), 26(4-5):643--669. preprint
    Most cited article in this journal. Years 2012-13.
2010
  1. H. Antil, M. Heinkenschloss, R.H.W. Hoppe, and D.C. Sorensen.
    Domain decomposition and model reduction for the numerical solution of PDE constrained optimization problems with localized optimization variables .
    Computing and Visualization in Science (2010), 13(6):249--264. link
  2. H. Antil, R. Glowinski, R.H.W. Hoppe, and C. Linsenmann, T.-W. Pan, and A. Wixforth.
    Modeling, Simulation, and Optimization of Surface Acoustic Wave Driven Microfluidic Biochips .
    Journal of Computational Mathematics (2010), 28(2):149--169. link
2009
  1. H. Antil.
    Shape Optimization Governed by the Heat and the Stokes Equations Using Domain Decomposition and Model Reduction (2009).
    Mathematisches Forschungsinstitut Oberwolfach, Report No. 04/2009, DOI: 10.4171/OWR/2009/04. link
  2. H. Antil, R. H.W. Hoppe, and C. Linsenmann.
    Adaptive Multilevel Interior Point Methods in PDE Constrained Optimization.
    Proc. Int. Conf. on Domain Decomposition Methods and Applications XVIII (M. Bercovier et al.; eds.), Lecture Notes in Computer Science and Engineering (2009), 70:15-26, Springer, Berlin-Heidelberg-New York.
2008
  1. H. Antil, R. H.W. Hoppe, and C. Linsenmann.
    Optimal design of stationary flow problems by path-following interior-point.
    Control and Cybernetics (2008) 37(4):771-796. preprint
  2. H. Antil, R. H.W. Hoppe, and C. Linsenmann.
    Adaptive Path-following Primal-Dual Interior Point Methods for Shape Optimization of Linear and Nonlinear Stokes Flow Problems.
    Lecture Notes in Computer Science (2008), 4818:259-266, Springer, Berlin-Heidelberg-New York.
  3. H. Antil , A. Gantner, R. H.W. Hoppe, D. Koster, K.G. Siebert and A. Wixforth.
    Modeling and Simulation of Piezoelectrically Agitated Acoustic Streaming on Microfluidic Biochips.
    Proc. 17th Int. Conf. on Domain Decomposition Methods (Langer, U. et al.; eds.), Lecture Notes in Computational Science and Engineering (2008), 60:305-312, Springer; Berlin Heidelberg-New York.
2007
  1. H. Antil , R. H.W. Hoppe, and C. Linsenmann.
    Path-following primal-dual interior-point methods for shape optimization of stationary flow problems.
    Journal of Numerical Mathematics (2007) 15(2):81-100. preprint

Others


  1. H. Antil.
    Optimization and Model Reduction of Time Dependent PDE-Constrained Optimization Problems: Applications to Acoustic Wave Driven Microfluidic Biochips.
    PhD Dissertation, Department of Mathematics, University of Houston (2009). online version