Publications

If you have questions regarding the publications, please feel free to contact me. Gooogle scholar page

Submitted Articles

[S8]  [new] Rank-Minimizing and Structured Model Inference
Pawan Goyal, Benjamin Peherstorfer, and Peter Benner
arXiv Preprint arXiv:2302.09521, Feb 2023.
@TechReport{morGoyPB23,
author = {Goyal, P., Peherstorfer, B., and Benner, P.},
title = {Rank-Minimizing and Structured Model Inference },
institution = {arXiv},
year = 2023,
type = {e-prints},
number = {2302.09521},
note = {stat.ML},
url = {https://arxiv.org/abs/2302.09521}
}
Please contact me for the code to generate the result of the paper.
[S7]  [new] Inference of Continuous Linear Systems from Data with Guaranteed Stability
Pawan Goyal, Igor Pontes Duff, and Peter Benner
arXiv Preprint arXiv:2301.10060, Jan 2023.
@TechReport{morGoyPB23,
author = {Goyal, P., Pontes Duff, I., and Benner, P.},
title = {Inference of Continuous Linear Systems from Data with Guaranteed Stability},
institution = {arXiv},
year = 2023,
type = {e-prints},
number = {2301.10060},
note = {math.LG},
url = {https://arxiv.org/abs/2301.10060}
}
[S6]  [new] Dominant Subspaces of High-Fidelity Nonlinear Structured Parametric Dynamical Systems and Model Reduction
Pawan Goyal, Igor Pontes Duff, and Peter Benner
arXiv Preprint arXiv:2301.09484, Jan 2023.
@TechReport{morGoyPB23,
author = {Goyal, P., Pontes Duff, I., and Benner, P.},
title = {Dominant Subspaces of High-Fidelity Nonlinear Structured Parametric Dynamical Systems and Model Reduction},
institution = {arXiv},
year = 2023,
type = {e-prints},
number = {2301.09484},
note = {math.NA},
url = {https://arxiv.org/abs/2301.09484}
}
Please contact me for the code to generate the result of the paper.
[S5] An Operator Inference Oriented Approach for Mechanical Systems
Yevgeniya Filanova, Igor Pontes Duff, Pawan Goyal, and Peter Benner
arXiv Preprint arXiv:2210.07710, Oct 2022.
@TechReport{morYevetal22,
author = {Yevgeniya Filanova, Igor Pontes Duff, Pawan Goyal, and Peter Benner},
title = {An Operator Inference Oriented Approach for Mechanical Systems},
institution = {arXiv},
year = 2022,
type = {e-print},
number = {2210.07710},
url = {https://arxiv.org/abs/2210.07710},
note = {math.DS}
}
[S4] Learning Low-Dimensional Quadratic-Embeddings of High-Fidelity Nonlinear Dynamics using Deep Learning
Pawan Goyal, and Peter Benner
arXiv Preprint arXiv:2111.12995, Nov 2021.
@TechReport{morGoyB21b,
author = {Goyal, P. and Benner, P.},
title = {Learning Low-Dimensional Quadratic-Embeddings of High-Fidelity Nonlinear Dynamics using Deep Learning},
institution = {arXiv},
year = 2021,
type = {e-print},
number = {2111.12995},
url = {https://arxiv.org/abs/2111.12995},
note = {cs.LG}
}
Codes can be found under the link .
[S3] LQResNet: A Deep Neural Network Architecture for Learning Dynamic Processes
Pawan Goyal, and Peter Benner
arXiv Preprint arXiv:2103.02249, Mar 2021.
@TechReport{LQResNet_GoyBen_21,
author = {Goyal, P. and Benner, P.},
title = {LQResNet: A Deep Neural Network Architecture for Learning Dynamic Processes},
institution = {arXiv},
year = 2021,
type = {e-prints},
number = {2103.02249},
note = {cs.LG},
url = {https://arxiv.org/abs/2103.02249}
}
Codes can be found under the link https://github.com/mpimd-csc/LQRes-Net.
[S2] Identification of Dominant Subspaces for Linear Structured Parametric Systems and Model Reduction
Peter Benner, Pawan Goyal, and Igor Pontes Duff
arXiv Preprint arXiv:1909.04597, Oct 2019.
In this paper, we discuss a novel model reduction framework for generalized linear systems. The transfer functions of these systems are assumed to have a special structure, e.g., coming from second-order linear systems and time-delay systems, and they may also have parameter dependencies. Firstly, we investigate the connection between classic interpolation-based model reduction methods with the reachability and observability subspaces of linear structured parametric systems. We show that if enough interpolation points are taken, the projection matrices of interpolation-based model reduction encode these subspaces. As a result, we are able to identify the dominant reachable and observable subspaces of the underlying system. Based on this, we propose a new model reduction algorithm combining these features leading to reduced-order systems. Furthermore, we pay special attention to computational aspects of the approach and discuss its applicability to a large-scale setting. We illustrate the efficiency of the proposed approach with several numerical large-scale benchmark examples.
@TechReport{morDuffGB19,
author = {Benner, P. and and Goyal, P. and Pontes Duff, I.},
title = {Identification of Dominant Subspaces for Linear Structured Parametric Systems and Model Reduction },
institution = {arXiv},
year = 2019,
type = {e-prints},
number = {1910.13945},
note = {math.NA},
url = {https://arxiv.org/abs/1910.13945}
}
Please contact me for the code to generate the result of the paper.
[S1] Balanced Truncation Model Order Reduction For Quadratic-Bilinear Control Systems
Peter Benner and Pawan Goyal
arXiv Preprint arXiv:1705.00160, April 2017.
We discuss balanced truncation model order reduction for large-scale quadratic-bilinear (QB) systems. Balanced truncation for linear systems mainly involves the computation of the Gramians of the system, namely reachability and observability Gramians. These Gramians are extended to a general nonlinear setting in Scherpen (1993), where it is shown that Gramians for nonlinear systems are the solutions of state-dependent nonlinear Hamilton-Jacobi equations. Therefore, they are not only difficult to compute for large-scale systems but also hard to utilize in the model reduction framework. In this paper, we propose algebraic Gramians for QB systems based on the underlying Volterra series representation of QB systems and their Hilbert adjoint systems. We then show their relations with a certain type of generalized quadratic Lyapunov equation. Furthermore, we present how these algebraic Gramians and energy functionals relate to each other. Moreover, we characterize the reachability and observability of QB systems based on the proposed algebraic Gramians. This allows us to find those states that are hard to control and hard to observe via an appropriate transformation based on the Gramians. Truncating such states yields reduced-order systems. Additionally, we present a truncated version of the Gramians for QB systems and discuss their advantages in the model reduction framework. We also investigate the Lyapunov stability of the reduced-order systems. We finally illustrate the efficiency of the proposed balancing-type model reduction for QB systems by means of various semi-discretized nonlinear partial differential equations and show its competitiveness with the existing moment-matching methods for QB systems.
@TechReport{morBenG17,
author = {Benner, P. and Goyal, P.},
title = {Balanced truncation model order reduction for
quadratic-bilinear systems},
institution = {arXiv},
year = 2017,
type = {e-prints},
number = {1705.00160},
note = {math.OC},
url = {https://arxiv.org/abs/1705.00160}
}
Please contact me for the code to generate the result of the paper.

Journal Articles

[J20]  [new] Neural ODEs for Irregular and Noisy Data
Pawan Goyal, and Peter Benner
Royal Society Open Science, 2023, to appear.
Preliminary version appeared as arXiv Preprint arXiv:2205.09479, May 2022.
@TechReport{morGoyB22,
author = {Goyal, P. and Benner, P.},
title = {Neural ODEs for Irregular and Noisy Data},
institution = {arXiv},
year = 2022,
type = {e-print},
number = {2205.09479},
url = {https://arxiv.org/abs/2205.09479},
note = {cs.LG}
}
[J19]  [new] An Artificial Neural Network for Surrogate Modeling of Stress Fields in Viscoplastic Polycrystalline Materials
Mohammad S. Khorrami, Jaber R. Mianroodi, Nima H. Siboni, Pawan Goyal, Bob Svendsen, Peter Benner, and Dierk Raabe
npj Computational Materials, Vol. 9, Issue 1, Art. 37, 10 pages, 2023.
DOI: 10.1038/s41524-023-00991-z
Preliminary version appeared as arXiv Preprint arXiv:2107.12950, Aug 2022.
@article{khorramietal_npj23,
author = {Mohammad S. Khorrami, Jaber R. Mianroodi, Nima H. Siboni, Pawan Goyal, Bob Svendsen, Peter Benner, and Dierk Raabe},
title = {An Artificial Neural Network for Surrogate Modeling of Stress Fields in Viscoplastic Polycrystalline Materials},
journal= {npj Computational Materials},
volume={9},
number={1},
pages={37},
year={2023},
}
[J18] Discovery of Nonlinear Dynamical Systems using a Runge-Kutta Inspired Dictionary-Based Sparse Regression Approach
Pawan Goyal, and Peter Benner
Proceedings of the Royal Society A, Vol. 478 (2262), p. 20210883, 2022.
DOI: 10.1098/rspa.2021.0883
Preliminary version appeared as arXiv Preprint arXiv:2105.04869, May 2021.
@Article{morGoyB22a,
author = {Goyal, P. and Benner, P.},
title = {Discovery of Nonlinear Dynamical Systems using a
{R}unge-{K}utta Inspired Dictionary-Based Sparse Regression
Approach},
journal = {Proc. Royal Society A: Mathematical, Physical and Engineering Sciences},
volume = {478},
number={2262},
pages = {20210883},
year = 2022,
doi = {10.1098/rspa.2021.0883}
}
Codes can be found under the link https://github.com/mpimd-csc/RK4-SinDy.
[J17] A Greedy Data Collection Scheme For Linear Dynamical Systems
Karim Cherifi, Pawan Goyal, and Peter Benner
Data-Centric Engineering, Vol. 3, e16 (14 pages), 2022.
DOI: 10.1017/dce.2022.16
Preliminary version appeared as arXiv Preprint arXiv:2107.12950, Jul 2021.
@Article{morCheGB21,
author= {Cherifi, K. and Goyal, P. and Benner, P.},
title= {A Greedy Data Collection Scheme for Linear Dynamical Systems},
journal= {Data-Centric Engineering},
year= {2022},
volume= {3},
pages= {e16},
doi= {10.1017/dce.2022.16},
publisher= {Cambridge University Press}
}
Codes can be found under the link https://github.com/mpimd-csc/Greedy_Measurement_Scheme.
[J16] A Non-Intrusive Method to Inferring Linear Port-Hamiltonian Realizations using Time-Domain Data
Karim Cherifi, Pawan Goyal, and Peter Benner
Electronic Transactions on Numerical Analysis (Special Issue on Scientific Machine Learning), Vol. 56, pp. 102-116, 2022.
DOI: 10.1553/etna_vol56s102
Preliminary version appeared as arXiv Preprint arXiv:2005.09371, May 2020.
@article{morCheGB22a,
author = {Cherifi, K. and Goyal, P. and Benner, P.},
title = {A Non-Intrusive Method to Inferring Linear Port-Hamiltonian Realizations using Time-Domain Data},
journal = {Electron. Trans. Numer. Anal.},
note = Special Issue on Scientific Machine Learning, year = 2022,
volume = 56,
pages = {102--116},
url = {https://epub.oeaw.ac.at/?arp=0x003d2e16}
}
Please contact me for the code to generate the result of the paper.
[J15] Gramians, Energy Functionals and Balanced Truncation for Linear Dynamical Systems with Quadratic Outputs
Peter Benner, Pawan Goyal, and Igor Pontes Duff
IEEE Transactions on Automatic Control , Vol 67, Issue 2, pp. 886-893, 2022.
DOI: 10.1109/TAC.2021.3086319
Preliminary version appeared as arXiv Preprint arXiv:1909.04597, Sep 2019.
@article{morBenGPD21,
author = {Benner, P. and Goyal, P. and Pontes Duff, I.},
title = {Gramians, Energy Functionals and Balanced Truncation for Linear Dynamical Systems with Quadratic Outputs},
journal = {IEEE Trans. on Automatic Control},
year = 2021,
url = {https://ieeexplore.ieee.org/document/9446632}
}
Please contact me for the code to generate the result of the paper.
[J14] Operator Inference and Physics-Informed Learning of Low-Dimensional Models for Incompressible Flows
Peter Benner, Pawan Goyal, Jan Heiland, and Igor Pontes Duff
Electronic Transactions on Numerical Analysis (Special Issue on Scientific Machine Learning), Vol. 56, pp. 28-51, 2022.
Preliminary version appeared as arXiv Preprint arXiv:2010.06701, Oct 2020.
@article{morBenGHetal22,
author = {Benner, P. and Goyal, P. and Heiland, J. and Pontes Duff, I.},
title = {Operator Inference and Physics-Informed Learning of Low-Dimensional Models for Incompressible Flows },
journal = {Electron. Trans. Numer. Anal.},
note = Special Issue on Scientific Machine Learning, year = 2022,
volume = 56,
pages = {28--51},
url = {https://epub.oeaw.ac.at/?arp=0x003d183f}
}
Codes can be found under the link DOI:10.5281/zenodo.4086018.
[J13] Learning Reduced-order Dynamics for a Parametrized Shallow Water Equation
Süleyman Yildiz, Pawan Goyal, Peter Benner, and Bülent Karasözen
International Journal for Numerical Methods in Fluids, Vol. 93, Issue 8, pp. 2803-2821, 2021.
DOI: 10.1002/fld.4998
Preliminary version appeared as arXiv Preprint arXiv:2007.14079, Jul 2020.
@article{morYildGBetal21,
author = {Yildiz, S. and Goyal, P. and Benner, P. and Karasözen, B.},
title = {Learning Reduced-order Dynamics for a Parametrized Shallow Water Equation},
journal = {Internat. J. Numerical Methods in Fluids},
year = 2021,
volume = 93,
pages = {2803--2821},
url = {https://onlinelibrary.wiley.com/doi/10.1002/fld.4998}
}
Please contact me for the code to generate the result of the paper.
[J12] Tomographic X-ray Scattering based on Invariant Reconstruction - Analysis of the 3D Nanostructure of Bovine Bone
Paolino De Falco, Richard Weinkamer, Wolfgang Wagermaier, Chenghao Li, Tim Snow, Nicholas J. Terrill, Himadri S. Gupta, Pawan Goyal, Martin Stoll, Peter Benner and Peter Fratzl
Journal of Applied Crystallograph, Vol. 54, pp. 486-497, 2021.
DOI: 10.1107/S1600576721000881
@article{de2021tomographic,
title={Tomographic {X}-ray scattering based on invariant reconstruction: analysis of the {3D} nanostructure of bovine bone},
author={De Falco, Paolino and Weinkamer, Richard and Wagermaier, Wolfgang and Li, Chenghao and Snow, Tim and Terrill,
Nicholas J and Gupta, Himadri S and Goyal, Pawan and Stoll, Martin and Benner, Peter and others},
journal={J. Applied Crystallography},
volume={54},
number={2},
year={2021},
doi = {10.1107/S1600576721000881}
}
Please contact me for the code to generate the result of the paper.
[J11] Interpolation-Based Model Order Reduction for Polynomial Systems
Peter Benner and Pawan Goyal
SIAM Journal for Scientitic Computing, Vol. 43, No. 1, pp. A84-A108, 2021.
DOI: 10.1137/19M1259171
Preliminary version appeared as arXiv Preprint arXiv:1904.11891, April 2019.
In this work, we investigate a model order reduction scheme for polynomial parametric systems. We begin with defining the generalized multivariate transfer functions for the system. Based on this, we aim at constructing a reduced-order system, interpolating the defined generalized transfer functions at a given set of interpolation points. Furthermore, we provide a method, inspired by the Loewner approach for linear and (quadratic-)bilinear systems, to determine a good-quality reduced-order system in an automatic way. We also discuss the computational issues related to the proposed method and a potential application of CUR matrix approximation in order to further speed-up simulations of reduced-order systems. We test the efficiency of the proposed methods via several numerical examples.
@article{morBenG21, author = {Benner, P. and Goyal, P.},
title = {Interpolation-Based Model Order Reduction for Polynomial Systems},
journal = {SIAM J. Sci. Comp},
year = 2021,
volume = {43},
number = {1},
pages = {A84--A108},
doi = {10.1137/19M1259171}
}
Code can be downloaded from here.
[J10] Low-Dimensional Approximations of High-Dimensional Asset Price Models
Martin Redmann, Christian Bayer, and Pawan Goyal
SIAM Journal on Financial Mathematics, Vol. 12, pp. 1-12, 2021.
DOI: 10.1137/20M1325666
Preliminary version appeared as arXiv Preprint arXiv:2003.06928, Mar 2020.
We consider high-dimensional asset price models that are reduced in their dimension in order to reduce the complexity of the problem or the effect of the curse of dimensionality in the context of option pricing. We apply model order reduction (MOR) to obtain a reduced system. MOR has been previously studied for asymptotically stable controlled stochastic systems with zero initial conditions. However, stochastic differential equations modeling price processes are uncontrolled, have non-zero initial states and are often unstable. Therefore, we extend MOR schemes and combine ideas of techniques known for deterministic systems. This leads to a method providing a good pathwise approximation. After explaining the reduction procedure, the error of the approximation is analyzed and the performance of the algorithm is shown conducting several numerical experiments. Within the numerics section, the benefit of the algorithm in the context of option pricing is pointed out.
@Article{morRedBG20,
author = {Redmamm, R and Bayer, C. and Goyal, P.},
title = {Low-Dimensional Approximations of High-Dimensional Asset Price Models },
journal = {SIAM Journal on Financial Mathematics},
volume={12},
number={1},
pages={1--28},
year={2021},
}
Please contact me for the code to generate the result of the paper.
[J9] Operator Inference for Non-Intrusive Model Reduction of Systems with Non-Polynomial Nonlinear Terms
Peter Benner, Pawan Goyal, Boris Kramer, Benjamin Peherstorfer, and Karen Willcox
Computer Methods in Applied Mechanics and Engineering, Vol. 372, pp. 113433, 2020.
DOI: 10.1016/j.cma.2020.113433
Preliminary version appeared as arXiv Preprint arXiv:2002.09726, Feb 2020.
This work presents a non-intrusive model reduction method to learn low-dimensional models of dynamical systems with non-polynomial nonlinear terms that are spatially local and that are given in analytic form. In contrast to state-of-the-art model reduction methods that are intrusive and thus require full knowledge of the governing equations and the operators of a full model of the discretized dynamical system, the proposed approach requires only the non-polynomial terms in analytic form and learns the rest of the dynamics from snapshots computed with a potentially black-box full-model solver. The proposed method learns operators for the linear and polynomially nonlinear dynamics via a least-squares problem, where the given non-polynomial terms are incorporated in the right-hand side. The least-squares problem is linear and thus can be solved efficiently in practice. The proposed method is demonstrated on three problems governed by partial differential equations, namely the diffusion-reaction Chafee-Infante model, a tubular reactor model for reactive flows, and a batch-chromatography model that describes a chemical separation process. The numerical results provide evidence that the proposed approach learns reduced models that achieve comparable accuracy as models constructed with state-of-the-art intrusive model reduction methods that require full knowledge of the governing equations.
@Article{morBenGKetal20, author = {Benner, P. and Goyal, P. and Kramer, B. and Peherstorfer, B. and Willcox, K.},
title = {Operator Inference for Non-Intrusive Model Reduction of Systems with Non-Polynomial Nonlinear Terms},
journal = {Comp. Meth. Appl. Mech. Eng.},
year = 2020,
volume = 372,
pages = 113433,
doi = {10.1016/j.cma.2020.113433}
}
Please contact me for the code to generate the result of the paper.
[J8] Identification of Port-Hamiltonian Systems from Frequency Response Data
Peter Benner, Pawan Goyal, and Paul Van Dooren
Systems and Control Letters, Vol. 143, pp. 104741, 2020.
DOI: 10.1016/j.sysconle.2020.104741
Preliminary version appeared as arXiv Preprint arXiv:1909.04597, Oct 2019.
In this paper, we study the identification problem of a passive system from tangential interpolation data. We present a simple construction approach based on the Mayo-Antoulas generalized realization theory that automatically yields a port-Hamiltonian realization for every strictly passive system with simple spectral zeros. Furthermore, we discuss the construction of a frequency-limited port-Hamiltonian realization. We illustrate the proposed method by means of several examples.
@TechReport{morBenGVP19,
author = {Benner, P. and and Goyal, P. and Van Dooren, P.},
title = {Identification of Port-{H}amiltonian Systems from Frequency Response Data },
institution = {arXiv},
year = 2019,
type = {e-prints},
number = {1911.00080},
note = {math.NA},
url = {https://arxiv.org/abs/1911.00080}
}
Please contact me for the code to generate the result of the paper.
[J7] Balanced Truncation for a Special Class of Bilinear Descriptor Systems
Igor Pontes Duff Pereira, Pawan Goyal, and Peter Benner
IEEE Control Systems Society Letters, Vol. 3, pp. 535-540, 2019.
DOI: 10.1109/LCSYS.2019.2911904
[J6] Time-Limited H2-Optimal Model Order Reduction
Pawan Goyal, Martin Redmann
Journal of Applied Mathematics and Compution, Vol. 355, pp. 184-197, 2019.
DOI: 10.1016/j.amc.2019.02.065
Preliminary version appeared as arXiv Preprint arXiv:1610.03279v1, December 2017.
[J5] H2-Quasi-Optimal Model Order Reduction for Quadratic-Bilinear Control Systems
Peter Benner, Pawan Goyal, and Serkan Gugercin
SIAM Journal on Matrix Analysis and Applications, Vol. 39, Issue 2, pp. 983-1032, 2018.
DOI: 10.1137/16M1098280
Preliminary version appeared as arXiv Preprint arXiv:1610.03279v1, October 2016.
[J4] Moment-Matching Based Model Reduction for Navier-Stokes Type Quadratic-Bilinear Descriptor Systems
Mian Ilyas Ahmad, Peter Benner, Pawan Goyal, and Jan Heiland
Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM), Vol. 97, No. 10, pp. 1252–1267, 2017.
DOI: 10.1002/zamm.201500262
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-18, October 2015.
[J3] POD-DEIM for Efficient Reduction of a Dynamic 2D Catalytic Reactor Model
Peter Benner, Jens Bremer, Lihong Feng, Pawan Goyal, and Kai Sundmacher
Computers & Chemical Engineering, Vol. 106, pp. 777-784, 2017.
DOI: 10.1016/j.compchemeng.2017.02.032
[J2] Krylov Subspace-based Model Reduction for a Class of Bilinear Descriptor Systems
Pawan Goyal, Mian Ilyas Ahmad, and Peter Benner
Journal of Computational and Applied Mathematics, Vol. 315, pp. 303–318, 2017.
DOI: 10.1016/j.cam.2016.11.009.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-07, May 2015.
[J1] Multipoint Interpolation of Volterra Series and H2-Model Reduction for a Family of Bilinear Descriptor Systems
Peter Benner and Pawan Goyal
Systems & Control Letters, Vol. 97, pp. 1-11, 2016.
DOI: 10.1016/j.sysconle.2016.08.008.
Preliminary version appeared as MPI Magdeburg Preprint MPIMD/15-16, September 2015.

Book Chapters

[BC3] Data-Driven Identification of Rayleigh-Damped Second-Order Systems
Igor Pontes Duff, Pawan Goyal, and Peter Benner
C. Beattie, P. Benner, M. Embree, S. Gugercin, S. Lefteriu (Eds.), Realization and Model Reduction of Dynamical Systems – A Festschrift in Honor of 70th Birthday of Thanos Antoulas, Springer, 2020.
Preliminary version appeared as arXiv Preprint arXiv:1909.04597, Oct 2019.
In this paper, we present a data-driven approach to identify second-order systems, having internal Rayleigh damping. This means that the damping matrix is given as a linear combination of the mass and stiffness matrices. These systems typically appear when performing various engineering studies, e.g., vibrational and structural analysis. In an experimental setup, the frequency response of a system can be measured via various approaches, for instance, by measuring the vibrations using an accelerometer. As a consequence, given frequency samples, the identification of the underlying system relies on rational approximation. To that aim, we propose an identification of the corresponding second-order system, extending the Loewner framework for this class of systems. The efficiency of the proposed method is demonstrated by means of various numerical benchmarks.
@TechReport{morDuffGB19,
author = {Pontes Duff, I. and Benner, P. and Goyal, P.},
title = {Data-Driven Identification of {R}ayleigh-Damped Second-Order Systems },
institution = {arXiv},
year = 2019,
type = {e-prints},
number = {1910.00838},
note = {math.NA},
url = {https://arxiv.org/abs/1910.00838}
}
Please contact me for the code to generate the result of the paper.
[BC2] An Iterative Model Reduction Scheme for Quadratic-Bilinear Descriptor Systems with an Application to Navier-Stokes Equations
Peter Benner and Pawan Goyal
In W. Keiper, A. Milde, S. Volkwein (Eds.), Reduced-Order Modeling (ROM) for Simulation and Optimization, pp. 1-19, Springer, Cham, 2018.
DOI: 10.1007/978-3-319-75319-5_1
Preliminary version appeared as arXiv Preprint arXiv:1705.00934, April 2017.
[BC1] Truncated Gramians for Bilinear Systems and their Advantages in Model Order Reduction
Peter Benner, Pawan Goyal, and Martin Redmann
In P. Benner, M. Ohlberger, T. Patera, G. Rozza, K. Urban (Eds.), Model Reduction of Parametrized Systems, MS&A - Modeling, Simulation and Applications, Springer International Publishing, Cham, Vol. 17, pp. 285-300, 2017.
DOI: 10.1007/978-3-319-58786-8_18

Peer-Reviewed Conference Papers

[CA6] A Quadratic Decoder Approach to Nonintrusive Reduced-Order Modeling of Nonlinear Dynamical Systems
Peter Benner, Pawan Goyal, Jan Heiland, and Igor Pontes Duff
Proceedings in Applied Mathematics and Mechanics, Accepted, 2022.
DOI: 10.1002/pamm.202200049
[CA5] Learning Dynamics from Noisy Measurements using Deep Learning with a Runge-Kutta Constraint
Pawan Goyal, and Peter Benner
Workshop Paper at The Symbiosis of Deep Learning and Differential Equations Workshop at NeurIPS 2021, published online, 2021.
[CA4] Nonlinear Model Order Reduction for Catalytic Tubular Reactors
Jens Bremer, Pawan Goyal, Lihong Feng, Peter Benner, and Kai Sundmacher
Proceedings of the 26th Symposium on Computer Aided Process Engineering (ESCAPE), Portorož, Slovenia, 12 -15 June 2016, pp. 2373-2378, 2016.
DOI: 10.1016/B978-0-444-63428-3.50400-8
[CA3] Algebraic Gramians for Quadratic-Bilinear Systems and their Application in Model Order Reduction
Peter Benner and Pawan Goyal
Proceedings of the 22nd International Symposium on Mathematical Theory of Networks and Systems - MTNS 2016, 12 - 15 July 2016, Minnesota, USA, pp. 81-83, 2016.
[CA2] An Iterative Model Order Reduction Scheme for a Special Class of Bilinear Descriptor Systems Appearing in Constraint Circuit Simulation
Pawan Goyal and Peter Benner
In M. Papadrakakis, V. Papadopoulos, G. Stefanou, V. Plevris (Eds.), Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering, pp. 4196-4212, 2016.
[CA1] Model Reduction of Quadratic-Bilinear Descriptor Systems via Carleman Bilinearization
Pawan Goyal, Mian Ilyas Ahmad, and Peter Benner
Proceedings of 2015 European Control Conference (ECC), 15-17 July, 2015. Linz, Austria, pp. 1177-1182, 2015.
DOI: 10.1109/ECC.2015.7330699

Theses

[T1] System-Theoretic Model Order Reduction for Bilinear and Quadratic-Bilinear Systems
Pawan Goyal
Ph.D. Thesis, Otto-von-Guericke University, Magdeburg, Germany 2018. [Download].