@TechReport{ForootaniKHGB24,
author = {Forootani, A., Kapadia, H., Chellappa, S., Goyal, P., and Benner, P.},
title = {GS-PINN: Greedy Sampling for Parameter Estimation in Partial Differential Equations},
institution = {arXiv},
year = 2024,
type = {e-prints},
number = {2405.08537v1},
note = {[math.DS]},
url = {https://arxiv.org/abs/2405.08537v1}
}

The code can be found using the link https://example.com/code.

@TechReport{PrzybillaPDGB24,
author = {Przybilla, J., Pontes Duff, I., Goyal, P., and Benner, P.},
title = {Balanced Truncation of Descriptor Systems with a Quadratic Output},
institution = {arXiv},
year = 2024,
type = {e-prints},
number = {2402.14716},
note = {math.OC},
url = {https://arxiv.org/abs/2402.14716}
}

The code can be found using the link [Insert Code Link].

@TechReport{morForGB23,
author = {Forootani, A., Goyal, P., and Benner, P.},
title = {A Robust SINDy Approach by Combining Neural Networks and an Integral Form},
institution = {arXiv},
year = 2023,
type = {e-prints},
number = {2309.07193},
note = {math.NA},
url = {https://arxiv.org/abs/2309.07193}
}

The code can be found using the link No code available yet..

@TechReport{morGoyYB23,
author = {Goyal, P., Yildiz, S., and Benner, P.},
title = {Deep Learning for Structure-Preserving Universal Stable Koopman-Inspired Embeddings for Nonlinear Canonical Hamiltonian Dynamics},
institution = {arXiv},
year = 2023,
type = {e-prints},
number = {2308.13835},
note = {math.DS},
url = {https://arxiv.org/abs/2308.13835}
}

The code can be found using the link https://gitlab.mpi-magdeburg.mpg.de/goyalp/koopman-hamiltonian.

@TechReport{morGoyPB24,
author = {Goyal, P., Pontes Duff, I., and Benner, P.},
title = {Guaranteed Stable Quadratic Models and their Applications in SINDy and Operator Inference},
institution = {arXiv},
year = 2024,
type = {e-prints},
number = {2308.13819},
note = {math.LG},
url = {https://arxiv.org/abs/2308.13819}
}

The code can be found using the link https://gitlab.mpi-magdeburg.mpg.de/goyalp/guaranteed_stable_quadratic_models.

@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}
}

The code can be found using the link https://gitlab.mpi-magdeburg.mpg.de/goyalp/learning_linear_stablesystems.

@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.

@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.

@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.

@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.

@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.

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.

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.