@article{63800,
  abstract     = {{In this contribution, we address the estimation of the frequency-dependent elastic parameters of polymers in the ultrasound range, which is formulated as an inverse problem. This inverse problem is implemented as a nonlinear regression-type optimization problem, in which the simulation signals are fitted to the measurement signals. These signals consist of displacement responses in waveguides, focusing on hollow cylindrical geometries to enhance the simulation efficiency. To accelerate the optimization and reduce the number of model evaluations and wait times, we propose two novel methods. First, we introduce an adaptation of the Levenberg–Marquardt method derived from a geometrical interpretation of the least-squares optimization problem. Second, we introduce an improved objective function based on the autocorrelated envelopes of the measurement and simulation signals. Given that this study primarily relies on simulation data to quantify optimization convergence, we aggregate the expected ranges of realistic material parameters and derive their distributions to ensure the reproducibility of optimizations with proper measurements. We demonstrate the effectiveness of our objective function modification and step adaptation for various materials with isotropic material symmetry by comparing them with the Broyden–Fletcher–Goldfarb–Shanno method. In all cases, our method reduces the total number of model evaluations, thereby shortening the time to identify the material parameters.}},
  author       = {{Itner, Dominik and Dreiling, Dmitrij and Gravenkamp, Hauke and Henning, Bernd and Birk, Carolin}},
  issn         = {{0888-3270}},
  journal      = {{Mechanical Systems and Signal Processing}},
  keywords     = {{Material parameter estimation, Waveguide, Nonlinear optimization, Inverse problem, Least squares}},
  pages        = {{113904}},
  title        = {{{A modified Levenberg–Marquardt method for estimating the elastic material parameters of polymer waveguides using residuals between autocorrelated frequency responses}}},
  doi          = {{https://doi.org/10.1016/j.ymssp.2026.113904}},
  volume       = {{247}},
  year         = {{2026}},
}

@unpublished{55159,
  abstract     = {{We introduce a method based on Gaussian process regression to identify discrete variational principles from observed solutions of a field theory. The method is based on the data-based identification of a discrete Lagrangian density. It is a geometric machine learning technique in the sense that the variational structure of the true field theory is reflected in the data-driven model by design. We provide a rigorous convergence statement of the method. The proof circumvents challenges posed by the ambiguity of discrete Lagrangian densities in the inverse problem of variational calculus.
Moreover, our method can be used to quantify model uncertainty in the equations of motions and any linear observable of the discrete field theory. This is illustrated on the example of the discrete wave equation and Schrödinger equation.
The article constitutes an extension of our previous article  arXiv:2404.19626 for the data-driven identification of (discrete) Lagrangians for variational dynamics from an ode setting to the setting of discrete pdes.}},
  author       = {{Offen, Christian}},
  keywords     = {{System identification, inverse problem of variational calculus, Gaussian process, Lagrangian learning, physics informed machine learning, geometry aware learning}},
  pages        = {{28}},
  title        = {{{Machine learning of discrete field theories with guaranteed convergence and uncertainty quantification}}},
  year         = {{2024}},
}

@inproceedings{13892,
  abstract     = {{Several ultrasonic approaches for material determination are formulated in terms of an (nonlinear) inverse problem, e.g. immersion technique (Castaings et al. (2000)) or plate-waveguide techniques (Marzani et al. (2012)). In this contribution we focus on cylindrical waveguides for ultrasonic material determination and especially on the sensitivity of recorded transmission signals to the material properties. We utilize composite scaled sensitivities to determine the information content that can be achieved by the setup to certain parameters and discuss the limitations of the approach.}},
  author       = {{Bause, Fabian and Gravenkamp, Hauke and Rautenberg, Jens and Henning, Bernd}},
  keywords     = {{Sensitivity inverse problem ultrasonic material determination}},
  pages        = {{204--207}},
  title        = {{{Model based sensitivity analysis in the determination of viscoelastic material properties using transmission measurements through circular waveguides}}},
  year         = {{2015}},
}

@article{13893,
  abstract     = {{In this contribution, we present an efficient approach for the transient and time-causal modeling of guided waves in viscoelastic cylindrical waveguides in the context of ultrasonic material characterization. We use the scaled boundary finite element method (SBFEM) for efficient computation of the phase velocity dispersion. Regarding the viscoelastic behavior of the materials under consideration, we propose a decomposition approach that considers the real-valued frequency dependence of the (visco-)elastic moduli and, separately, of their attenuation. The modal expansion approach is utilized to take the transmitting and receiving transducers into account and to propagate the excited waveguide modes through a waveguide of finite length. The effectiveness of the proposed simulation model is shown by comparison with a standard transient FEM simulation as well as simulation results based on the exact solution of the complex-valued viscoelastic guided wave problem. Two material models are discussed, namely the fractional Zener model and the anti-Zener model; we re-interpret the latter in terms of the Rayleigh damping model. Measurements are taken on a polypropylene sample and the proposed transient simulation model is used for inverse material characterization. The extracted material properties may then be used in computer-aided design of ultrasonic systems.}},
  author       = {{Bause, Fabian and Gravenkamp, Hauke and Rautenberg, Jens and Henning, Bernd}},
  issn         = {{0957-0233}},
  journal      = {{Measurement Science and Technology}},
  keywords     = {{viscoelasticity, ultrasonics, guided waves, inverse problem, scaled boundary finite element method}},
  number       = {{095602 (17pp)}},
  title        = {{{Transient modeling of ultrasonic guided waves in circular viscoelastic waveguides for inverse material characterization}}},
  doi          = {{10.1088/0957-0233/26/9/095602}},
  volume       = {{26}},
  year         = {{2015}},
}