Contributed Talks I

Date & Time: Monday, September 28, 2026 | 16:30 - 19:00
Place: tba
Chairs: Willy Dörfler, Sebastian Krumscheid

Speaker: Stefan Karch (Karlsruhe Institute of Technology) and Willy Dörfler
Title: A Space and Time Adaptive Algorithm for the Landau--Lifshitz--Gilbert Equation
Abstract: The Landau-Lifshitz-Gilbert (LLG) equation serves as the fundamental model for describing magnetization dynamics in ferromagnetic materials. Since highly localized phenomena, such as domain walls in space or rapid switching events in time, occur in practice, adaptive methods are well-suited to resolve these local structures. In this talk, we construct a space and time adaptive algorithm based on the linearly implicit backward difference formulae (BDF) in time and higher-order Lagrangian finite elements in space, whose reliability is ensured by an a posteriori error bound. Finally, we demonstrate the effectiveness of the full adaptive algorithm in numerical experiments.

Speaker: Stefan Funkner (Karlsruhe Institute of Technology)
Title: Inverse Problems for Longitudinal Beam Dynamics: From Phase-Space Tomography to Wake-Function Reconstruction
Abstract: Accurate knowledge of the longitudinal phase-space distribution is essential for understanding and controlling short electron bunches in modern accelerators. Since the relevant beam properties are generally not directly accessible, they must be inferred from indirect measurements. This gives rise to a hierarchy of inverse problems connecting beam dynamics, diagnostics, and collective effects.

The underlying evolution of the longitudinal phase-space density is described by the Vlasov–Fokker–Planck equation. In a first approximation, the dynamics induces an effective rotation in phase space, while measured bunch profiles can be interpreted as projections of the evolving density. The reconstruction of the phase-space distribution can therefore be formulated as a tomographic inverse problem closely related to the inversion of the Radon transform.

More advanced reconstruction methods incorporate the full Vlasov–Fokker–Planck dynamics as a model constraint. In addition, the electro-optical diagnostic can be included in the forward model through its impulse-response function, allowing beam dynamics and measurement effects to be treated consistently.

Finally, the self-interaction of the electron bunch enters the Vlasov–Fokker–Planck model through the longitudinal wake function. By combining measured equilibrium profiles with corresponding Haïssinski solutions, the wake function itself can be reconstructed as an additional inverse problem. Together, these examples demonstrate how inverse-problem methodology provides a unifying framework for recovering hidden beam properties and interaction mechanisms from longitudinal beam-profile measurements.

Speaker: Thomas Sturges  (Karlsruhe Institute of Technology) 
Title: Beyond the Standard FFT Grid: Fractional DFTs for Flexible Fourier Optics
Abstract: The fast Fourier transform is exceptionally efficient, but it ties the sampling grid in Fourier space to the grid on which the input is given. This constraint is often accepted as an unavoidable part of Fourier-based simulation, even though the desired output resolution and field of view may be dictated by the application rather than by the input sampling.

To see where this restriction arises, we begin with the continuous Fourier transform and approximate its integral by a Riemann sum. The resulting expression closely resembles a discrete Fourier transform, but only becomes a standard DFT when the output-grid spacing is set to the reciprocal of the total sampled length of the input grid. It is this particular structure that allows the standard FFT algorithm to be applied directly. If the input and output grid spacings are instead chosen independently, the same Riemann sum takes the form of a fractional DFT. Using an idea due to Bailey and Swarztrauber, based on Bluestein’s algorithm, this transform can be rewritten as a convolution and evaluated using FFTs. It consequently retains the desirable O (N log N) computational complexity, rather than the O(N^2) cost of evaluating the sum directly, albeit with a larger constant prefactor than a standard FFT.

I will illustrate this approach using examples from Fourier optics. In FFT-based simulations, the grid in the focal plane of a lens is linked to the wavelength, focal length, and input sampling, while the angular spectrum method conventionally returns the propagated field on the same spatial grid as the input. A flexible Fourier transform allows the observation grid to be chosen independently, so that the calculation can target a desired resolution and field of view. This does not circumvent the information limits imposed by the input sampling, but it separates those limits from the choice of where the resulting field is evaluated.

Speaker: Sebastian Krumscheid, Emil Løvbak (Karlsruhe Institute of Technology)
Title: Metropolis-Hastings Acceptance Behavior for Bayesian Inversion with Random Forward Solvers
Abstract: In various application domains, one wishes to determine which parameter values should be used for a model to match its simulation output with measurement data. In practice however, measurement error on the data means that, at best, one can produce a so-called posterior probability distribution of these parameter values, given an assumed noise model. The Metropolis-Hastings is a straightforward approach that constructs a Markov chain with this posterior distribution as its invariant distribution. The parameter samples in the chain are selected through an accept-reject strategy, that accepts proposal samples, based on their likelihood, relative to that of the previous accepted sample.

Evaluating this likelihood requires the solution of the given model. Therefore, any errors in the discrete solver will result in errors in the likelihood evaluation. In this presentation, we discuss the case where Metropolis-Hastings is run on top of a stochastic solver, such
as a Monte Carlo particle solver. In this case, the likelihood—and thus the acceptance probability—becomes a random variable who’s variance scales with the number of random trajectories simulated by the solver [1]. We discuss the mismatch between theory and practice in this setting. To this end, we combine classical error analysis and simulation results to understand the behavior of the pseudomarginal Markov chains in this setting. We then present practical approaches for efficient estimation in such settings.

[1] Løvbak, E., Krumscheid, S., An Investigation into the Distribution of Ratios of Particle Solver-based Likelihoods. arXiv:2508.05303 (2025).

Speaker: Egor Malitskiy (Karlsruhe Institute of Technology)
Title: Neural Energy-Based Sampling: Navigating Complex Landscapes Without Target Data
Abstract: Sampling molecular conformations according to Boltzmann distributions plays a critical role in computational chemistry and drug discovery, where understanding structural stability and binding affinities is essential. In energy-based sampling, the challenge lies in the complete absence of target dataset samples; models must rely solely on unnormalized, physics-based energy functions p(x) \(\infty\) exp(-E(x)).

Classical simulation techniques, such as Markov Chain Monte Carlo and standard Molecular Dynamics, frequently suffer from severe slow-mixing issues. When confronted with high energy barriers, these methods become trapped in local minima, failing to adequately explore metastable states and capture the full conformational diversity of the system.

This talk provides an overview of recent algorithmic advances designed to overcome these sampling bottlenecks. We examine how modern neural samplers leverage concepts from stochastic optimal control, measure transport, and score matching to build scalable, trainable transport maps that enable fast and global exploration of complex, high-dimensional probability distributions.

Speaker: Hai Dang Nguyen Pham (Karlsruhe Institute of Technology)
Title: Model-adaptivity and Full waveform inversion for a space-time discretization of visco-acoustic waves
Abstract: Full waveform inversion (FWI) reconstructs subsurface material parameters, such as wave speed and attenuation, from seismic measurements by repeatedly solving a wave propagation problem within an iterative optimization scheme (Rheinbay, PhD thesis, Karlsruhe 2024). The attenuation entering this forward problem is commonly  modeled using visco-acoustic formulations based on the Generalized Standard Linear Solid (GSLS) framework (Blanch, Robertsson, Symes, Geophysics 1995). The accuracy of these models depends on the number of relaxation mechanisms used to approximate the desired attenuation behavior, but each additional mechanism introduces new state variables and increases the computational cost -- a cost that is amplified  by the many forward solves required during inversion. Existing approaches typically employ a fixed number of relaxation mechanisms throughout the computational domain, regardless of the local complexity of the wave field.

We present a model-adaptive strategy that adjusts the number of relaxation mechanisms locally in space and time according to the evolving solution. Regions not yet affected by the wave field, or exhibiting simple behavior, are represented by a reduced model, while regions with pronounced attenuation are locally enriched.

This adaptive strategy is embedded in a high-order space-time discontinuous Galerkin discretization (Ziegler, PhD thesis, Karlsruhe 2020). Numerical experiments on heterogeneous benchmarks, including the Marmousi model, show that it substantially reduces computational cost while preserving the accuracy required for realistic wave propagation, making it a promising step towards more efficient forward solves in full waveform inversion.