Michael Günther

Dmitry Shcherbakov, Matthias Ehrhardt, Jacob Finkenrath et al.

We study a novel class of numerical integrators, the adapted nested force-gradient schemes, used within the molecular dynamics step of the Hybrid Monte Carlo (HMC) algorithm. We test these methods in the Schwinger model on the lattice, a well known benchmark problem. We derive the analytical basis of nested force-gradient type methods and demonstrate the advantage of the proposed approach, namely reduced computational costs compared with other numerical integration schemes in HMC.

Michael Günther, Isabelle Mohr, Daniel James Williams et al.

Many use cases require retrieving smaller portions of text, and dense vector-based retrieval systems often perform better with shorter text segments, as the semantics are less likely to be over-compressed in the embeddings. Consequently, practitioners often split text documents into smaller chunks and encode them separately. However, chunk embeddings created in this way can lose contextual information from surrounding chunks, resulting in sub-optimal representations. In this paper, we introduce a novel method called late chunking, which leverages long context embedding models to first embed all tokens of the long text, with chunking applied after the transformer model and just before mean pooling - hence the term late in its naming. The resulting chunk embeddings capture the full contextual information, leading to superior results across various retrieval tasks. The method is generic enough to be applied to a wide range of long-context embedding models and works without additional training. To further increase the effectiveness of late chunking, we propose a dedicated fine-tuning approach for embedding models.

Long Teng, Aleksandr Lapitckii, Michael Günther

In this work we study a multi-step scheme on time-space grids proposed by W. Zhao et al. [28] for solving backward stochastic differential equations, where Lagrange interpolating polynomials are used to approximate the time-integrands with given values of these integrands at chosen multiple time levels. For a better stability and the admission of more time levels we investigate the application of spline instead of Lagrange interpolating polynomials to approximate the time-integrands. The resulting scheme is a semi-discretization in the time direction involving conditional expectations, which can be numerically solved by using the Gaussian quadrature rules and polynomial interpolations on the spatial grids. Several numerical examples including applications in finance are presented to demonstrate the high accuracy and stability of our new multi-step scheme.

Peter Zaspel, Michael Günther

Port-Hamiltonian systems (pHS) allow for a structure-preserving modeling of dynamical systems. Coupling pHS via linear relations between input and output defines an overall pHS, which is structure preserving. However, in multiphysics applications, some subsystems do not allow for a physical pHS description, as (a) this is not available or (b) too expensive. Here, data-driven approaches can be used to deliver a pHS for such subsystems, which can then be coupled to the other subsystems in a structure-preserving way. In this work, we derive a data-driven identification approach for port-Hamiltonian differential algebraic equation (DAE) systems. The approach uses input and state space data to estimate nonlinear effort functions of pH-DAEs. As underlying technique, we us (multi-task) Gaussian processes. This work thereby extends over the current state of the art, in which only port-Hamiltonian ordinary differential equation systems could be identified via Gaussian processes. We apply this approach successfully to two applications from network design and constrained multibody system dynamics, based on pH-DAE system of index one and three, respectively.

Michael Günther, Andreas Brendel, Walter Kellermann

In multichannel signal processing with distributed sensors, choosing the optimal subset of observed sensor signals to be exploited is crucial in order to maximize algorithmic performance and reduce computational load, ideally both at the same time. In the acoustic domain, signal cross-correlation is a natural choice to quantify the usefulness of microphone signals, i.e., microphone utility, for array processing, but its estimation requires that the uncoded signals are synchronized and transmitted between nodes. In resource-constrained environments like acoustic sensor networks, low data transmission rates often make transmission of all observed signals to the centralized location infeasible, thus discouraging direct estimation of signal cross-correlation. Instead, we employ characteristic features of the recorded signals to estimate the usefulness of individual microphone signals. In this contribution, we provide a comprehensive analysis of model-based microphone utility estimation approaches that use signal features and, as an alternative, also propose machine learning-based estimation methods that identify optimal sensor signal utility features. The performance of both approaches is validated experimentally using both simulated and recorded acoustic data, comprising a variety of realistic and practically relevant acoustic scenarios including moving and static sources.