arXiv subjects

Felix Gruber

Publications and source records attributed to Felix Gruber.

7 recordsLinked to original sources

arXiv2026

Orientation Mapping via Dictionary Indexing of AC-STEM Kikuchi patterns using Open-source Software

The properties of polycrystalline materials are strongly influenced by the spatial arrangement and orientations of individual grains within the microstructure, making nanoscale characterization of grain orientation essential. This is also often the case for small grains in the nm regime explored using scanning transmission electron microscopy (STEM). Automated crystal orientation mapping (ACOM) is traditionally performed using spot-like diffraction patterns. In contrast, orientation mapping based on transmission Kikuchi diffraction (TKD) using an aberration-corrected (AC) convergent STEM probe remains relatively underexplored, despite its superior orientation sensitivity and higher spatial resolution. In this work, we present an open-source software-based template-matching approach for orientation mapping using AC-STEM TKD. A master pattern (a simulated angular distribution of Kikuchi band intensities on the unit sphere) is first generated through a dynamical simulation implemented in open-source software. This resulting pattern is subsequently imported into another open-source package for geometric simulations and orientation indexing. We demonstrate the capability of the proposed method by applying it to orientation mapping in BaZr0.4Ce0.4Y0.1Yb0.1O3-{\delta} (BZCYYb4411) fuel-cell material and LiNiO2 (LNO) lithium-ion battery cathode material. The best-matched simulated patterns exhibit strong agreement with experimental data, even under the challenging conditions with limited diffraction space available for matching.

cond-mat.mtrl-sci↗

arXiv2026

Efficient Uniform Feasible-Set Sampling for Approximate Linear MPC

Model Predictive Control (MPC) offers safe and near-optimal control but suffers from high computational costs. Approximate MPC (AMPC) mitigates this by learning a cheaper surrogate policy, typically by training a neural network on state-MPC input pairs. Generating training data is a major bottleneck, requiring solving the MPC for numerous states sampled from its feasible set. Since this feasible set is implicitly defined and unknown, efficient sampling is nontrivial but crucial. We propose the linear MPC Hit-and-Run (LMPC-HR) sampler for linear MPC with polyhedral constraints. We identify the feasible set boundaries along search directions, a crucial step within HR, by formulating the problem as a convex linear program, replacing expensive iterative searches with a single optimization step. A numerical study demonstrates that LMPC-HR reduces the computational cost of generating uniformly distributed samples from the feasible set by an order of magnitude compared to standard baselines.

eess.SY↗

arXiv2025

Statistically Consistent Approximate Model Predictive Control

Model Predictive Control (MPC) offers rigorous safety and performance guarantees but is computationally intensive. Approximate MPC (AMPC) aims to circumvent this drawback by learning a computationally cheaper surrogate policy. Common approaches focus on imitation learning (IL) via behavioral cloning (BC), minimizing a mean-squared-error loss on a collection of state-input pairs. However, BC fundamentally fails to provide accurate approximations when MPC solutions are set-valued due to non-convex constraints or local minima. We propose a two-stage IL procedure to accurately approximate nonlinear, potentially set-valued MPC policies. The method integrates an approximation of the MPC's optimal value function into a one-step look-ahead loss function, and thereby embeds the MPC's constraint and performance objectives into the IL objective. This is achieved by adopting a stabilizing soft constrained MPC formulation, which reflects constraint violations in the optimal value function by combining a constraint tightening with slack penalties. We prove statistical consistency for policies that exactly minimize our IL objective, implying convergence to a safe and stabilizing control law, and establish input-to-state stability guarantees for approximate minimizers. Simulations demonstrate improved performance compared to BC.

eess.SY↗

arXiv2025

Tunable Real-Time Safety Filters via Set-Based Control Barrier Functions

Safety filters for industrial constrained systems are required to combine certified constraint satisfaction, predictable online computation, and a transparent tuning interface. Existing set-based filters are based on a well-established control invariant set design that scales favorably with state and input constraints, but typically intervene only at the set boundary. Control barrier function (CBF)-based filters, by contrast, provide tunable intervention but require a scalar barrier construction. This paper proposes a set-based CBF safety filter that turns a convex control invariant set directly into a tunable barrier via its Minkowski functional. The resulting filter is formulated as a single-level quadratic program (QP) in which one class-$\mathcal{K}^e$ parameter sets the intervention aggressiveness. Explicit convex formulations are derived for polytopic, zonotopic, and MPC-based invariant sets. Under standard bounded-disturbance assumptions, the resulting safety filter guarantees constraint satisfaction and asymptotic recovery into the invariant set. For tight real-time budgets, a learning-based approximation enables online acceleration, while the formal safety guarantees remain tied to the exact formulation. The method is validated in numerical studies and on a permanent-magnet synchronous motor drive, where an explicit QP implementation evaluates within a 150 microseconds sampling window and has a worst-case execution time of 28.04 microseconds.

eess.SY↗

arXiv2019

An Adaptive Nested Source Term Iteration for Radiative Transfer Equations

We propose a new approach to the numerical solution of radiative transfer equations with certified a posteriori error bounds. A key role is played by stable Petrov--Galerkin type variational formulations of parametric transport equations and corresponding radiative transfer equations. This allows us to formulate an iteration in a suitable, infinite dimensional function space that is guaranteed to converge with a fixed error reduction per step. The numerical scheme is then based on approximately realizing this iteration within dynamically updated accuracy tolerances that still ensure convergence to the exact solution. To advance this iteration two operations need to be performed within suitably tightened accuracy tolerances. First, the global scattering operator needs to be approximately applied to the current iterate within a tolerance comparable to the current accuracy level. Second, parameter dependent linear transport equations need to be solved, again at the required accuracy of the iteration. To ensure that the stage dependent error tolerances are met, one has to employ rigorous a posteriori error bounds which, in our case, rest on a Discontinuous Petrov--Galerkin (DPG) scheme. These a posteriori bounds are not only crucial for guaranteeing the convergence of the perturbed iteration but are also used to generate adapted parameter dependent spatial meshes. This turns out to significantly reduce overall computational complexity. Since the global operator is only applied, we avoid the need to solve linear systems with densely populated matrices. Moreover, the approximate application of the global scatterer accelerated through low-rank approximation and matrix compression techniques. The theoretical findings are illustrated and complemented by numerical experiments with non-trivial scattering kernels.

math.NA↗

arXiv2017

Sparsity-Sensitive Finite Abstraction

Abstraction of a continuous-space model into a finite state and input dynamical model is a key step in formal controller synthesis tools. To date, these software tools have been limited to systems of modest size (typically $\leq$ 6 dimensions) because the abstraction procedure suffers from an exponential runtime with respect to the sum of state and input dimensions. We present a simple modification to the abstraction algorithm that dramatically reduces the computation time for systems exhibiting a sparse interconnection structure. This modified procedure recovers the same abstraction as the one computed by a brute force algorithm that disregards the sparsity. Examples highlight speed-ups from existing benchmarks in the literature, synthesis of a safety supervisory controller for a 12-dimensional and abstraction of a 51-dimensional vehicular traffic network.

eess.SY↗

arXiv2016

The DUNE-DPG library for solving PDEs with Discontinuous Petrov--Galerkin finite elements

In the numerical solution of partial differential equations (PDEs), a central question is the one of building variational formulations that are inf-sup stable not only at the infinite-dimensional level, but also at the finite-dimensional one. This guarantees that residuals can be used to tightly bound errors from below and above and is crucial for a posteriori error control and the development of adaptive strategies. In this framework, the so-called Discontinuous Petrov--Galerkin (DPG) concept can be viewed as a systematic strategy of contriving variational formulations which possess these desirable stability properties, see e. g. Broersen et al. [2015]. In this paper, we present a C++ library, Dune-DPG, which serves to implement and solve such variational formulations. The library is built upon the multipurpose finite element package Dune (see Blatt et al. [2016]). One of the main features of Dune-DPG is its flexibility which is achieved by a highly modular structure. The library can solve in practice some important classes of PDEs (whose range goes beyond classical second order elliptic problems and includes e. g. transport dominated problems). As a result, Dune-DPG can also be used to address other problems like optimal control with the DPG approach.

math.NA↗