arXiv subjects

Marcus Noack

Publications and source records attributed to Marcus Noack.

3 recordsLinked to original sources

arXiv2026

Wasserstein-type Gaussian Process Regressions for Input Measurement Uncertainty

Gaussian process (GP) regression is widely used for uncertainty quantification, yet the standard formulation assumes noise-free covariates. When inputs are measured with error, this errors-in-variables (EIV) setting can lead to optimistically narrow posterior intervals and biased decisions. We study GP regression under input measurement uncertainty by representing each noisy input as a probability measure and defining covariance through Wasserstein distances between these measures. Building on this perspective, we instantiate a deterministic projected Wasserstein ARD (PWA) kernel whose one-dimensional components admit closed-form expressions and whose product structure yields a scalable, positive-definite kernel on distributions. Unlike latent-input GP models, PWA-based GPs (\PWAGPs) handle input noise without introducing unobserved covariates or Monte Carlo projections, making uncertainty quantification more transparent and robust.

stat.ME↗

arXiv2025

Noise-Aware Optimization in Nominally Identical Manufacturing and Measuring Systems for High-Throughput Parallel Workflows

Device-to-device variability in experimental noise critically impacts reproducibility, especially in automated, high-throughput systems like additive manufacturing farms. While manageable in small labs, such variability can escalate into serious risks at larger scales, such as architectural 3D printing, where noise may cause structural or economic failures. This contribution presents a noise-aware decision-making algorithm that quantifies and models device-specific noise profiles to manage variability adaptively. It uses distributional analysis and pairwise divergence metrics with clustering to choose between single-device and robust multi-device Bayesian optimization strategies. Unlike conventional methods that assume homogeneous devices or generic robustness, this framework explicitly leverages inter-device differences to enhance performance, reproducibility, and efficiency. An experimental case study involving three nominally identical 3D printers (same brand, model, and close serial numbers) demonstrates reduced redundancy, lower resource usage, and improved reliability. Overall, this framework establishes a paradigm for precision- and resource-aware optimization in scalable, automated experimental platforms.

cs.DC↗

arXiv2024

Polyatomic Complexes: A topologically-informed learning representation for atomistic systems

A representation of a molecule or material should be invariant to the symmetries of physics, unique, continuous, efficient and general. These properties, however, are hard to satisfy at once: a descriptor invariant under the full orthogonal group $O(3)$ gives a molecule and its mirror image the same value, and so cannot distinguish enantiomers whose properties differ. Pozdnyakov showed this follows from the invariance itself, not from a lack of parameters. We show the criteria can be met at once if the geometric map is graded by the sign character of $O(3)$ and pooled multisymmetrically. We construct such a map $\Phi$: its even block factors through the Gram matrix and is provably chirality-blind, while its parity-odd block of signed triple products separates enantiomers on an open dense full-measure set of interacting configurations. Two standard obstructions to uniqueness, fixed output length and componentwise pooling, are artifacts of the pooling rule, removed by multisymmetric power sums of order at most $N$. We establish uniqueness for a complete descriptor $\Phi^\star$ built from the distance matrix, signed volumes and atom types, injective up to $SE(3)\times S_N$ on all configurations. $\Phi^\star$ is non-constructive, however; the implemented map is the bounded-cutoff $\Phi$, generically injective, pooling at order $2$, running in $O(N^2)$, or $O(N)$ with neighbor lists. The algebraic core is machine-checked in Lean 4. Because the underlying object is a cell complex, it also yields invariant, stable topological features $\Psi$ (persistent homology and a Hodge-Laplacian spectrum) encoding global ring and cage structure invisible to bounded-cutoff descriptors. The pair $(\Phi,\Psi)$ feeds a compact parity-graded equivariant transformer.

cs.LG↗