We develop a novel physics informed deep learning approach for solving nonlinear drift-diffusion equations on metric graphs. These models represent an important model class with a large number of applications in areas ranging from transport in biological cells to the motion of human crowds. While traditional numerical schemes require a large amount of tailoring, especially in the case of model design or parameter identification problems, physics informed deep operator networks (DeepONets) have emerged as a versatile tool for the solution of partial differential equations with the particular advantage that they easily incorporate parameter identification questions. We here present an approach where we first learn three DeepONet models for representative inflow, inner and outflow edges, resp., and then subsequently couple these models for the solution of the drift-diffusion metric graph problem by relying on an edge-based domain decomposition approach. We illustrate that our framework is applicable for the accurate evaluation of graph-coupled physics models and is well suited for solving optimization or inverse problems on these coupled networks.

Chemical–mechanical planarization (CMP) is a critical and complex process in semiconductor manufacturing, where high precision and tight tolerances demand sophisticated process control. Machine learning (ML) has emerged as a promising tool to support this need. However, the literature is fragmented across domains and often lacks concrete guidance on deploying ML methods in real-world CMP environments. This review addresses that gap and provides actionable insights for both academic researchers and industrial practitioners. This work systematically analyzes peer-reviewed publications at the intersection of ML and CMP. It offers three significant contributions: First, it provides a detailed assessment of the types and sources of data used in CMP-related ML studies, distinguishing between equipment-level data, process-level data, and product-level data. Second, it introduces a structured classification of ML applications across four key areas: Research and Development, Real-Time Process Control, Equipment Health Monitoring, and Post-Process Feedback and Analysis. Third, it synthesizes commonly reported challenges along the data science pipeline. Where available, practical solutions and implementation strategies are discussed. Across these areas, existing studies illustrate ML’s potential to, among other things, enable more adaptive control, reduce metrology demands, enhance defect detection, and support layout- and process-aware design optimization, highlighting its growing role in CMP process innovation. The review concludes by outlining open research gaps and proposing future directions, including the development of benchmark datasets, integration of domain knowledge, and extension of modeling efforts to additional targets such as dishing and within-wafer non-uniformity. While focused on CMP, many challenges discussed, such as data leakage, sparse target labeling, and hybrid modeling, are relevant across engineering informatics. Addressing them in CMP can inform the broader development of robust and adaptable ML systems in intelligent manufacturing.

Real-world autonomous driving systems must make safe decisions in the face of rare and diverse traffic scenarios. Current state-of-the-art planners are mostly evaluated on real-world datasets like nuScenes (open-loop) or nuPlan (closed-loop). In particular nuPlan seems to be an expressive evaluation method since it is based on real-world data and closed-loop, yet it mostly covers basic driving scenarios. This makes it difficult to judge a planner’s capabilities to generalize to rarely-seen situations. Therefore, we propose a novel closed-loop benchmark interPlan containing several edge cases and challenging driving scenarios. We assess existing state-of-the-art planners on our benchmark and show that neither rule-based nor learning-based planners can safely navigate the interPlan scenarios.A recently evolving direction is the usage of foundation models like large language models (LLM) to handle generalization. We evaluate an LLM-only planner and introduce a novel hybrid planner that combines an LLM-based behavior planner with a rule-based motion planner that achieves state-of-the-art performance on our benchmark.

Predicting the future motion of surrounding vehicles is a crucial enabler for safe autonomous driving. The field of motion prediction has seen large progress recently with State-of-the-Art (SotA) models achieving impressive results on large-scale public benchmarks. However, recent work revealed that learning-based methods are prone to predict off-road trajectories in challenging scenarios. These can be created by perturbing existing scenarios with additional turns in front of the target vehicle while the motion history is left unchanged. We argue that this indicates that SotA models do not consider the map information sufficiently and demonstrate how this can be solved by representing the model inputs and outputs in a Frenet frame defined by lane centreline sequences. To this end, we present a general wrapper that leverages a Frenet representation of the scene, and that can be applied to SotA models without changing their architecture. We demonstrate the effectiveness of this approach in a comprehensive benchmark comprising two SotA motion prediction models. Our experiments show that this reduces the off-road rate in challenging scenarios by more than 90%, without sacrificing average performance. Code and supplementary material are available under: https://mh0797.github.io/stayontrack/.

An increasing amount of the collected data are high-dimensional multi-way arrays (tensors), and it is crucial for efficient learning algorithms to exploit this tensorial structure as much as possible. The ever present curse of dimensionality for high dimensional data and the loss of structure when vectorizing the data motivates the use of tailored low-rank tensor classification methods. In the presence of small amounts of training data, kernel methods offer an attractive choice as they provide the possibility for a nonlinear decision boundary. We develop the Tensor Train Multi-way Multi-level Kernel (TT-MMK), which combines the simplicity of the Canonical Polyadic decomposition, the classification power of the Dual Structure-preserving Support Vector Machine, and the reliability of the Tensor Train (TT) approximation. We show by experiments that the TT-MMK method is usually more reliable computationally, less sensitive to tuning parameters, and gives higher prediction accuracy in the SVM classification when benchmarked against other state-of-the-art techniques.

Abstract Graph Convolutional Networks (GCNs) have proven to be successful tools for semi-supervised classification on graph-based datasets. We propose a new GCN variant whose three-part filter space is targeted at dense graphs. Our examples include graphs generated from 3D point clouds with an increased focus on non-local information, as well as hypergraphs based on categorical data of real-world problems. These graphs differ from the common sparse benchmark graphs in terms of the spectral properties of their graph Laplacian. Most notably we observe large eigengaps, which are unfavorable for popular existing GCN architectures. Our method overcomes these issues by utilizing the pseudoinverse of the Laplacian. Another key ingredient is a low-rank approximation of the convolutional matrix, ensuring computational efficiency and increasing accuracy at the same time. We outline how the necessary eigeninformation can be computed efficiently in each applications and discuss the appropriate choice of the only metaparameter, the approximation rank. We finally showcase our method’s performance regarding runtime and accuracy in various experiments with real-world datasets.

The Cahn--Hilliard equation provides a simple and fast tool for binary image inpainting. By now, two generalizations to gray value images exist: bitwise binary inpainting and TV-H$^{-1}$ inpainting. This paper outlines a model based on the vector-valued Cahn--Hilliard equation. Additionally, we generalize our approach to a fractional-in-space version. Fourier spectral methods provide efficient solvers since they yield a fully diagonal scheme. Furthermore, their application to three spatial dimensions is straightforward. Numerical examples show the superiority of the proposed fractional Cahn--Hilliard inpainting approach over its nonfractional version. It improves the peak signal-to-noise ratio and structural similarity index. Likewise, the experiments confirm that the proposed model competes with previous inpainting methods, such as the total variation inpainting approach and its fourth-order variant.

The solution of Cahn--Hilliard variational inequalities is of interest in many applications. We discuss the use of them as a tool for binary image inpainting. This has been done before using double-well potentials but not for nonsmooth potentials as considered here. The existing bound constraints are incorporated via the Moreau--Yosida regularization technique. We develop effective preconditioners for the efficient solution of the Newton steps associated with the fast solution of the Moreau--Yosida regularized problem. Numerical results illustrate the efficiency of our approach. Moreover, precise eigenvalue intervals are given for the preconditioned system using a double-well potential. A comparison between the smooth and nonsmooth Cahn--Hilliard inpainting models shows that the latter achieves better results.