Abstract In industrial manufacturing, deploying deep learning models for visual inspection is mostly hindered by the high and often intractable cost of collecting and annotating large-scale training datasets. While image synthesis from 3D CAD models is a common solution, the individual techniques of domain and rendering randomization to create rich synthetic training datasets have been well studied mainly in simple domains. Hence, their effectiveness on complex industrial tasks with densely arranged and similar objects remains unclear. In this paper, we investigate the sim-to-real generalization performance of standard object detectors on the complex industrial application of terminal strip object detection, carefully combining randomization and domain knowledge. We describe step-by-step the creation of our image synthesis pipeline that achieves high realism with minimal implementation effort and explain how this approach could be transferred to other industrial settings. Moreover, we created a dataset comprising 30,000 synthetic images and 300 manually annotated real images of terminal strips, which is publicly available for reference and future research. To provide a baseline as a lower bound of the expectable performance in these challenging industrial parts detection tasks, we show the sim-to-real generalization performance of standard object detectors on our dataset based on a fully synthetic training. While all considered models behave similarly, the transformer-based DINO model achieves the best score with 98.40% mean average precision on the real test set, demonstrating that our pipeline enables high quality detections in complex industrial environments from existing CAD data and with a manageable image synthesis effort.

Active learning of physical systems must commonly respect practical safety constraints, which restricts the exploration of the design space. Gaussian Processes (GPs) and their calibrated uncertainty estimations are widely used for this purpose. In many technical applications the design space is explored via continuous trajectories, along which the safety needs to be assessed. This is particularly challenging for strict safety requirements in GP methods, as it employs computationally expensive Monte Carlo sampling of high quantiles. We address these challenges by providing provable safety bounds based on the adaptively sampled median of the supremum of the posterior GP. Our method significantly reduces the number of samples required for estimating high safety probabilities, resulting in faster evaluation without sacrificing accuracy and exploration speed. The effectiveness of our safe active learning approach is demonstrated through extensive simulations and validated using a real-world engine example.

Partial differential equations (PDEs) are important tools to model physical systems and including them into machine learning models is an important way of incorporating physical knowledge. Given any system of linear PDEs with constant coefficients, we propose a family of Gaussian process (GP) priors, which we call EPGP, such that all realizations are exact solutions of this system. We apply the Ehrenpreis-Palamodov fundamental principle, which works as a non-linear Fourier transform, to construct GP kernels mirroring standard spectral methods for GPs. Our approach can infer probable solutions of linear PDE systems from any data such as noisy measurements, or pointwise defined initial and boundary conditions. Constructing EPGP-priors is algorithmic, generally applicable, and comes with a sparse version (S-EPGP) that learns the relevant spectral frequencies and works better for big data sets. We demonstrate our approach on three families of systems of PDEs, the heat equation, wave equation, and Maxwell’s equations, where we improve upon the state of the art in computation time and precision, in some experiments by several orders of magnitude.

Cyber-physical production systems have emerged with the rise of Industry 4.0 in different industrial fields. Especially the food sector, where inhomogeneous input products like beer/yeast suspensions with different qualities and properties have yet slowed down automation, has potential for this evolution. This contribution presents optimization methods for a dynamical cross-flow filtration plant which is driven by an advanced control concept in combination with data driven product monitoring via inline near infrared spectroscopy (NIR) in order to improve energy savings and filtration performance. Using a hierarchical control and optimization structure, the non stationary batch process is steered towards a high production rate with low energy consumption for a variety of different input products.

Data in many applications follows systems of Ordinary Differential Equations (ODEs).This paper presents a novel algorithmic and symbolic construction for covariance functions of Gaussian Processes (GPs) with realizations strictly following a system of linear homogeneous ODEs with constant coefficients, which we call LODE-GPs. Introducing this strong inductive bias into a GP improves modelling of such data. Using smith normal form algorithms, a symbolic technique, we overcome two current restrictions in the state of the art: (1) the need for certain uniqueness conditions in the set of solutions, typically assumed in classical ODE solvers and their probabilistic counterparts, and (2) the restriction to controllable systems, typically assumed when encoding differential equations in covariance functions. We show the effectiveness of LODE-GPs in a number of experiments, for example learning physically interpretable parameters by maximizing the likelihood.

One goal in Bayesian machine learning is to encode prior knowledge into prior distributions, to model data efficiently. We consider prior knowledge from systems of linear partial differential equations together with their boundary conditions. We construct multi-output Gaussian process priors with realizations in the solution set of such systems, in particular only such solutions can be represented by Gaussian process regression. The construction is fully algorithmic via Gröbner bases and it does not employ any approximation. It builds these priors combining two parametrizations via a pullback: the first parametrizes the solutions for the system of differential equations and the second parametrizes all functions adhering to the boundary conditions.

We algorithmically construct multi-output Gaussian process priors which satisfy linear differential equations. Our approach attempts to parametrize all solutions of the equations using Gröbner bases. If successful, a push forward Gaussian process along the paramerization is the desired prior. We consider several examples from physics, geomathmatics and control, among them the full inhomogeneous system of Maxwell's equations. By bringing together stochastic learning and computeralgebra in a novel way, we combine noisy observations with precise algebraic computations.