Uncovering causal relationships is a fundamental problem across science and engineering. However, most existing causal discovery methods assume acyclicity and direct access to the system variables -- assumptions that fail to hold in many real-world settings. For instance, in genomics, cyclic regulatory networks are common, and measurements are often corrupted by instrumental noise. To address these challenges, we propose RECLAIM, a causal discovery framework that natively handles both cycles and measurement noise. RECLAIM learns the causal graph structure by maximizing the likelihood of the observed measurements via expectation-maximization (EM), using residual normalizing flows for tractable likelihood computation. We consider two measurement models: (i) Gaussian additive noise, and (ii) a linear measurement system with additive Gaussian noise. We provide theoretical consistency guarantees for both the settings. Experiments on synthetic data and real-world protein signaling datasets demonstrate the efficacy of the proposed method.

Probability theory has become the predominant framework for quantifying uncertainty across scientific and engineering disciplines, with a particular focus on measurement and control systems. However, the widespread reliance on simple Gaussian assumptions--particularly in control theory, manufacturing, and measurement systems--can result in incomplete representations and multistage lossy approximations of complex phenomena, including inaccurate propagation of uncertainty through multi stage processes. This work proposes a comprehensive yet computationally tractable framework for representing and propagating quantitative attributes arising in measurement systems using Probability Density Functions (PDFs). Recognizing the constraints imposed by finite memory in software systems, we advocate for the use of Gaussian Mixture Models (GMMs), a principled extension of the familiar Gaussian framework, as they are universal approximators of PDFs whose complexity can be tuned to trade off approximation accuracy against memory and computation. From both mathematical and computational perspectives, GMMs enable high performance and, in many cases, closed form solutions of essential operations in control and measurement. The paper presents practical applications within manufacturing and measurement contexts especially circular factory, demonstrating how the GMMs framework supports accurate representation and propagation of measurement uncertainty and offers improved accuracy--compared to the traditional Gaussian framework--while keeping the computations tractable.

Unlike most vision tasks that have per-sample ground-truth, image synthesis tasks target generating unseen data and hence are usually evaluated through a distributional distance between one set of real samples and another set of generated samples.

We consider the problem of designing a data-driven nonlinear state estimation (DANSE) method that uses (noisy) nonlinear measurements of a process whose underlying state transition model (STM) is unknown. Such a process is referred to as a model-free process. A recurrent neural network (RNN) provides parameters of a Gaussian prior that characterize the state of the model-free process, using all previous measurements at a given time point. In the case of DANSE, the measurement system was linear, leading to a closed-form solution for the state posterior. However, the presence of a nonlinear measurement system renders a closed-form solution infeasible. Instead, the second-order statistics of the state posterior are computed using the nonlinear measurements observed at the time point. We address the nonlinear measurements using a reparameterization trick-based particle sampling approach, and estimate the second-order statistics of the state posterior. The proposed method is referred to as particle-based DANSE (pDANSE). The RNN of pDANSE uses sequential measurements efficiently and avoids the use of computationally intensive sequential Monte-Carlo (SMC) and/or ancestral sampling. We describe the semi-supervised learning method for pDANSE, which transitions to unsupervised learning in the absence of labeled data. Using a stochastic Lorenz-$63$ system as a benchmark process, we experimentally demonstrate the state estimation performance for four nonlinear measurement systems. We explore cubic nonlinearity and a camera-model nonlinearity where unsupervised learning is used; then we explore half-wave rectification nonlinearity and Cartesian-to-spherical nonlinearity where semi-supervised learning is used. The performance of state estimation is shown to be competitive vis-à-vis particle filters that have complete knowledge of the STM of the Lorenz-$63$ system.

Solving inverse problems -- recovering signals from incomplete or noisy measurements -- is fundamental in science and engineering. Score-based generative models (SGMs) have recently emerged as a powerful framework for this task. Two main paradigms have formed: unsupervised approaches that adapt pretrained generative models to inverse problems, and supervised bridge methods that train stochastic processes conditioned on paired clean and corrupted data. While the former typically assume knowledge of the measurement model, the latter have largely overlooked this structural information. We introduce System embedded Diffusion Bridge Models (SDBs), a new class of supervised bridge methods that explicitly embed the known linear measurement system into the coefficients of a matrix-valued SDE. This principled integration yields consistent improvements across diverse linear inverse problems and demonstrates robust generalization under system misspecification between training and deployment, offering a promising solution to real-world applications.

Our presentation is organized for following reasons: In Section 2.3, we present the

Abstract-- Compared with gears and linkages, wires constitute a lightweight, low-friction transmission mechanism. However, because wires are flexible materials, they tend to introduce large modeling errors, and their adoption in industrial and research robots remains limited. In this study, we built a Universal Wire T esting Machine that enables measurement and adjustment of wire characteristics to improve the performance of wire-driven mechanisms. Using this testing machine, we carried out removal of initial wire stretch, measurement of tension transmission efficiency for eight different diameters of passive pulleys, and measurement of the dynamic behavior of variable-length wires. Finally, we applied the data obtained from this testing machine to the force control of an actual wire-driven robot, reducing the end-effector force error . Compared with gears and linkages, wires offer a low-friction, low-inertia transmission mechanism.

Rail and wheel interaction functionality is pivotal to the railway system safety, requiring accurate measurement systems for optimal safety monitoring operation. This paper introduces an innovative onboard measurement system for monitoring wheel flange wear depth, utilizing displacement and temperature sensors. Laboratory experiments are conducted to emulate wheel flange wear depth and surrounding temperature fluctuations in different periods of time. Employing collected data, the training of machine learning algorithms that are based on regression models, is dynamically automated. Further experimentation results, using standards procedures, validate the system's efficacy. To enhance accuracy, an infinite impulse response filter (IIR) that mitigates vehicle dynamics and sensor noise is designed. Filter parameters were computed based on specifications derived from a Fast Fourier Transform analysis of locomotive simulations and emulation experiments data. The results show that the dynamic machine learning algorithm effectively counter sensor nonlinear response to temperature effects, achieving an accuracy of 96.5 %, with a minimal runtime. The real-time noise reduction via IIR filter enhances the accuracy up to 98.2 %. Integrated with railway communication embedded systems such as Internet of Things devices, this advanced monitoring system offers unparalleled real-time insights into wheel flange wear and track irregular conditions that cause it, ensuring heightened safety and efficiency in railway systems operations.