We address the problem of denoising data from a Gaussian mixture using a two-layer non-linear autoencoder with tied weights and a skip connection.

Most knowledge graphs (KGs) are incomplete, which motivates one important research topic on automatically complementing knowledge graphs.

Numerical simulations have revolutionized the industrial design process by reducing prototyping costs, design iterations, and enabling product engineers to explore the design space more efficiently. However, the growing scale of simulations demands substantial expert knowledge, computational resources, and time. A key challenge is identifying input parameters that yield optimal results, as iterative simulations are costly and can have a large environmental impact. This paper presents an AI-assisted workflow that reduces expert involvement in parameter optimization through the use of Bayesian optimization. Furthermore, we present an active learning variant of the approach, assisting the expert if desired. A deep learning model provides an initial parameter estimate, from which the optimization cycle iteratively refines the design until a termination condition (e.g., energy budget or iteration limit) is met. We demonstrate our approach, based on a sheet metal forming process, and show how it enables us to accelerate the exploration of the design space while reducing the need for expert involvement.

Deterministic Lateral Displacement (DLD) devices are widely used in microfluidics for label-free, size-based separation of particles and cells, with particular promise in isolating circulating tumor cells (CTCs) for early cancer diagnostics. This study focuses on the optimization of DLD design parameters, such as row shift fraction, post size, and gap distance, to enhance the selective isolation of lung cancer cells based on their physical properties. To overcome the challenges of rare CTC detection and reduce reliance on computationally intensive simulations, machine learning models including gradient boosting, k-nearest neighbors, random forest, and multilayer perceptron (MLP) regressors are employed. Trained on a large, numerically validated dataset, these models predict particle trajectories and identify optimal device configurations, enabling high-throughput and cost-effective DLD design. Beyond trajectory prediction, the models aid in isolating critical design variables, offering a systematic, data-driven framework for automated DLD optimization. This integrative approach advances the development of scalable and precise microfluidic systems for cancer diagnostics, contributing to the broader goals of early detection and personalized medicine.

High-resolution imaging from array data in unknown inhomogeneous ambient media requires estimating both the medium properties and the object characteristics. For diverse measurements collected from different sources in different, changing media, we introduce in this paper an algorithm that recovers the ambient media properties needed for high-resolution imaging as well as the source locations and strengths that constitute the imaging target. This algorithm extends and improves upon our previous work on imaging through random media using array data. Previously, we addressed imaging through a single unknown random medium, either weakly scattering [ 1 ] or strongly scattering [ 2 ].

Reservoir computing is a powerful framework for real-time information processing, characterized by its high computational ability and quick learning, with applications ranging from machine learning to biological systems. In this paper, we investigate how the computational ability of reservoir recurrent neural networks (RNNs) scales with an increasing number of readout neurons. First, we demonstrate that the memory capacity of a reservoir RNN scales sublinearly with the number of readout neurons. To elucidate this observation, we develop a theoretical framework for analytically deriving memory capacity that incorporates the effect of neuronal correlations, which have been ignored in prior theoretical work for analytical simplicity. Our theory successfully relates the sublinear scaling of memory capacity to the strength of neuronal correlations. Furthermore, we show this principle holds across diverse types of RNNs, even those beyond the direct applicability of our theory. Next, we numerically investigate the scaling behavior of nonlinear computational ability, which, alongside memory capacity, is crucial for overall computational performance. Our numerical simulations reveal that as memory capacity growth becomes sublinear, increasing the number of readout neurons successively enables nonlinear processing at progressively higher polynomial orders. Our theoretical framework suggests that neuronal correlations govern not only memory capacity but also the sequential growth of nonlinear computational capabilities. Our findings establish a foundation for designing scalable and cost-effective reservoir computing, providing novel insights into the interplay among neuronal correlations, linear memory, and nonlinear processing.

One of the most surprising empirical observations in deep learning is the generalization of overpa-rameterized models that can perfectly interpolate the data. The "double descent" curve, referring to the test error first increasing then decreasing with model complexity, has been both empirically and

Data-driven acceleration of scientific computing workflows has been a high-profile aim of machine learning (ML) for science, with numerical simulation of transient partial differential equations (PDEs) being one of the main applications. The focus thus far has been on methods that require classical simulations to train, which when combined with the data-hungriness and optimization challenges of neural networks has caused difficulties in demonstrating a convincing advantage against strong classical baselines. We consider an alternative paradigm in which the learner uses a classical solver's own data to accelerate it, enabling a one-shot speedup of the simulation. Concretely, since transient PDEs often require solving a sequence of related linear systems, the feedback from repeated calls to a linear solver such as preconditioned conjugate gradient (PCG) can be used by a bandit algorithm to online-learn an adaptive sequence of solver configurations (e.g. preconditioners). The method we develop, PCGBandit, is implemented directly on top of the popular open source software OpenFOAM, which we use to show its effectiveness on a set of fluid and magnetohydrodynamics (MHD) problems.