Scientific imaging often involves long acquisition times to obtain high-quality data, especially when probing complex, heterogeneous systems. However, reducing acquisition time to increase throughput inevitably introduces significant noise into the measurements. We present a machine learning approach that not only denoises low-quality measurements with calibrated uncertainty bounds, but also reveals emergent structure in the latent space. By using ensembles of lightweight, randomly structured neural networks trained via conformal quantile regression, our method performs reliable denoising while uncovering interpretable spatial and chemical features – without requiring labels or segmentation. Unlike conventional approaches focused solely on image restoration, our framework leverages the denoising process itself to drive the emergence of meaningful representations. We validate the approach on real-world geobiochemical imaging data, showing how it supports confident interpretation and guides experimental design under resource constraints.

A mathematical model and numerical framework are presented for computing multi-physics multi-layer coating flow dynamics, with applications to the leveling of multi-layer paint films. The algorithm combines finite difference level set methods and high-order accurate sharp-interface implicit mesh discontinuous Galerkin methods to capture a complex set of multi-physics, incorporating Marangoni-driven multi-phase interfacial flow and the transport, mixing, and evaporation of multiple dissolved species. In particular, we develop several numerical methods for this multi-physics problem, including: high-order local discontinuous Galerkin methods for Poisson problems with Robin boundary conditions on implicitly-defined domains, to capture solvent evaporation; finite difference surface gradient methods, to robustly and accurately incorporate Marangoni stresses; and a coupled multi-physics time stepping approach, to incorporate all the different solvers at play including quasi-Newtonian fluid flow. The framework is applicable to an arbitrary number of layers and dissolved species; here, we apply it in a variety of settings, including multi-solvent evaporative paint dynamics, the flow and leveling of multi-layer automobile paint coatings in both 2D and 3D, and an examination of interfacial turbulence within a multi-layer matter cascade. Our results reproduce several phenomena observed in experiment, such as the formation of Marangoni plumes and Bénard cells. We also use the model to study the impact of long-wave deformational surface modes on immersed interfaces as well as the emergence of the final multi-layer film profile.

Flatbed scanners are commonly used for root analysis, but typical manual segmentation methods are time-consuming and prone to errors, especially in large-scale, multi-plant studies. Furthermore, the complex nature of root structures combined with noisy backgrounds in images complicates automated analysis. Addressing these challenges, this article introduces RhizoNet, a deep learning-based workflow to semantically segment plant root scans. Utilizing a sophisticated Residual U-Net architecture, RhizoNet enhances prediction accuracy and employs a convex hull operation for delineation of the primary root component. Its main objective is to accurately segment root biomass and monitor its growth over time. RhizoNet processes color scans of plants grown in a hydroponic system known as EcoFAB, subjected to specific nutritional treatments. The root detection model using RhizoNet demonstrates strong generalization in the validation tests of all experiments despite variable treatments. The main contributions are the standardization of root segmentation and phenotyping, systematic and accelerated analysis of thousands of images, significantly aiding in the precise assessment of root growth dynamics under varying plant conditions, and offering a path toward self-driving labs.

ABSTRACTDigital cameras have the ability to capture daily images of plant roots, allowing for the estimation of root biomass. However, the complexities of root structures and noisy image backgrounds pose challenges for advanced phenotyping. Manual segmentation methods are laborious and prone to errors, which hinders experiments involving several plants. This paper introduces Rhizonet, a supervised deep learning approach for semantic segmentation of plant root images. Rhizonet harnesses a Residual U-Net backbone to enhance prediction accuracy, incorporating a convex hull operation to precisely outline the largest connected component. The primary objective is to accurately segment the biomass of the roots and analyze their growth over time. The input data comprises color images of various plant samples within a hydroponic environment known as EcoFAB, subject to specific nutrition treatments. Validation tests demonstrate the robust generalization of the model across experiments. This research pioneers advances in root segmentation and phenotype analysis by standardizing processes and facilitating the analysis of thousands of images while reducing subjectivity. The proposed root segmentation algorithms contribute significantly to the precise assessment of the dynamics of root growth under diverse plant conditions.

The global automotive industry sprayed over 2.6 billion liters of paint in 2018, much of which through electrostatic rotary bell atomization, a highly complex process involving the fluid mechanics of rapidly rotating thin films tearing apart into micrometer-thin filaments and droplets. Coating operations account for 65% of the energy usage in a typical automotive assembly plant, representing 10,000s of gigawatt-hours each year in the United States alone. Optimization of these processes would allow for improved robustness, reduced material waste, increased throughput, and significantly reduced energy usage. Here, we introduce a high-fidelity mathematical and algorithmic framework to analyze rotary bell atomization dynamics at industrially relevant conditions. Our approach couples laboratory experiment with the development of robust non-Newtonian fluid models; devises high-order accurate numerical methods to compute the coupled bell, paint, and gas dynamics; and efficiently exploits high-performance supercomputing architectures. These advances have yielded insight into key dynamics, including i) parametric trends in film, sheeting, and filament characteristics as a function of fluid rheology, delivery rates, and bell speed; ii) the impact of nonuniform film thicknesses on atomization performance; and iii) an understanding of spray composition via primary and secondary atomization. These findings result in coating design principles that are poised to improve energy- and cost-efficiency in a wide array of industrial and manufacturing settings.

Host cell invasion by intracellular, eukaryotic parasites, like the many important species within the phylum Api-complexa, is a remarkable and active process involving the coordinated action of many apical organelles and other structures. To date, capturing how these various structures interact during invasion has been difficult to observe in detail. Here, we used cryogenic electron tomography to generate images of the apical complex of Toxoplasma gondii tachyzoites under conditions that mimic resting parasites and those primed to invade through addition of a calcium ionophore. Using AI-based image-processing we were able to annotate 48 tomograms to identify and extract densities of the relevant subcellular organelles and accurately analyze features in 3D. We describe an interaction between an anteriorly located apical vesicle and a rhoptry tip that occurs only in the ionophore-stimulated parasites and that is associated with dramatic changes in the vesicle’s shape in what appears to be a stalled fusion event. We also present information to support the presumption that this vesicle originates from the well-described vesicles that parallel the intraconoidal microtubules and that the latter two structures are linked by a novel tether. Lastly, we show that a previously described rosette is found associated with more than just the anterior-most apical vesicle, indicating that multiple such vesicles are primed to enable rhoptry secretion.

X-ray tomography is widely used for three-dimensional structure determination in many areas of science, from the millimeter to the nanometer scale. The resolution and quality of the 3D reconstruction is limited by the availability of alignment parameters that correct for the mechanical shifts of the sample or sample stage for the images that constitute a scan. In this paper we describe an algorithm for marker-free, fully automated and accurately aligned and reconstructed X-ray tomography data. Our approach solves the tomographic reconstruction jointly with projection data alignment based on a rigid-body deformation model. We demonstrate the robustness of our method on both synthetic phantom and experimental data and show that our method is highly efficient in recovering relatively large alignment errors without prior knowledge of a low resolution approximation of the 3D structure or a reasonable estimate of alignment parameters.

Host cell invasion by intracellular, eukaryotic parasites within the phylum Apicomplexa is a remarkable and active process involving the coordinated action of apical organelles and other structures. To date, capturing how these structures interact during invasion has been difficult to observe in detail. Here, we used cryogenic electron tomography to image the apical complex of Toxoplasma gondii tachyzoites under conditions that mimic resting parasites and those primed to invade through stimulation with calcium ionophore. Through the application of mixed-scale dense networks for image processing, we developed a highly efficient pipeline for annotation of tomograms, enabling us to identify and extract densities of relevant subcellular organelles and accurately analyze features in 3-D. The results reveal a dramatic change in the shape of the anteriorly located apical vesicle upon its apparent fusion with a rhoptry that occurs only in the stimulated parasites. We also present information indicating that this vesicle originates from the vesicles that parallel the intraconoidal microtubules and that the latter two structures are linked by a novel tether. We show that a rosette structure previously proposed to be involved in rhoptry secretion is associated with apical vesicles beyond just the most anterior one. This result, suggesting multiple vesicles are primed to enable rhoptry secretion, may shed light on the mechanisms Toxoplasma employs to enable repeated invasion attempts. Using the same approach, we examine Plasmodium falciparum merozoites and show that they too possess an apical vesicle just beneath a rosette, demonstrating evolutionary conservation of this overall subcellular organization.

The physical sciences community is increasingly taking advantage of the possibilities offered by modern data science to solve problems in experimental chemistry and potentially to change the way we design, conduct and understand results from experiments. Successfully exploiting these opportunities involves considerable challenges. In this Expert Recommendation, we focus on experimental co-design and its importance to experimental chemistry. We provide examples of how data science is changing the way we conduct experiments, and we outline opportunities for further integration of data science and experimental chemistry to advance these fields. Our recommendations include establishing stronger links between chemists and data scientists; developing chemistry-specific data science methods; integrating algorithms, software and hardware to ‘co-design’ chemistry experiments from inception; and combining diverse and disparate data sources into a data network for chemistry research.

Gaussian process regression is a widely-applied method for function approximation and uncertainty quantification. The technique has gained popularity recently in the machine learning community due to its robustness and interpretability. The mathematical methods we discuss in this paper are an extension of the Gaussian-process framework. We are proposing advanced kernel designs that only allow for functions with certain desirable characteristics to be elements of the reproducing kernel Hilbert space (RKHS) that underlies all kernel methods and serves as the sample space for Gaussian process regression. These desirable characteristics reflect the underlying physics; two obvious examples are symmetry and periodicity constraints. In addition, non-stationary kernel designs can be defined in the same framework to yield flexible multi-task Gaussian processes. We will show the impact of advanced kernel designs on Gaussian processes using several synthetic and two scientific data sets. The results show that including domain knowledge, communicated through advanced kernel designs, has a significant impact on the accuracy and relevance of the function approximation.

Host cell invasion by intracellular, eukaryotic parasites within the phylum Apicomplexa, is a remarkable and active process involving the coordinated action of apical organelles and other structures. To date, capturing how these structures interact during invasion has been difficult to observe in detail. Here, we used cryogenic electron tomography to image the apical complex of Toxoplasma gondii tachyzoites under conditions that mimic resting parasites and those primed to invade through stimulation with calcium ionophore. Through the application of Mixed Scale Dense networks for image-processing, we developed a highly efficient pipeline for annotation of tomograms, enabling us to identify and extract densities of relevant subcellular organelles and accurately analyze features in 3D. The results reveal a dramatic change in the shape of the anteriorly located apical vesicle upon its apparent fusion with a rhoptry, that occurs only in the stimulated parasites. We also present information indicating that this vesicle originates from the vesicles that parallel the intraconoidal microtubules and that the latter two structures are linked by a novel tether. We show that a rosette structure previously proposed to be involved in rhoptry secretion is associated with apical vesicles beyond just the most anterior one. This result, suggesting multiple vesicles are primed to enable rhoptry secretion, may shed light on the mechanisms Toxoplasma employs to enable repeated invasion attempts. Using the same approach, we examine Plasmodium falciparum merozoites and show that they too possess an apical vesicle just beneath a rosette, demonstrating evolutionary conservation of this overall subcellular organization. Significance Statement Parasites in the phylum Apicomplexa are responsible for some of the most important parasitic diseases of humans, such as malaria and toxoplasmosis. Invasion by these obligatory, intracellular parasites depends on protein injection into the host cell. Using cryogenic electron tomography, we reveal evolutionarily conserved features shared by the invasive forms of Plasmodium falciparum and Toxoplasma gondii . By comparing resting Toxoplasma tachyzoites with those primed to invade we also gain new insight into the very first steps in invasion. For this work, we take an interdisciplinary approach, adopting a mixed-scale dense neural network that enables efficient and objective processing of the data. Combined, the results provide new information on how these important parasites accomplish the essential step of invasion.

Moving interfaces are key components of many dynamic industrial processes, in which complex interface physics determine much of the underlying action and performance. Level set methods, and their descendents, have been valuable in providing robust mathematical formulations and numerical algorithms for tracking the dynamics of these evolving interfaces. In manufacturing applications, these methods have shed light on a variety of industrial processes, including the design of industrial inkjet plotters, the mechanics of electrojetting, shape and evolution in industrial foams, and rotary bell devices in automotive painting. In this review, we discuss some of those applications, illustrating shared algorithmic challenges, and show how to tailor these methods to meet those challenges.

The execution and analysis of complex experiments are challenged by the vast dimensionality of the underlying parameter spaces. Although an increase in data-acquisition rates should allow broader querying of the parameter space, the complexity of experiments and the subtle dependence of the model function on input parameters remains daunting owing to the sheer number of variables. New strategies for autonomous data acquisition are being developed, with one promising direction being the use of Gaussian process regression (GPR). GPR is a quick, non-parametric and robust approximation and uncertainty quantification method that can be applied directly to autonomous data acquisition. We review GPR-driven autonomous experimentation and illustrate its functionality using real-world examples from large experimental facilities in the USA and France. We introduce the basics of a GPR-driven autonomous loop with a focus on Gaussian processes, and then shift the focus to the infrastructure that needs to be built around GPR to create a closed loop. Finally, the case studies we discuss show that Gaussian-process-based autonomous data acquisition is a widely applicable method that can facilitate the optimal use of instruments and facilities by enabling the efficient acquisition of high-value datasets. Gaussian process regression (GPR) is a powerful, non-parametric and robust technique for uncertainty quantification and function approximation that can be applied to optimal and autonomous data acquisition. This Review introduces the basics of GPR and discusses several use cases from different fields.

Coefficients for translational and rotational diffusion characterize the Brownian motion of particles. Emerging X-ray photon correlation spectroscopy (XPCS) experiments probe a broad range of length scales and time scales and are well-suited for investigation of Brownian motion. While methods for estimating the translational diffusion coefficients from XPCS are well-developed, there are no algorithms for measuring the rotational diffusion coefficients based on XPCS, even though the required raw data are accessible from such experiments. In this paper, we propose angular-temporal cross-correlation analysis of XPCS data and show that this information can be used to design a numerical algorithm (Multi-Tiered Estimation for Correlation Spectroscopy [MTECS]) for predicting the rotational diffusion coefficient utilizing the cross-correlation: This approach is applicable to other wavelengths beyond this regime. We verify the accuracy of this algorithmic approach across a range of simulated data.

The Center for Advanced Mathematics for Energy Research Applications (CAMERA) is an integrated, cross-disciplinary center aimed at inventing, developing, and delivering the fundamental new mathematics required to capitalize on experimental investigations at scientific facilities. Jointly funded by the Office of Advanced Scientific Computing Research (ASCR) and the Office of Basic Energy Sciences (BES) within the US Department of Energy’s Office of Science, CAMERA identifies areas in experimental science that can be aided by new mathematical insights, develops the needed algorithmic tools, and delivers them as user-friendly software to the experimental community.

Droplet pairs interact when exposed to electric fields, being crucial parameters in this process the initial droplet separations and the electric field intensity. We present an algorithm for the evolution of perfectly conducting and non-viscous fluids using a level set technique. Topological changes of the free boundary are automatically included in the formulation and passing through singular times is computationally possible. Numerical results on electro-hydrodynamic droplet pairs reveal three different types of droplets evolution: droplets do not coalesce, droplets coalesce, and droplets recoil after contact failing to coalesce. A comparison of numerical results with laboratory experiments is also addressed.