We present a data-efficient, multiscale framework for predicting the density profiles of confined fluids at the nanoscale. While accurate density estimates require prohibitively long timescales that are inaccessible by ab initio molecular dynamics (AIMD) simulations, machine-learned molecular dynamics (MLMD) offers a scalable alternative, enabling the generation of force predictions at ab initio accuracy with reduced computational cost. However, despite their efficiency, MLMD simulations remain constrained by femtosecond timesteps, which limit their practicality for computing long-time averages needed for accurate density estimation. To address this, we propose a conditional denoising diffusion probabilistic model (DDPM) based quasi-continuum approach that predicts the long-time behavior of force profiles along the confinement direction, conditioned on noisy forces extracted from a limited AIMD dataset. The predicted smooth forces are then linked to continuum theory via the Nernst-Planck equation to reveal the underlying density behavior. We test the framework on water confined between two graphene nanoscale slits and demonstrate that density profiles for channel widths outside of the training domain can be recovered with ab initio accuracy. Compared to AIMD and MLMD simulations, our method achieves orders-of-magnitude speed-up in runtime and requires significantly less training data than prior works.

Electron density prediction stands as a cornerstone challenge in molecular systems, pivotal for various applications such as understanding molecular interactions and conducting precise quantum mechanical calculations. However, the scaling of density functional theory (DFT) calculations is prohibitively expensive. Machine learning methods provide an alternative, offering efficiency and accuracy. We introduce a novel SE(3)-equivariant architecture, drawing inspiration from Slater-Type Orbitals (STO), to learn representations of molecular electronic structures. Our approach offers an alternative functional form for learned orbital-like molecular representation. We showcase the effectiveness of our method by achieving SOTA prediction accuracy of molecular electron density with 30-70\% improvement over other work on Molecular Dynamics data.

Hybrid modeling aims to augment traditional theory-driven models with machine learning components that learn unknown parameters, sub-models or correction terms from data. In this work, we build on FluxRGNN, a recently developed hybrid model of continental-scale bird migration, which combines a movement model inspired by fluid dynamics with recurrent neural networks that capture the complex decision-making processes of birds. While FluxRGNN has been shown to successfully predict key migration patterns, its spatial resolution is constrained by the typically sparse observations obtained from weather radars. Additionally, its trainable components lack explicit incentives to adequately predict take-off and landing events. Both aspects limit our ability to interpret model results ecologically. To address this, we propose two major modifications that allow for more detailed predictions on any desired tessellation while providing control over the interpretability of model components. In experiments on the U.S. weather radar network, the enhanced model effectively leverages the underlying movement model, resulting in strong extrapolation capabilities to unobserved locations.

Drawing inspiration from the domain of image super-resolution, we view the electron density as a 3D grayscale image and use a convolutional residual network to transform a crude and trivially generated guess of the molecular density into an accurate ground-state quantum mechanical density. We find that this model outperforms all prior density prediction approaches. Because the input is itself a real-space density, the predictions are equivariant to molecular symmetry transformations even though the model is not constructed to be. Due to its simplicity, the model is directly applicable to unseen molecular conformations and chemical elements. We show that fine-tuning on limited new data provides high accuracy even in challenging cases of exotic elements and charge states. Our work suggests new routes to learning real-space physical quantities drawing from the established ideas of image processing.

Accurate estimation of thermospheric density is critical for precise modeling of satellite drag forces in low Earth orbit (LEO). Improving this estimation is crucial to tasks such as state estimation, collision avoidance, and re-entry calculations. The largest source of uncertainty in determining thermospheric density is modeling the effects of space weather driven by solar and geomagnetic activity. Current operational models rely on ground-based proxy indices which imperfectly correlate with the complexity of solar outputs and geomagnetic responses. In this work, we directly incorporate NASA's Solar Dynamics Observatory (SDO) extreme ultraviolet (EUV) spectral images into a neural thermospheric density model to determine whether the predictive performance of the model is increased by using space-based EUV imagery data instead of, or in addition to, the ground-based proxy indices. We demonstrate that EUV imagery can enable predictions with much higher temporal resolution and replace ground-based proxies while significantly increasing performance relative to current operational models. Our method paves the way for assimilating EUV image data into operational thermospheric density forecasting models for use in LEO satellite navigation processes.

Purpose: High breast density is associated with reduced efficacy of mammographic screening and increased risk of developing breast cancer. Accurate and reliable automated density estimates can be used for direct risk prediction and passing density related information to further predictive models. Expert reader assessments of density show a strong relationship to cancer risk but also inter-reader variation. The effect of label variability on model performance is important when considering how to utilise automated methods for both research and clinical purposes. Methods: We utilise subsets of images with density labels to train a deep transfer learning model which is used to assess how label variability affects the mapping from representation to prediction. We then create two end-to-end deep learning models which allow us to investigate the effect of label variability on the model representation formed. Results: We show that the trained mappings from representations to labels are altered considerably by the variability of reader scores. Training on labels with distribution variation removed causes the Spearman rank correlation coefficients to rise from $0.751\pm0.002$ to either $0.815\pm0.006$ when averaging across readers or $0.844\pm0.002$ when averaging across images. However, when we train different models to investigate the representation effect we see little difference, with Spearman rank correlation coefficients of $0.846\pm0.006$ and $0.850\pm0.006$ showing no statistically significant difference in the quality of the model representation with regard to density prediction. Conclusions: We show that the mapping between representation and mammographic density prediction is significantly affected by label variability. However, the effect of the label variability on the model representation is limited.

Round particles and their properties are easy to describe mathematically. But the less round or spherical the shape, the harder it becomes to make predictions about their behavior. In his doctoral thesis at the Technical University of Kaiserslautern (TUK), Robert Hesse has trained a neural network to automatically determine the packing density and flowability of non-spherical particles. Few particles in nature or in industrial production are exactly round; instead, there are a multitude of variants and shape characteristics. This is exactly what makes it so complicated to describe non-spherical particles and optimize their handling based on the description.

Counting people in dense crowds is a demanding task even for humans. This is primarily due to the large variability in appearance of people. Often people are only seen as a bunch of blobs. Occlusions, pose variations and background clutter further compound the difficulty. In this scenario, identifying a person requires larger spatial context and semantics of the scene. But the current state-of-the-art CNN regressors for crowd counting are feedforward and use only limited spatial context to detect people. They look for local crowd patterns to regress the crowd density map, resulting in false predictions. Hence, we propose top-down feedback to correct the initial prediction of the CNN. Our architecture consists of a bottom-up CNN along with a separate top-down CNN to generate feedback. The bottom-up network, which regresses the crowd density map, has two columns of CNN with different receptive fields. Features from various layers of the bottom-up CNN are fed to the top-down network. The feedback, thus generated, is applied on the lower layers of the bottom-up network in the form of multiplicative gating. This masking weighs activations of the bottom-up network at spatial as well as feature levels to correct the density prediction. We evaluate the performance of our model on all major crowd datasets and show the effectiveness of top-down feedback.