Open Access

Multispectral, non-commercial satellite data faces a tradeoff between spatial and temporal resolution. On the one hand, several sensors produce data with high spatial resolution, but have revisiting times of several days. On the other hand, multiple sensors provide more frequently updated images, but only at medium to low spatial resolutions. Super-resolution is a machine learning technique that can potentially bridge this gap by creating high resolution instances from the frequently updated but low-resolution images of satellites. In satellite imagery, this approach has so far been mostly used on optical RGB imagery. Here, we present a deep learning approach on satellite based super-resolution using ASTER and MODIS data, two multispectral sensors on board of the same NASA satellite “Terra”. Both have complementary properties: while MODIS produces daily updated images with medium to low resolutions between 250 and 1000m, ASTER measures the same area at least every 16 days with significantly higher resolutions of 30 to 90m. Since the two sensors are mounted on the same satellite, they can be combined to create high- and low-resolution image pairs for identical areas at identical times. We downloaded 50,000 10x10km image pairs for random, non-oceanic regions in Europe and the Mediterranean from Google Earth Engine. The resulting dataset was split, and 80% were employed to train a generative flow matching model using the MODIS images as guiding information for the generation process. After training, high-resolution instances of the remaining MODIS samples were created by averaging 50 generated instances of one scene. The Peak Signal-to-Noise Ratio (PSNR) and Structural Similarity Index Measure (SSIM) were calculated for model validation, showing significantly improved values compared to the baseline of bicubic interpolation. This highlights the potential of using inter-sensor image pairs for super-resolution in general. The resulting data of high temporal and spatial resolution is especially useful to monitor rapidly changing sceneries. We tested our model for several active wildfire occurrences, for which daily propagation was visible in MODIS, as well as in high-resolution Planet imagery. The resolution of the fire outlines was improved realistically, and the individually generated instances of each scene could be used to quantify the uncertainty of the burned area in the final high-resolution image.

With recent advances in generative machine learning, different models have been adapted to predict novel materials, and new architectures are emerging frequently. While several metrics allow for the rating of individual characteristics (e.g., quality or novelty) of generated crystal structures on an instance level, approaches that evaluate the general performance of generative models for materials prediction are missing. To close this gap, we developed the Transport Novelty Distance (TNovD). This metric evaluates generative models by jointly judging the novelty and quality of all newly generated crystal structures. Thereto, the Wasserstein distance is calculated on an abstract feature space distribution derived from the chemical and physical characteristics of the materials. These features are created by embedding the crystals description with an invariant Graph Neural Network (GNN) that was trained with the InfoNCE loss on the identical set of materials as the generative model. Using contrastive learning allows to not only account for materials themselves, but also for their augmented counterparts and differently sized supercells. Based on the resulting feature space, couplings between generated and train set are calculated and split into a quality and a memorization regime by a threshold. This allows to evaluate quality and novelty simultaneously. The TNovD was tested on various toy experiments for memorization and different cases of crystal structure degeneration. Additionally, we validated it on the MP20 validation set and the WBM substitution dataset. The experiments results demonstrate the TNovD capabilities of detecting both memorization and low-quality materials. Afterwards, we benchmark the performance of several popular material generative models with the MP20 validation data. While introduced for materials, our TNovD framework is domain-agnostic and can be adapted for other areas in the space of chemical compounds, such as images and molecules.

Recent advances in generative machine learning have opened new possibilities for the discovery and design of novel materials. However, as these models become more sophisticated, the need for rigorous and meaningful evaluation metrics has grown. Existing evaluation approaches often fail to capture both the quality and novelty of generated structures, limiting our ability to assess true generative performance. In this paper, we introduce the Transport Novelty Distance (TNovD) to judge generative models used for materials discovery jointly by the quality and novelty of the generated materials. Based on ideas from optimal transport theory, TNovD uses a coupling between the features of the training and generated sets, which is used to penalize quality and memorization independently. The two regimes are defined by thresholding the pairwise distances of trained and generated features. The features are generated from crystal structures using a graph neural network that is trained to distinguish between materials, their augmented counterparts, and differently sized supercells using contrastive learning. We evaluate our proposed metric on typical toy experiments relevant for crystal structure prediction, including memorization, noise injection and lattice deformations. Additionally, we validate the TNovD on the MP20 validation set and the WBM substitution dataset, demonstrating that it is capable of detecting both memorized structures and unrealistic material representations that are outside of the training data distribution. We also benchmark the performance of several popular material generative models. While introduced for materials, our TNovD framework is domain-agnostic and can be adapted for other areas, such as images and molecules.

Environmental and scarcity issues of common functional magnetic materials for, e.g., permanent magnets have intensified the search for rare-earth-free alternatives. This challenge is increasingly met by machine learning of magnetic properties of transition-metal compounds. Surprisingly, bond-angle-derived features were not found to be relevant for magnetic structure prediction in previous studies using DFT-computed labels. This contrasts with the Kanamori-Goodenough-Anderson (KGA) rules of superexchange, present in every magnetism textbook. These semiempirical rules predict whether a nearest-neighbor magnetic interaction in insulators is FM or AFM based on the bond angle, orbital symmetry, and orbital occupancy. For some cases, the rules can be simplified further to only consider the bond angle of neighboring magnetic sites (KGA rules of thumb). We review magnetism—bond angle trends within the MAGNDATA database, the largest collection of experimentally determined magnetic structures. Observed trends follow the KGA rules of thumb, and exceptions can be rationalized. In contrast, bond angles in a popular theoretical DFT database show very different trends and do not depend on the magnetic ordering. Building on our analysis, we engineer heuristic-derived features for the machine learning of magnetic structures. We introduce a new, informative label for predicting magnetic structures that can be extended to magnetic sites and structures of arbitrary complexity. We show that features derived from the heuristic are of high importance for this machine learning task. Beyond this, our model enables the prediction of non-collinear magnetic structures. Further, we analyze local and global structural trends of non-collinear magnets in the MAGNDATA database.

Environmental and scarcity issues of common functional magnetic materials for, e.g., permanent magnets have intensified the search for rare-earth-free alternatives. This challenge is increasingly met by machine learning of magnetic properties of transition-metal compounds. Surprisingly, bond-angle-derived features were not found to be relevant for magnetic structure prediction in previous studies using DFT-computed labels. This contrasts with the Kanamori-Goodenough-Anderson (KGA) rules of superexchange, present in every magnetism textbook. These semiempirical rules predict whether a nearest-neighbor magnetic interaction in insulators is FM or AFM based on the bond angle, orbital symmetry, and orbital occupancy. For some cases, the rules can be simplified further to only consider the bond angle of neighboring magnetic sites (KGA rules of thumb). We review magnetism—bond angle trends within the MAGNDATA database, the largest collection of experimentally determined magnetic structures. Observed trends follow the KGA rules of thumb, and exceptions can be rationalized. In contrast, bond angles in a popular theoretical DFT database show very different trends and do not depend on the magnetic ordering. Building on our analysis, we engineer heuristic-derived features for the machine learning of magnetic structures. We introduce a new, informative label for predicting magnetic structures that can be extended to magnetic sites and structures of arbitrary complexity. We show that features derived from the heuristic are of high importance for this machine learning task. Beyond this, our model enables the prediction of non-collinear magnetic structures. Further, we analyze local and global structural trends of non-collinear magnets in the MAGNDATA database.