Graph Coloring Approach to Solving Sudoku with Oscillatory Neural Networks

Oscillatory Neural Networks (ONNs) present an attractive physics-based computing paradigm rooted in the dynamics of a network of typically fully coupled oscillators aiming to minimize an underlying energy function. In this paper, we propose an ONN-based solver for one well-known constrained combinatorial optimization problem, namely a Sudoku, by formulating the problem as a Graph Coloring problem. By modifying the already existing Graph Coloring solver to a computationally cheaper version and introducing an additional term ensuring the fulfillment of the Sudoku constraints, our solver is shown to significantly outperform the existing HNN- and ONN solvers in terms of accuracy. In particular, we are able to achieve nearly flawless accuracies on $4 \times 4$ as well as rather high accuracies on $9 \times 9$ Sudoku puzzles for different numbers of unknown digits.

Is sub-metre resolution necessary for cocoa mapping? A landscape-stratified evaluation of very high resolution imagery, decametric Earth Observation inputs, and operational products in Cote d'Ivoire

Accurate cocoa mapping is increasingly important for deforestation monitoring, supply-chain transparency, and regulatory applications. Spatial aggregation in conventional medium-resolution Earth observation (EO) imagery may limit cocoa detection in heterogeneous smallholder landscapes. In Cote d'Ivoire, we therefore evaluated how mapping performance varies across landscape conditions, whether very high resolution (VHR) imagery provides a meaningful advantage, and whether foundation-model embeddings improve decametric cocoa mapping. We developed models using 0.5 m Pleiades VHR imagery, a 10 m Sentinel-2 annual composite, and embeddings from TESSERA and AlphaEarth Foundations (AEF), and additionally assessed four publicly available cocoa mapping products. Performance was evaluated through a landscape-stratified accuracy assessment using 2,821 independently interpreted reference points distributed across gradients of tree cover density and landscape fragmentation. The VHR model achieved the highest performance (F1 = 0.92) and maintained F1-scores above 0.90 across all strata. Among the decametric inputs, TESSERA performed best (F1 = 0.86), followed by AEF (F1 = 0.82) and Sentinel-2 (F1 = 0.76). Of the existing cocoa products, the Kalischek product performed best (F1 = 0.83), comparable to the internally trained AEF model. Performance differences between VHR and decametric approaches increased with fragmentation and under low and high tree cover density conditions. Targeted VHR acquisition may therefore be particularly beneficial in complex cocoa landscapes, while foundation-model embeddings offer a scalable alternative for large-area mapping.

Thermodynamics-Inspired Computing with Oscillatory Neural Networks for Inverse Matrix Computation

We describe a thermodynamic-inspired computing paradigm based on oscillatory neural networks (ONNs). While ONNs have been widely studied as Ising machines for tackling complex combinatorial optimization problems, this work investigates their feasibility in solving linear algebra problems, specifically the inverse matrix. Grounded in thermodynamic principles, we analytically demonstrate that the linear approximation of the coupled Kuramoto oscillator model leads to the inverse matrix solution. Numerical simulations validate the theoretical framework, and we examine the parameter regimes that computation has the highest accuracy.

From Rows to Yields: How Foundation Models for Tabular Data Simplify Crop Yield Prediction

We present an application of a foundation model for small- to medium-sized tabular data (TabPFN), to sub-national yield forecasting task in South Africa. TabPFN has recently demonstrated superior performance compared to traditional machine learning (ML) models in various regression and classification tasks. We used the dekadal (10-days) time series of Earth Observation (EO; FAPAR and soil moisture) and gridded weather data (air temperature, precipitation and radiation) to forecast the yield of summer crops at the sub-national level. The crop yield data was available for 23 years and for up to 8 provinces. Covariate variables for TabPFN (i.e., EO and weather) were extracted by region and aggregated at a monthly scale. We benchmarked the results of the TabPFN against six ML models and three baseline models. Leave-one-year-out cross-validation experiment setting was used in order to ensure the assessment of the models capacity to forecast an unseen year. Results showed that TabPFN and ML models exhibit comparable accuracy, outperforming the baselines. Nonetheless, TabPFN demonstrated superior practical utility due to its significantly faster tuning time and reduced requirement for feature engineering. This renders TabPFN a more viable option for real-world operation yield forecasting applications, where efficiency and ease of implementation are paramount.

Lagrange Oscillatory Neural Networks for Constraint Satisfaction and Optimization

Physics-inspired computing paradigms are receiving renewed attention to enhance efficiency in compute-intensive tasks such as artificial intelligence and optimization. Similar to Hopfield neural networks, oscillatory neural networks (ONNs) minimize an Ising energy function that embeds the solutions of hard combinatorial optimization problems. Despite their success in solving unconstrained optimization problems, Ising machines still face challenges with constrained problems as they can get stuck at infeasible local minima. In this paper, we introduce a Lagrange ONN (LagONN) designed to escape infeasible states based on the theory of Lagrange multipliers. Unlike existing oscillatory Ising machines, LagONN employs additional Lagrange oscillators to guide the system towards feasible states in an augmented energy landscape and settles only when constraints are met. Taking the maximum satisfiability problem with three literals as a use case (Max-3-SAT), we harness LagONN's constraint satisfaction mechanism to find optimal solutions for random SATlib instances with up to 200 variables and 860 clauses, which provides a deterministic alternative to simulated annealing for coupled oscillators. We further discuss the potential of Lagrange oscillators to address other constraints, such as phase copying, which is useful in oscillatory Ising machines with limited connectivity.

Ai4Fapar: How artificial intelligence can help to forecast the seasonal earth observation signal

This paper investigated the potential of a multivariate Transformer model to forecast the temporal trajectory of the Fraction of Absorbed Photosynthetically Active Radiation (FAPAR) for short (1 month) and long horizon (more than 1 month) periods at the regional level in Europe and North Africa. The input data covers the period from 2002 to 2022 and includes remote sensing and weather data for modelling FAPAR predictions. The model was evaluated using a leave one year out cross-validation and compared with the climatological benchmark. Results show that the transformer model outperforms the benchmark model for one month forecasting horizon, after which the climatological benchmark is better. The RMSE values of the transformer model ranged from 0.02 to 0.04 FAPAR units for the first 2 months of predictions. Overall, the tested Transformer model is a valid method for FAPAR forecasting, especially when combined with weather data and used for short-term predictions.

Convolutional Neural Networks for Global Human Settlements Mapping from Sentinel-2 Satellite Imagery

Spatially consistent and up-to-date maps of human settlements are crucial for addressing policies related to urbanization and sustainability especially in the era of an increasingly urbanized world. The availability of open and free Sentinel-2 data of the Copernicus Earth Observation programme offers a new opportunity for wall-to-wall mapping of human settlements at a global scale. This paper presents a deep-learning-based framework for a fully automated extraction of built-up areas at a spatial resolution of 10 meters from a global composite of Sentinel-2 imagery. A multi-neuro modelling methodology, building on a simple Convolution Neural Networks architecture for pixel-wise image classification of built-up areas is developed. The deployment of the model on the global Sentinel-2 image composite provides the most detailed and complete map reporting about built-up areas for reference year 2018. The validation of the results with an independent reference dataset of building footprints covering 277 sites across the world, establishes the reliability of the built-up layer produced by the proposed framework and the model robustness. The results of this study contribute to cutting-edge research in the field of automated built-up areas mapping from remote sensing data and establish a new reference layer for the analysis of the spatial distribution of human settlements across the rural-urban continuum