Simon Becker

Joana Reuss, Jan Macdonald, Simon Becker et al.

We introduce EuroCropsML, an analysis-ready remote sensing machine learning dataset for time series crop type classification of agricultural parcels in Europe. It is the first dataset designed to benchmark transnational few-shot crop type classification algorithms that supports advancements in algorithmic development and research comparability. It comprises 706 683 multi-class labeled data points across 176 classes, featuring annual time series of per-parcel median pixel values from Sentinel-2 L1C data for 2021, along with crop type labels and spatial coordinates. Based on the open-source EuroCrops collection, EuroCropsML is publicly available on Zenodo.

Simon Becker, Carsten Hartmann

Along the ideas of Curtain and Glover, we extend the balanced truncation method for infinite-dimensional linear systems to bilinear and stochastic systems. Specifically , we apply Hilbert space techniques used in many-body quantum mechanics to establish error bounds for the truncated system and prove convergence results. The functional analytic setting allows us to obtain mixed Hardy space error bounds for both finite-and infinite-dimensional systems, and it is then applied to the model reduction of stochastic evolution equations driven by Wiener noise.

Joana Reuss, Jan Macdonald, Simon Becker et al.

Accurate crop-type classification from satellite time series is essential for agricultural monitoring. While various machine learning algorithms have been developed to enhance performance on data-scarce tasks, their evaluation often lacks real-world scenarios. Consequently, their efficacy in challenging practical applications has not yet been profoundly assessed. To facilitate future research in this domain, we present the first comprehensive benchmark for evaluating supervised and SSL methods for crop-type classification under real-world conditions. This benchmark study relies on the EuroCropsML time-series dataset, which combines farmer-reported crop data with Sentinel-2 satellite observations from Estonia, Latvia, and Portugal. Our findings indicate that MAML-based meta-learning algorithms achieve slightly higher accuracy compared to supervised transfer learning and SSL methods. However, compared to simpler transfer learning, the improvement of meta-learning comes at the cost of increased computational demands and training time. Moreover, supervised methods benefit most when pre-trained and fine-tuned on geographically close regions. In addition, while SSL generally lags behind meta-learning, it demonstrates advantages over training from scratch, particularly in capturing fine-grained features essential for real-world crop-type classification, and also surpasses standard transfer learning. This highlights its practical value when labeled pre-training crop data is scarce. Our insights underscore the trade-offs between accuracy and computational demand in selecting supervised machine learning methods for real-world crop-type classification tasks and highlight the difficulties of knowledge transfer across diverse geographic regions. Furthermore, they demonstrate the practical value of SSL approaches when labeled pre-training crop data is scarce.

Simon Becker, Yao Zhang, Alpha A. Lee

Deep neural networks are workhorse models in machine learning with multiple layers of non-linear functions composed in series. Their loss function is highly non-convex, yet empirically even gradient descent minimisation is sufficient to arrive at accurate and predictive models. It is hitherto unknown why are deep neural networks easily optimizable. We analyze the energy landscape of a spin glass model of deep neural networks using random matrix theory and algebraic geometry. We analytically show that the multilayered structure holds the key to optimizability: Fixing the number of parameters and increasing network depth, the number of stationary points in the loss function decreases, minima become more clustered in parameter space, and the tradeoff between the depth and width of minima becomes less severe. Our analytical results are numerically verified through comparison with neural networks trained on a set of classical benchmark datasets. Our model uncovers generic design principles of machine learning models.