Abteilung Systemanalyse, Integrated Assessment und Modellierung

We review the main methods used to study spin glasses. In the first part, we focus on methods for fully connected models and systems defined on a tree. These include the replica method, the Thouless-Anderson-Palmer formalism, the cavity method, and the dynamical mean-field theory. In the second part, we deal with the description of low-dimensional systems, mostly in three spatial dimensions, which are mostly studied through numerical simulations. We conclude by mentioning some of the main open problems in the field.

Weunveil the multifractal behavior of Ising spin glasses in their low-temperature phase. Using the Janus II custom-built supercomputer, the spin-glass correlation function is studied locally. Dramatic fluctuations are found when pairs of sites at the same distance are compared. The scaling of these fluctuations, as the spin-glass coherence length grows with time, is characterized through the computation of the singularity spectrum and its corresponding Legendre transform. A comparatively small number of site pairs controls the average correlation that governs the response to a magnetic field. We explain how this scenario of dramatic fluctuations (at length scales smaller than the coherence length) can be reconciled with the smooth, self-averaging behavior that has long been considered to describe spin-glass dynamics.

Understanding and controlling biasing effects in neural networks is crucial for ensuring accurate and fair model performance. In the context of classification problems, we derive a theoretical analysis demonstrating that the structure of a deep neural network (DNN) can condition the model to assign all predictions to the same class, even before the beginning of training, and in the absence of explicit biases. We prove that, besides dataset properties, the presence of this phenomenon, which we call Initial Guessing Bias (IGB), is influenced by model choices including dataset preprocessing methods, and architectural decisions, such as activation functions, max-pooling layers, and network depth. Our analysis of IGB provides valuable information for selecting network architectures and initializing models. We also highlight theoretical consequences, such as a breakdown of node-permutation symmetry, a violation of self-averaging and non-trivial effects that depth has on IGB.

The root zone is a vital part of the Earth system and a key element in hydrology, ecology, agronomy, and land surface processes. However, its definition varies across disciplines, creating barriers to interdisciplinary understanding. Moreover, characterizing the root zone is challenging due to a lack of consensus on definitions, estimation methods, and their merits and limitations. This opinion paper provides a holistic definition of the root zone from a hydrology perspective, including its moisture storage, deficit, and storage capacity. We demonstrate that the root zone plays a critical role in the biosphere, pedosphere, rhizosphere, lithosphere, atmosphere, and cryosphere of the Earth system. We underscore the limitations of the traditional reductionist approach in modelling this complex and dynamic zone and advocate for a shift towards a holistic, ecosystem-centred approach. We argue that a holistic approach offers a more systematic, simple, dynamic, scalable, and observable way to describe and predict the role of the root zone in Earth system science.

Regulation of chemicals requires knowledge of their toxicological effects on a large number of species, which has traditionally been acquired through in vivo testing. The recent effort to find alternatives based on machine learning, however, has not focused on guaranteeing transparency, comparability and reproducibility, which makes it difficult to assess advantages and disadvantages of these methods. Also, comparable baseline performances are needed. In this study, we trained regression models on the ADORE "t-F2F" challenge proposed in [Schür et al., Nature Scientific data, 2023] to predict acute mortality, measured as LC50 (lethal concentration 50), of organic compounds on fishes. We trained LASSO, random forest (RF), XGBoost, Gaussian process (GP) regression models, and found a series of aspects that are stable across models: (i) using mass or molar concentrations does not affect performances; (ii) the performances are only weakly dependent on the molecular representations of the chemicals, but (iii) strongly on how the data is split. Overall, the tree-based models RF and XGBoost performed best and we were able to predict the log10-transformed LC50 with a root mean square error of 0.90, which corresponds to an order of magnitude on the original LC50 scale. On a local level, on the other hand, the models are not able to consistently predict the toxicity of individual chemicals accurately enough. Predictions for single chemicals are mostly influenced by a few chemical properties while taxonomic traits are not captured sufficiently by the models. We discuss technical and conceptual improvements for these challenges to enhance the suitability of in silico methods to environmental hazard assessment. Accordingly, this work showcases state-of-the-art models and contributes to the ongoing discussion on regulatory integration.