Corrosion poses a significant challenge to the performance of aluminum alloys, particularly in marine environments. This study investigates the application of machine learning (ML) algorithms to predict and optimize corrosion resistance, utilizing a comprehensive open-source dataset compiled from various sources. The dataset encompasses corrosion rate data and environmental conditions, preprocessed to standardize units and formats. We explored two different approaches, a direct approach, where the material's composition and environmental conditions were used as inputs to predict corrosion rates; and an inverse approach, where corrosion rate served as the input to identify suitable material compositions as output. We employed and compared three distinct ML methodologies for forward predictions: Random Forest regression, optimized via grid search; a feed-forward neural network, utilizing ReLU activation and Adam optimization; and Gaussian Process Regression (GPR), implemented with GPyTorch and employing various kernel functions. The Random Forest and neural network models provided predictive capabilities based on elemental compositions and environmental conditions. Notably, Gaussian Process Regression demonstrated superior performance, particularly with hybrid kernel functions. Log-transformed GPR further refined predictions. This study highlights the efficacy of ML, particularly GPR, in predicting corrosion rates and material properties.

Multiscale systems are ubiquitous in science and technology, but are notoriously challenging to simulate as short spatiotemporal scales must be appropriately linked to emergent bulk physics. When expensive high-dimensional dynamical systems are coarse-grained into low-dimensional models, the entropic loss of information leads to emergent physics which are dissipative, history-dependent, and stochastic. To machine learn coarse-grained dynamics from time-series observations of particle trajectories, we propose a framework using the metriplectic bracket formalism that preserves these properties by construction; most notably, the framework guarantees discrete notions of the first and second laws of thermodynamics, conservation of momentum, and a discrete fluctuation-dissipation balance crucial for capturing non-equilibrium statistics. We introduce the mathematical framework abstractly before specializing to a particle discretization. As labels are generally unavailable for entropic state variables, we introduce a novel self-supervised learning strategy to identify emergent structural variables. We validate the method on benchmark systems and demonstrate its utility on two challenging examples: (1) coarse-graining star polymers at challenging levels of coarse-graining while preserving non-equilibrium statistics, and (2) learning models from high-speed video of colloidal suspensions that capture coupling between local rearrangement events and emergent stochastic dynamics. We provide open-source implementations in both PyTorch and LAMMPS, enabling large-scale inference and extensibility to diverse particle-based systems.

We study the fundamental problem of learning a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to the next based on a spectral representation of the system. Using techniques from online convex optimization, we prove vanishing prediction error for any nonlinear dynamical system that has finitely many marginally stable modes, with rates governed by a novel quantitative control-theoretic notion of learnability. The main technical component of our method is a new spectral filtering algorithm for linear dynamical systems, which incorporates past observations and applies to general noisy and marginally stable systems. This significantly generalizes the original spectral filtering algorithm to both asymmetric dynamics as well as incorporating noise correction, and is of independent interest.

Large language models are increasingly used as judges (LLM-as-a-judge) to evaluate model outputs at scale, but their assessments often diverge systematically from human judgments. We present Bridge, a unified statistical framework that explicitly bridges human and LLM evaluations under both absolute scoring and pairwise comparison paradigms. Bridge posits a latent human preference score for each prompt-response pair and models LLM deviations as linear transformations of covariates that capture sources of discrepancies. This offers a simple and principled framework for refining LLM ratings and characterizing systematic discrepancies between humans and LLMs. We provide an efficient fitting algorithm with asymptotic guarantees for statistical inference. Using six LLM judges and two benchmarks (BigGen Bench and Chatbot Arena), Bridge achieves higher agreement with human ratings (accuracy, calibration, and KL divergence) and exposes systematic human-LLM gaps.

We propose a method for evaluating the robustness of a widely used LLM ranking system -- the Bradley--Terry ranking system -- to dropping a worst-case very small fraction of evaluation data. Our approach is computationally fast and easy to adopt. When we apply our method to matchups from two popular human-preference platforms, Chatbot Arena and MT-Bench, we find that the Bradley--Terry rankings of top-performing models are remarkably sensitive to the removal of a small fraction of evaluations. Our framework also identifies the specific evaluations most responsible for such ranking flips, allowing for inspections of these influential preferences. We observe that the rankings derived from MT-Bench preferences are notably more robust than those from Chatbot Arena, likely due to MT-bench's use of expert annotators and carefully constructed prompts. Finally, we find that rankings based on crowdsourced human-evaluated systems are just as sensitive as those based on LLM-as-a-judge evaluations, where in both, dropping as little as 0.02% of the total evaluations in the dataset can change the top-ranked model.

Dynamic relational structures play a central role in many AI tasks, but their evolving nature presents challenges for consistent and interpretable representation. A common approach is to learn time-varying node embeddings, whose effectiveness depends on satisfying key stability properties. In this paper, we propose Unfolded Laplacian Spectral Embedding, a new method that extends the Unfolded Adjacency Spectral Embedding framework to normalized Laplacians while preserving both cross-sectional and longitudinal stability. We provide formal proof that our method satisfies these stability conditions. In addition, as a bonus of using the Laplacian matrix, we establish a new Cheeger-style inequality that connects the embeddings to the conductance of the underlying dynamic graphs. Empirical evaluations on synthetic and real-world datasets support our theoretical findings and demonstrate the strong performance of our method. These results establish a principled and stable framework for dynamic network representation grounded in spectral graph theory.

We present a novel framework for predicting next actions in soccer possessions by leveraging path signatures to encode their complex spatio-temporal structure. Unlike existing approaches, we do not rely on fixed historical windows and handcrafted features, but rather encode the entire recent possession, thereby avoiding the inclusion of potentially irrelevant or misleading historical information. Path signatures naturally capture the order and interaction of events, providing a mathematically grounded feature encoding for variable-length time series of irregular sampling frequencies without the necessity for manual feature engineering. Our proposed approach outperforms a transformer-based benchmark across various loss metrics and considerably reduces computational cost. Building on these results, we introduce a new possession evaluation metric based on well-established frameworks in soccer analytics, incorporating both predicted action type probabilities and action location. Our metric shows greater reliability than existing metrics in domain-specific comparisons. Finally, we validate our approach through a detailed analysis of the 2017/18 Premier League season and discuss further applications and future extensions.