Disentangling Slow and Fast Temporal Dynamics in Degradation Inference with Hierarchical Differential Models Mengjie Zhao, Olga Fink Learned latent states align well with true physical degradation. The framework shows robust generalization to unseen conditions. The primary latent component serves as an interpretable health indicator. Abstract Reliable inference of system degradation from sensor data is fundamental to condition monitoring and prognostics in engineered systems. Since degradation is rarely observable and measurable, it must be inferred to enable accurate health assessment and decision-making. This is particularly challenging because operational and environmental variations dominate system behavior, while degradation introduces only subtle, long-term changes. Consequently, sensor data primarily reflect short-term operational variability, making it difficult to disentangle the underlying degradation process. Residual-based methods are widely employed, but the residuals remain entangled with operational history, often resulting in noisy and unreliable degradation estimation, particularly in systems with dynamic responses. Other approaches often focus on modeling degradation-aware degradation dynamics but overlook how operational history drives long-term degradation. Neural Ordinary Equations (NODEs) offer a promising framework for inferring latent dynamics, but the time-scale separation in slow-fast systems introduces numerical stiffness and complicates training, while degradation disentanglement remains difficult. To address these limitations, we propose a novel Hierarchical Controlled Differential Equation (H-CDE) framework that incorporates a slow (degradation) and a fast (operation) CDE component in a unified architecture. Through comprehensive evaluations on both dynamic response (e.g., bridges) and steady state (e.g., aero-engine) systems, we demonstrate that H-CDE effectively disentangles degradation from operational dynamics and outperforms residual-based baselines, yielding more accurate, robust, and interpretable inference. Introduction Ensuring the reliability and safety of complex engineered systems, ranging from critical infrastructure [1] to industrial machinery [2] and aerospace structures [3], relies on continuous monitoring of their health state. A key indicator of system health is the level of degradation, whose progression enables estimation of the remaining useful life (RUL). Accurate RUL predictions support predictive maintenance strategies and help avoid both unexpected failures and unnecessarily conservative component replacements [4, 5].

At its core, the package implements an efficient Mode Jumping Markov Chain Monte Carlo (MJMCMC) algorithm, designed to improve mixing in multi-modal posterior landscapes within Bayesian generalized linear models. In addition, it provides a genetically modified MJMCMC (GMJMCMC) algorithm that introduces nonlinear feature generation, thereby enabling the estimation of Bayesian generalized nonlinear models (BGNLMs). Within this framework, the algorithm maintains and updates populations of transformed features, computes their posterior probabilities, and evaluates the posteriors of models constructed from them. We demonstrate the effective use of FBMS for both inferential and predictive modeling in Gaussian regression, focusing on different instances of the BGNLM class of models. Furthermore, through a broad set of applications, we illustrate how the methodology can be extended to increasingly complex modeling scenarios, extending to other response distributions and mixed effect models.

We introduce a Partial Functional Dynamic Backdoor Diffusion-based Causal Model (PFD-BDCM), specifically designed for causal inference in the presence of unmeasured confounders with spatial heterogeneity and temporal dependency. The proposed PFD-BDCM framework addresses the restrictions of the existing approaches by uniquely integrating models for complex spatio-temporal dynamics with the analysis of multi-resolution variables. Specifically, the framework systematically mitigates confounding bias by integrating valid backdoor adjustment sets into a diffusion-based sampling mechanism. Moreover, it accounts for the intricate dynamics of unmeasured confounders through the deployment of region-specific structural equations and conditional autoregressive processes, and accommodates variables observed at heterogeneous resolutions via basis expansions for functional data. Our theoretical analysis establishes error bounds for counterfactual estimates of PFD-BDCM, formally linking reconstruction accuracy to counterfactual fidelity under monotonicity assumptions of structural equation and invertibility assumptions of encoding function. Empirical evaluations on synthetic datasets and real-world air pollution data demonstrate PFD-BDCM's superiority over existing methods.

This work proposes and studies the distributed resource allocation problem in asynchronous and stochastic settings. We consider a distributed system with multiple workers and a coordinating server with heterogeneous computation and communication times. We explore an approximate stochastic primal-dual approach with the aim of 1) adhering to the resource budget constraints, 2) allowing for the asynchronicity between the workers and the server, and 3) relying on the locally available stochastic gradients. We analyze our Asynchronous stochastic Primal-Dual (Asyn-PD) algorithm and prove its convergence in the second moment to the saddle point solution of the approximate problem at the rate of $O(1/t)$, where $t$ is the iteration number. Furthermore, we verify our algorithm numerically to validate the analytically derived convergence results, and demonstrate the advantages of utilizing our asynchronous algorithm rather than deploying a synchronous algorithm where the server must wait until it gets update from all workers.

Industrial-scale battery management involves various types of tasks, such as estimation, prediction, and system-level diagnostics. Each task employs distinct data across temporal scales, sensor resolutions, and data channels. Building task-specific methods requires a great deal of data and engineering effort, which limits the scalability of intelligent battery management. Here we present the Flexible Masked Autoencoder (FMAE), a flexible pretraining framework that can learn with missing battery data channels and capture inter-correlations across data snippets. FMAE learns unified battery representations from heterogeneous data and can be adopted by different tasks with minimal data and engineering efforts. Experimentally, FMAE consistently outperforms all task-specific methods across five battery management tasks with eleven battery datasets. On remaining life prediction tasks, FMAE uses 50 times less inference data while maintaining state-of-the-art results. Moreover, when real-world data lack certain information, such as system voltage, FMAE can still be applied with marginal performance impact, achieving comparable results with the best hand-crafted features. FMAE demonstrates a practical route to a flexible, data-efficient model that simplifies real-world multi-task management of dynamical systems.

Storm surge is one of the deadliest hazards posed by tropical cyclones (TCs), yet assessing its current and future risk is difficult due to the phenomenon's rarity and physical complexity. Recent advances in artificial intelligence applications to natural hazard modeling suggest a new avenue for addressing this problem. We utilize a deep learning storm surge model to efficiently estimate coastal surge risk in the United States from 900,000 synthetic TC events, accounting for projected changes in TC behavior and sea levels. The derived historical 100-year surge (the event with a 1% yearly exceedance probability) agrees well with historical observations and other modeling techniques. When coupled with an inundation model, we find that heightened TC intensities and sea levels by the end of the century result in a 50% increase in population at risk. Key findings include markedly heightened risk in Florida, and critical thresholds identified in Georgia and South Carolina.

Recent work has proposed machine learning (ML) approaches as fast surrogates for solving AC optimal power flow (AC-OPF), with claims of significant speed-ups and high accuracy. In this paper, we revisit these claims through a systematic evaluation of ML models against a set of simple yet carefully designed linear baselines. We introduce OPFormer-V, a transformer-based model for predicting bus voltages, and compare it to both the state-of-the-art DeepOPF-V model and simple linear methods. Our findings reveal that, while OPFormer-V improves over DeepOPF-V, the relative gains of the ML approaches considered are less pronounced than expected. Simple linear baselines can achieve comparable performance. These results highlight the importance of including strong linear baselines in future evaluations.

Photonic computing promises energy-efficient acceleration for optimization and learning, yet discrete combinatorial search and continuous function approximation have largely required distinct devices and control stacks. Here we unify k-local Ising optimization and optical Kolmogorov-Arnold network (KAN) learning on a single photonic platform, establishing a critical convergence point in optical computing. We introduce an SLM-centric primitive that realizes, in one stroke, all-optical k-local Ising interactions and fully optical KAN layers. The key idea is to convert the structural nonlinearity of a nominally linear scatterer into a per-window computational resource by adding a single relay pass through the same spatial light modulator: a folded 4f relay re-images the first Fourier plane onto the SLM so that each selected clique or channel occupies a disjoint window with its own second pass phase patch. Propagation remains linear in the optical field, yet the measured intensity in each window becomes a freely programmable polynomial of the clique sum or projection amplitude. This yields native, per clique k-local couplings without nonlinear media and, in parallel, the many independent univariate nonlinearities required by KAN layers, all trainable with in-situ physical gradients using two frames (forward and adjoint). We outline implementations on spatial photonic Ising machines, injection-locked vertical cavity surface emitting laser (VCSEL) arrays, and Microsoft analog optical computers; in all cases the hardware change is one extra lens and a fold (or an on-chip 4f loop), enabling a minimal overhead, massively parallel route to high-order Ising optimization and trainable, all-optical KAN processing on one platform.

Sparse observations and coarse-resolution climate models limit effective regional decision-making, underscoring the need for robust downscaling. However, existing AI methods struggle with generalization across variables and geographies and are constrained by the quadratic complexity of Vision Transformer (ViT) self-attention. We introduce ORBIT-2, a scalable foundation model for global, hyper-resolution climate downscaling. ORBIT-2 incorporates two key innovations: (1) Residual Slim ViT (Reslim), a lightweight architecture with residual learning and Bayesian regularization for efficient, robust prediction; and (2) TILES, a tile-wise sequence scaling algorithm that reduces self-attention complexity from quadratic to linear, enabling long-sequence processing and massive parallelism. ORBIT-2 scales to 10 billion parameters across 65,536 GPUs, achieving up to 4.1 exaFLOPS sustained throughput and 74--98% strong scaling efficiency. It supports downscaling to 0.9 km global resolution and processes sequences up to 4.2 billion tokens. On 7 km resolution benchmarks, ORBIT-2 achieves high accuracy with $R^2$ scores in the range of 0.98--0.99 against observational data.

Future robotic systems operating in real-world environments will require on-board embodied intelligence without continuous cloud connection, balancing capabilities with constraints on computational power and memory. This work presents an extension of the R1-zero approach, which enables the usage of low parameter-count Large Language Models (LLMs) in the robotic domain. The R1-Zero approach was originally developed to enable mathematical reasoning in LLMs using static datasets. We extend it to the robotics domain through integration in a closed-loop Reinforcement Learning (RL) framework. This extension enhances reasoning in Embodied Artificial Intelligence (Embodied AI) settings without relying solely on distillation of large models through Supervised Fine-Tuning (SFT). We show that small-scale LLMs can achieve effective reasoning performance by learning through closed-loop interaction with their environment, which enables tasks that previously required significantly larger models. In an autonomous driving setting, a performance gain of 20.2%-points over the SFT-based baseline is observed with a Qwen2.5-1.5B model. Using the proposed training procedure, Qwen2.5-3B achieves a 63.3% control adaptability score, surpassing the 58.5% obtained by the much larger, cloud-bound GPT-4o. These results highlight that practical, on-board deployment of small LLMs is not only feasible but can outperform larger models if trained through environmental feedback, underscoring the importance of an interactive learning framework for robotic Embodied AI, one grounded in practical experience rather than static supervision.