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arXiv:2508.19448v1 Announce Type: cross Abstract: Many natural systems exhibit cyclo-stationary behavior characterized by periodic forcing such as annual and diurnal cycles. We present a data-driven method leveraging recent advances in score-based generative modeling to construct reduced-order models for such cyclo-stationary time series. Our approach accurately reproduces the statistical properties and temporal correlations of the original data, enabling efficient generation of synthetic trajectories. We demonstrate the performance of the method through application to the Planet Simulator (PlaSim) climate model, constructing a reduced-order model for the 20 leading principal components of surface temperature driven by the annual cycle. The resulting surrogate model accurately reproduces the marginal and joint probability distributions, autocorrelation functions, and spatial coherence of the original climate system across multiple validation metrics. The approach offers substantial computational advantages, enabling generation of centuries of synthetic climate data in minutes compared to weeks required for equivalent full model simulations. This work opens new possibilities for efficient modeling of periodically forced systems across diverse scientific domains, providing a principled framework for balancing computational efficiency with physical fidelity in reduced-order modeling applications.

arXiv:2508.19249v1 Announce Type: cross Abstract: We present a new efficient hybrid parameter estimation method based on the idea, that if nonlinear dynamic models are stated in terms of a system of equations that is linear in terms of the parameters, then regularized ordinary least squares can be used to estimate these parameters from time series data. We introduce the term "Physics-Informed Regression" (PIR) to describe the proposed data-driven hybrid technique as a way to bridge theory and data by use of ordinary least squares to efficiently perform parameter estimation of the model coefficients of different parameter-linear models; providing examples of models based on nonlinear ordinary equations (ODE) and partial differential equations (PDE). The focus is on parameter estimation on a selection of ODE and PDE models, each illustrating performance in different model characteristics. For two relevant epidemic models of different complexity and number of parameters, PIR is tested and compared against the related technique, physics-informed neural networks (PINN), both on synthetic data generated from known target parameters and on real public Danish time series data collected during the COVID-19 pandemic in Denmark. Both methods were able to estimate the target parameters, while PIR showed to perform noticeably better, especially on a compartment model with higher complexity. Given the difference in computational speed, it is concluded that the PIR method is superior to PINN for the models considered. It is also demonstrated how PIR can be applied to estimate the time-varying parameters of a compartment model that is fitted using real Danish data from the COVID-19 pandemic obtained during a period from 2020 to 2021. The study shows how data-driven and physics-informed techniques may support reliable and fast -- possibly real-time -- parameter estimation in parameter-linear nonlinear dynamic models.

arXiv:2508.11693v1 Announce Type: cross Abstract: Track Circuits (TC) are the main signalling devices used to detect the presence of a train on a rail track. It has been used since the 19th century and nowadays there are many types depending on the technology. As a general classification, Track Circuits can be divided into 2 main groups, DC (Direct Current) and AC (Alternating Current) circuits. This work is focused on a particular AC track circuit, called "Smart Train Detection System" (STDS), designed with both high and low-frequency bands. This approach uses STDS current data applied to an SVM (support vector machine) classifier as a type of failure identifier. The main purpose of this work consists on determine automatically which is the component of the track that is failing to improve the maintenance action. Model was trained to classify 15 different failures that belong to 3 more general categories. The method was tested with field data from 10 different track circuits and validated by the STDS track circuit expert and maintainers. All use cases were correctly classified by the method.

arXiv:2508.19897v1 Announce Type: new Abstract: Generative diffusion models have emerged as a powerful class of models in machine learning, yet a unified theoretical understanding of their operation is still developing. This perspective paper provides an integrated perspective on generative diffusion by connecting their dynamic, information-theoretic, and thermodynamic properties under a unified mathematical framework. We demonstrate that the rate of conditional entropy production during generation (i.e. the generative bandwidth) is directly governed by the expected divergence of the score function's vector field. This divergence, in turn, is linked to the branching of trajectories and generative bifurcations, which we characterize as symmetry-breaking phase transitions in the energy landscape. This synthesis offers a powerful insight: the process of generation is fundamentally driven by the controlled, noise-induced breaking of (approximate) symmetries, where peaks in information transfer correspond to critical transitions between possible outcomes. The score function acts as a dynamic non-linear filter that regulates the bandwidth of the noise by suppressing fluctuations that are incompatible with the data.

arXiv:2508.19841v1 Announce Type: new Abstract: We present a probabilistic, data-driven surrogate model for predicting the radiative properties of nanoparticle embedded scattering media. The model uses conditional normalizing flows, which learn the conditional distribution of optical outputs, including reflectance, absorbance, and transmittance, given input parameters such as the absorption coefficient, scattering coefficient, anisotropy factor, and particle size distribution. We generate training data using Monte Carlo radiative transfer simulations, with optical properties derived from Mie theory. Unlike conventional neural networks, the conditional normalizing flow model yields full posterior predictive distributions, enabling both accurate forecasts and principled uncertainty quantification. Our results demonstrate that this model achieves high predictive accuracy and reliable uncertainty estimates, establishing it as a powerful and efficient surrogate for radiative transfer simulations.

arXiv:2508.19468v1 Announce Type: cross Abstract: We present an extension of the Levenberg-Marquardt algorithm for fitting multichannel nuclear cross section data. Our approach offers a practical and robust alternative to conventional trust-region methods for analyzing experimental data. The CoH$_3$ code, based on the Hauser-Feshbach statistical model, involves a large number of interdependent parameters, making optimization challenging due to the presence of "sloppy" directions in parameter space. To address the uneven distribution of experimental data across reaction channels, we construct a weighted Fisher Information Metric by integrating prior distributions over dataset weights. This framework enables a more balanced treatment of heterogeneous data, improving both parameter estimation and convergence robustness. We show that the resulting weighted Levenberg-Marquardt method yields more physically consistent fits for both raw and smoothed datasets, using experimental data for ${}^{148}$Sm as a representative example. Additionally, we introduce a geometric scaling strategy to accelerate convergence -- a method based on the local geometry of the manifold.

arXiv:2508.19563v1 Announce Type: cross Abstract: Large Language Models (LLMs) are being applied in a wide array of settings, well beyond the typical language-oriented use cases. In particular, LLMs are increasingly used as a plug-and-play method for fitting data and generating predictions. Prior work has shown that LLMs, via in-context learning or supervised fine-tuning, can perform competitively with many tabular supervised learning techniques in terms of predictive performance. However, we identify a critical vulnerability of using LLMs for data fitting -- making changes to data representation that are completely irrelevant to the underlying learning task can drastically alter LLMs' predictions on the same data. For example, simply changing variable names can sway the size of prediction error by as much as 82% in certain settings. Such prediction sensitivity with respect to task-irrelevant variations manifests under both in-context learning and supervised fine-tuning, for both close-weight and open-weight general-purpose LLMs. Moreover, by examining the attention scores of an open-weight LLM, we discover a non-uniform attention pattern: training examples and variable names/values which happen to occupy certain positions in the prompt receive more attention when output tokens are generated, even though different positions are expected to receive roughly the same attention. This partially explains the sensitivity in the presence of task-irrelevant variations. We also consider a state-of-the-art tabular foundation model (TabPFN) trained specifically for data fitting. Despite being explicitly designed to achieve prediction robustness, TabPFN is still not immune to task-irrelevant variations. Overall, despite LLMs' impressive predictive capabilities, currently they lack even the basic level of robustness to be used as a principled data-fitting tool.

arXiv:2508.17077v2 Announce Type: replace Abstract: Current experimental scientists have been increasingly relying on simulation-based inference (SBI) to invert complex non-linear models with intractable likelihoods. However, posterior approximations obtained with SBI are often miscalibrated, causing credible regions to undercover true parameters. We develop $texttt{CP4SBI}$, a model-agnostic conformal calibration framework that constructs credible sets with local Bayesian coverage. Our two proposed variants, namely local calibration via regression trees and CDF-based calibration, enable finite-sample local coverage guarantees for any scoring function, including HPD, symmetric, and quantile-based regions. Experiments on widely used SBI benchmarks demonstrate that our approach improves the quality of uncertainty quantification for neural posterior estimators using both normalizing flows and score-diffusion modeling.

arXiv:2508.19780v1 Announce Type: cross Abstract: Most machine learning models are designed to maximize predictive accuracy. In this work, we explore a different goal: building classifiers that are interesting. An ``interesting classifier'' is one that uses unusual or unexpected features, even if its accuracy is lower than the best possible model. For example, predicting room congestion from CO2 levels achieves near-perfect accuracy but is unsurprising. In contrast, predicting room congestion from humidity is less accurate yet more nuanced and intriguing. We introduce EUREKA, a simple framework that selects features according to their perceived interestingness. Our method leverages large language models to rank features by their interestingness and then builds interpretable classifiers using only the selected interesting features. Across several benchmark datasets, EUREKA consistently identifies features that are non-obvious yet still predictive. For example, in the Occupancy Detection dataset, our method favors humidity over CO2 levels and light intensity, producing classifiers that achieve meaningful accuracy while offering insights. In the Twin Papers dataset, our method discovers the rule that papers with a colon in the title are more likely to be cited in the future. We argue that such models can support new ways of knowledge discovery and communication, especially in settings where moderate accuracy is sufficient but novelty and interpretability are valued.

arXiv:2308.00913v3 Announce Type: replace-cross Abstract: A hierarchical Bayesian framework is introduced for developing tree-based mixture models for time series, partly motivated by applications in finance and forecasting. At the top level, meaningful discrete states are identified as appropriately quantised values of some of the most recent samples. At the bottom level, a different, arbitrary base model is associated with each state. This defines a very general framework that can be used in conjunction with any existing model class to build flexible and interpretable mixture models. We call this the Bayesian Context Trees State Space Model, or the BCT-X framework. Appropriate algorithmic tools are described, which allow for effective and efficient Bayesian inference and learning; these algorithms can be updated sequentially, facilitating online forecasting. The utility of the general framework is illustrated in the particular instances when AR or ARCH models are used as base models. The latter results in a mixture model that offers a powerful way of modelling the well-known volatility asymmetries in financial data, revealing a novel, important feature of stock market index data, in the form of an enhanced leverage effect. In forecasting, the BCT-X methods are found to outperform several state-of-the-art techniques, both in terms of accuracy and computational requirements.