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arXiv2026

FluxDisco: Symbolic Regression for Stoichiometric Dynamical Systems via Monte Carlo Graph Search

Dynamical symbolic regression methods identify governing differential equations from noisy data, balancing interpretability and predictive accuracy. However, standard methods often produce expressions that violate known physical laws. To address this, we propose FluxDisco, a physics-informed framework tailored for flux-based, stoichiometric ODE systems. By leveraging a known stoichiometry, we reduce the expression search space and ensure physical adherence. Our framework adapts the Monte Carlo Graph Search algorithm for the unique challenges associated with joint flux discovery of stoichiometric systems. We evaluate our method across a range of physical and biological systems, demonstrating its ability to accurately recover governing dynamics through interpretable equations.

stat.ML↗

arXiv2026

Thermodynamic Human-Computer Interaction

Target acquisition is often modeled separately for desktop, mobile, and other interaction modalities. We present Thermodynamic HCI, a framework that splits interaction into thermal equilibrium and non-equilibrium regimes. The theory generalizes across interaction modalities by representing agent-target interaction using kinetic and potential energies. We derive the movement time of Fitts' law and the speed-accuracy tradeoff observed in Schmidt's law from the principles of thermal physics. Furthermore, we develop theorems that describe how target properties, such as the color of a button, affect user accuracy. The target acquisition model, derived from the theory, when evaluated on desktop and mobile website prefetching experiments, achieved an accuracy of 98% for both cursor and touchscreen based interaction. For every clicked link, it produced a fetch:click ratio of 1.37 for desktop and 1.75 for mobile.

cs.HC↗

arXiv2026

Neural-Network Maxent: a general extension with learned nonlinearity, applied to time-series for Desert Locust distribution modelling

Species Distribution Modelling (SDM) is essential for understanding how environmental conditions shape biodiversity, particularly for destructive pests such as the Desert Locust (Schistocerca gregaria), whose breeding dynamics are tightly coupled to rapidly evolving environmental conditions. Maxent has become the dominant method for presence-only data, but its reliance on a linear combination of hand chosen feature transforms limits its ability to capture the nonlinear, temporal relationships common in ecological monitoring, where covariates such as precipitation, soil moisture, and vegetation indices evolve meaningfully over time. Standard implementations flatten time-series covariates into independent features, discarding sequential structure that carries critical signal. We introduce RNN Maxent, an extension of the Maxent framework that replaces the fixed feature dictionary with a neural network, specifically a Gated Recurrent Unit (GRU), trained end to end via backpropagation. The approach preserves Maxent's presence only statistical foundations, background normalization, and probability calibration, differing only in that the nonlinearity is learned from data rather than fixed in advance. We apply RNN Maxent to map suitable habitat for the Desert Locust using 50 day environmental time series derived from ERA5 Land, MODIS, and Sentinel 3, maintaining a 7 day gap between covariates and presence records to yield forecasting behavior. Compared against standard Maxent, RNN Maxent improves performance across metrics (ROC AUC 0.862 std 0.036 vs. 0.792; F1 0.671 std 0.056 vs. 0.590).

cs.LG↗

arXiv2026

Auditing Frozen-Encoder Anomaly Detection Across Mechanical Systems: Representation Provenance, Calibration, and Protocol Effects

This version reports a reproducibility audit of the frozen-encoder experiments presented in version 1. The numerical discrimination results are reproducible from the preserved artifacts, but their original attribution to interferometric pretraining is not supported. The released checkpoint contains a nested model state that loads without missing parameters, whereas loading the outer checkpoint dictionary leaves almost the entire EfficientNet-B0 feature stack uninitialized. Preserved embeddings labelled as interferometric have norms of order $10^{-12}$, matching freshly initialized EfficientNet-B0 networks and differing by more than twelve orders of magnitude from the preserved ImageNet embeddings. A second, separately preserved near-zero embedding set produces almost the same IMS 4th-test anomaly scores ($r=0.987$) and record-level discrimination (AUC $0.9812$ versus $0.9818$). We therefore withdraw the causal claim that IMS performance demonstrates a morphological prior transferred from gravitational-wave instrumentation. We reanalyse the controlled IMS splits at matched observed false-positive rates and add multivariate classical signal baselines. The near-zero representations retain strong tail separation, particularly in the 2nd and 4th IMS runs, but this is now interpreted as an exploratory architecture-and-initialization effect coupled to Mahalanobis scoring. A separate PRONOSTIA audit shows that the original large warning times were induced by a lifetime-fraction baseline; under fixed-time evaluation, a ten-feature classical baseline outperforms the preserved encoder scores. These results illustrate how checkpoint provenance, finite-sample calibration, architecture, and target-domain baselines can create an appearance of cross-domain transfer. They also define the controls required before assigning physical meaning to frozen-representation anomaly scores.

astro-ph.IM↗

arXiv2026

iPINN for Broadband CARS Phase Retrieval: A Framework for Function Approximation and Inverse Modeling Problems in Nonlinear Spectroscopy

Phase retrieval in broadband coherent anti-Stokes Raman spectroscopy (BCARS) is an ill-posed inverse problem. The Raman-like signal is encoded in the imaginary part of the resonant susceptibility, which mixes coherently with a non-resonant background (NRB) that varies across acquisitions. We introduce an inverse physics-informed neural network (iPINN) that predicts Lorentzian peak parameters from raw BCARS spectra and reconstructs the resonant susceptibility through a differentiable analytical forward model. A transformer encoder assigns spectral features to 24 learnable peak slots, and a multi-view consistency loss enforces invariance across NRB pattern, NRB strength, and noise. Unlike direct spectral regression approaches, the method retains accuracy under varying acquisition conditions. On a public benchmark, iPINN achieves the lowest error among the tested baselines (MAE 0.016 vs. next-best 0.046). On 28 zero-shot test spectra acquired across seven solvents and four focal positions, accuracy is depth-invariant in five of seven solvents. These results show that inverse parametric prediction with a differentiable physical decoder supports robust phase retrieval across measurement conditions.

cs.LG↗

arXiv2026

Accelerate Vector Diffusion Maps by Landmarks

We propose a landmark-constrained algorithm, LA-VDM (Landmark Accelerated Vector Diffusion Maps), to accelerate the Vector Diffusion Maps (VDM) framework built upon the Graph Connection Laplacian (GCL), which captures pairwise connection relationships within complex datasets. LA-VDM introduces a novel two-stage normalization that effectively address nonuniform sampling densities in both the data and the landmark sets. Under a manifold model with the frame bundle structure, we show that we can accurately recover the parallel transport with landmark-constrained diffusion from a point cloud, and hence asymptotically LA-VDM converges to the connection Laplacian. The performance and accuracy of LA-VDM are demonstrated through experiments on simulated datasets and an application to nonlocal image denoising.

stat.ML↗

arXiv2026

ButterMamba: Butterworth-Enhanced Spatial-Temporal Mamba for Efficient Traffic Flow Prediction

Accurate traffic flow prediction is fundamental to intelligent transportation systems, playing a pivotal role in urban mobility optimization and smart city development. While Graph Neural Networks (GNNs) integrated with time series forecasting have emerged as promising solutions, two critical limitations persist: (1) the quadratic complexity of attention-based architectures hinders real-time deployment in large-scale networks, and (2) high-frequency noise in sensor data significantly degrades prediction reliability. These challenges are particularly acute in metropolitan scenarios where both computational efficiency and noise robustness are paramount. To address these limitations, we introduce \textbf{ButterMamba}, a novel and efficient framework based on State Space Models (SSMs). ButterMamba consists of two key components: (1) a Butterworth Spectral Filtering module that preprocesses the data by removing high-frequency noise, allowing the model to focus on significant underlying trends, and (2) a Spatial-Temporal State Mixer that uses a parallel Mamba architecture to efficiently capture both long-range temporal dependencies and complex spatial correlations across the road network. By decoupling noise filtering from spatial-temporal modeling, ButterMamba achieves superior predictive accuracy with linear computational complexity. Extensive experiments on three public datasets demonstrate that ButterMamba not only outperforms existing state-of-the-art models in terms of prediction accuracy but also considerably reduces training time and memory usage.

physics.soc-ph↗

arXiv2026

Localizing Global Discrepancies: Marginal Contributions and Contextual Anomaly Detection

Global goodness-of-fit and discrepancy statistics can establish that a sample departs from a reference distribution without identifying which observations drive the departure. We develop a framework for this localization problem by assigning to each observation its conditional or marginal contribution across random statistical contexts. This connects resampling diagnostics and data valuation to projection theory and event-level anomaly detection. For symmetric statistics, fixed-size replacement is exactly equivalent to centered conditional localization. For U-statistics, the addition score equals the first Hoeffding/Hájek contribution; for smooth distributional functionals it is related at leading order to the influence function; and for unbiased known-background MMD it reduces exactly to the MMD witness. This viewpoint also yields more efficient estimators. Matched-context subtraction removes fluctuations unrelated to the observation, while for pairwise MMD the event-containing terms give a simple localizer. On the LHC Olympics anomaly-detection benchmark, the pair estimator converges to the direct empirical MMD witness with the predicted 1/(Rm^2) scaling, where m is batch size and R the number of batches. At m=1000 and R=5x106 it reaches correlation 0.9993 with essentially identical AUC. We also ask when context contains information beyond an event's own features. In a shared-latent toy model, the full single-event signal and background distributions are identical by construction, forcing isolated-event AUC=0.5. Discriminating information survives only in cross-event dependence induced by the shared latent parameter; the ensemble recovers this information, whereas an independent-latent control does not. This separates two roles of context: efficient localization of a global discrepancy and genuinely additional class information when the alternative contains shared structure.

stat.ML↗

arXiv2026

Functional Connectivity Networks for Transportation Delay Analysis: from Theory to Software

Within the endeavour of modelling and understanding the propagation of delays in transportation networks, an approach that has attracted increasing interest in the last decade is the creation of functional network representations. These graphs map elements of interest (e.g. airports or stations) as nodes, and derive pairwise propagation patterns from their dynamics through correlation and causality tests. In spite of multiple notable results, this approach still lacks a coherent framework, with decisions related to many fundamental steps being left to the judgement of the researcher. We here provide an introduction to the theory behind functional networks for transportation systems, detailing the main steps and the associated pitfalls. We further introduce a Python package, delaynet, designed to support the researcher in the reconstruction and analysis of such networks. We finally present an analysis of the propagation of delays in the Swiss train system; and discuss future research steps.

physics.soc-ph↗

arXiv2025

DPGIIL: Dirichlet Process-Deep Generative Model-Integrated Incremental Learning for Clustering in Transmissibility-based Online Structural Anomaly Detection

Clustering based on vibration responses, such as transmissibility functions (TFs), is promising in structural anomaly detection. However, most existing methods struggle to determine the optimal cluster number, handle high-dimensional streaming data, and rely heavily on manually engineered features due to their shallow structures. To address these issues, this work proposes a novel clustering framework, referred to as Dirichlet process-deep generative model-integrated incremental learning (DPGIIL), for online structural anomaly detection, which combines the advantages of deep generative models (DGMs) in representation learning and the Dirichlet process mixture model (DPMM) in identifying distinct patterns in observed data. Within the context of variational Bayesian inference, a lower bound on the log marginal likelihood of DPGIIL, tighter than the evidence lower bound, is derived analytically, which enables the joint optimization of DGM and DPMM parameters, thereby allowing the DPMM to regularize the DGM's feature extraction process. Additionally, a greedy split-merge scheme-based coordinate ascent variational inference method is devised to accelerate the optimization. The summary statistics of the DPMM, along with the network parameters, are used to retain information about previous data for incremental learning. For online structural anomaly detection, DPGIIL can not only detect anomalies by dynamically assigning incoming data to new clusters but also indicate different structural states using distinct clusters, thereby providing additional information about the operating conditions of the monitored structure compared to traditional anomaly detectors. Three case studies demonstrate the dynamic adaptability of the proposed method and show that it outperforms some state-of-the-art approaches in both structural anomaly detection and clustering.

cs.LG↗

arXiv2025

From Occurrence to Consequence: A Comprehensive Data-driven Analysis of Building Fire Risk

Building fires pose a persistent threat to life, property, and infrastructure, emphasizing the need for advanced risk mitigation strategies. This study presents a data-driven framework analyzing U.S. fire risks by integrating over one million fire incident reports with diverse fire-relevant datasets, including social determinants, building inventories, weather conditions, and incident-specific factors. By adapting machine learning models, we identify key risk factors influencing fire occurrence and consequences. Our findings show that vulnerable communities, characterized by socioeconomic disparities or the prevalence of outdated or vacant buildings, face higher fire risks. Incident-specific factors, such as fire origins and safety features, strongly influence fire consequences. Buildings equipped with fire detectors and automatic extinguishing systems experience significantly lower fire spread and injury risks. By pinpointing high-risk areas and populations, this research supports targeted interventions, including mandating fire safety systems and providing subsidies for disadvantaged communities. These measures can enhance fire prevention, protect vulnerable groups, and promote safer, more equitable communities.

cs.LG↗