Constitutive models are fundamental to solid mechanics and materials science, underpinning the quantitative description and prediction of material responses under diverse loading conditions. Traditional phenomenological models, which are derived through empirical fitting, often lack generalizability and rely heavily on expert intuition and predefined functional forms. In this work, we propose a graph - based equation discovery framework for the automated discovery of constitutive laws directly from multisourc e experimental data. This framework expresses equations as directed graphs, where nodes represent operators and variables, edges denote computational relations, and edge features encode parametric dependencies . This enables the generation and optimization of free - form symbolic expressions with undetermined material - specific parameters . Through the proposed framework, we have discovered new constitutive models for strain - rate effects in alloy steel materials and the deformation behavior of lithium metal. Com pared with conventional empirical models, these new models exhibit compact analytical structures and achieve higher accuracy. The proposed graph - based equation discovery framework provides a generalizable and interpretable approach for data - driven scientific mode l ling, particularly in contexts where traditional empirical formulations are inadequate for representing complex physical phenomena. Keywords: Constitutive model, graph, equation discovery, solid mechanics, data - driven modelling . Introduction Constitutive laws serve as fundamental elements in solid mechanics, establishing the relationship between kinematic measures and static quantities to characterize material - specific behavior. Unlike conservation principles and kinematic relations, which are derived from first principles and regarded as axiomatic foundations, constitutive models encapsulate empirical descriptions of material responses to external stimuli . Accordingly, they are typically established through phenomenological approaches, guided by systematic experimentation and theoretical generalization, to characterize nonlinear behaviors across varying conditions ( 1) . The accuracy and generality of constitutive models are critical for the reliability of mechanical analysis, directly influencing both theoretical developments and practical applications in computational mechanics and materials engineering.

Accurate thermospheric density prediction is crucial for reliable satellite operations in Low Earth Orbits, especially at high solar and geomagnetic activity. Physics-based models such as TIE-GCM offer high fidelity but are computationally expensive, while empirical models like NRLMSIS are efficient yet lack predictive power. This work presents a transformer-based model that forecasts densities up to three days ahead and is intended as a drop-in replacement for an empirical baseline. Unlike recent approaches, it avoids spatial reduction and complex input pipelines, operating directly on a compact input set. Validated on real-world data, the model improves key prediction metrics and shows potential to support mission planning.

Galaxies are often modelled as composites of separable components with distinct spectral signatures, implying that different wavelength ranges are only weakly correlated. They are not. We present a data-driven model which exploits subtle correlations between physical processes to accurately predict infrared (IR) WISE photometry from a neural summary of optical SDSS spectra. The model achieves accuracies of $\chi^2_N \approx 1$ for all photometric bands in WISE, as well as good colors. We are also able to tightly constrain typically IR-derived properties, e.g. the bolometric luminosities of AGN and dust parameters such as $\mathrm{q_{PAH}}$. We find that current SED-fitting methods are incapable of making comparable predictions, and that model misspecification often leads to correlated biases in star-formation rates and AGN luminosities. To help improve SED models, we determine what features of the optical spectrum are responsible for our improved predictions, and identify several lines (CaII, SrII, FeI, [OII] and H$\alpha$), which point to the complex chronology of star formation and chemical enrichment being incorrectly modelled.

Contextuality is a distinguishing feature of quantum mechanics and there is growing evidence that it is a necessary condition for quantum advantage. In order to make use of it, researchers have been asking whether similar phenomena arise in other domains. The answer has been yes, e.g. in behavioural sciences. However, one has to move to frameworks that take some degree of signalling into account. Two such frameworks exist: (1) a signalling-corrected sheaf theoretic model, and (2) the Contextuality-by-Default (CbD) framework. This paper provides the first large scale experimental evidence for a yes answer in natural language. We construct a linguistic schema modelled over a contextual quantum scenario, instantiate it in the Simple English Wikipedia and extract probability distributions for the instances using the large language model BERT. This led to the discovery of 77,118 sheaf-contextual and 36,938,948 CbD contextual instances. We proved that the contextual instances came from semantically similar words, by deriving an equation between degrees of contextuality and Euclidean distances of BERT's embedding vectors. A regression model further reveals that Euclidean distance is indeed the best statistical predictor of contextuality. Our linguistic schema is a variant of the co-reference resolution challenge. These results are an indication that quantum methods may be advantageous in language tasks.

We introduce SymbolFit, a framework that automates parametric modeling by using symbolic regression to perform a machine-search for functions that fit the data, while simultaneously providing uncertainty estimates in a single run. Traditionally, constructing a parametric model to accurately describe binned data has been a manual and iterative process, requiring an adequate functional form to be determined before the fit can be performed. The main challenge arises when the appropriate functional forms cannot be derived from first principles, especially when there is no underlying true closed-form function for the distribution. In this work, we address this problem by utilizing symbolic regression, a machine learning technique that explores a vast space of candidate functions without needing a predefined functional form, treating the functional form itself as a trainable parameter. Our approach is demonstrated in data analysis applications in high-energy physics experiments at the CERN Large Hadron Collider (LHC). We demonstrate its effectiveness and efficiency using five real proton-proton collision datasets from new physics searches at the LHC, namely the background modeling in resonance searches for high-mass dijet, trijet, paired-dijet, diphoton, and dimuon events. We also validate the framework using several toy datasets with one and more variables.

We introduce a novel neural architecture termed thermoNET, designed to represent thermospheric density in satellite orbital propagation using a reduced amount of differentiable computations. Due to the appearance of a neural network on the right-hand side of the equations of motion, the resulting satellite dynamics is governed by a NeuralODE, a neural Ordinary Differential Equation, characterized by its fully differentiable nature, allowing the derivation of variational equations (hence of the state transition matrix) and facilitating its use in connection to advanced numerical techniques such as Taylor-based numerical propagation and differential algebraic techniques. Efficient training of the network parameters occurs through two distinct approaches. In the first approach, the network undergoes training independently of spacecraft dynamics, engaging in a pure regression task against ground truth models, including JB-08 and NRLMSISE-00. In the second paradigm, network parameters are learned based on observed dynamics, adapting through ODE sensitivities. In both cases, the outcome is a flexible, compact model of the thermosphere density greatly enhancing numerical propagation efficiency while maintaining accuracy in the orbital predictions.

Sheaves are mathematical objects consisting of a base which constitutes a topological space and the data associated with each open set thereof, e.g. continuous functions defined on the open sets. Sheaves have originally been used in algebraic topology and logic. Recently, they have also modelled events such as physical experiments and natural language disambiguation processes. We extend the latter models from lexical ambiguities to discourse ambiguities arising from anaphora. To begin, we calculated a new measure of contextuality for a dataset of basic anaphoric discourses, resulting in a higher proportion of contextual models--82.9%--compared to previous work which only yielded 3.17% contextual models. Then, we show how an extension of the natural language processing challenge, known as the Winograd Schema, which involves anaphoric ambiguities can be modelled on the Bell-CHSH scenario with a contextual fraction of 0.096.

Keywords: carbon fiber reinforced polymer, concrete, confinement effect, strength, particle swarm optimization, grey wolf optimizer, bat algorithm Abstract This article deals with the study of predicting the confinement effect of carbon fiber reinforced polymers (CFRPs) on concrete cylinder strength using metaheuristics-based artificial neural networks. Three metaheuristic models are implemented including particle swarm optimization (PSO), grey wolf optimizer (GWO), and bat algorithm (BA). These algorithms are trained on the data using an objective function of mean square error and their predicted results are validated against the experimental studies and finite element analysis. The study shows that the hybrid model of PSO predicted the strength of CFRP-confined concrete cylinders with maximum accuracy of 99.13% and GWO predicted the results with an accuracy of 98.17%. The high accuracy of axial compressive strength predictions demonstrated that these prediction models are a reliable solution to the empirical methods. The prediction models are especially suitable for avoiding full-scale time-consuming experimental tests that make the process quick and economical. 1 Introduction Fiber-reinforced polymer is a composite material comprising fibers of either glass, aramid, or carbon and a polymer matrix. These fibers improve the properties of the polymer matrix mechanically including its stiffness and strength. The popularity of these composites has increased significantly in civil engineering due to their ability to strengthen concrete structural members. FRPs can be used either as a bar or plates embedded in concrete as an internal reinforcement and can be used as an external reinforcement by wrapping FRP sheets to existing structural members. The FRP bars have significantly higher strength than the steel reinforcement bars. They are highly durable and resistant to chemicals, corrosion (Cousin et al. 2019, Ananthkumar et al. 2020, Zhang et al. 2020), and radiation, their higher strength-to-weight ratio (Zhou et al. 2019) makes them ideal for structures that require high strength but need not be heavy. They can be molded into any required shape that provides higher design flexibility. Moreover, it has a lower environmental impact (Lee and Jain 2009), unlike concrete and timber.

Ambiguity is a natural language phenomenon occurring at different levels of syntax, semantics, and pragmatics. It is widely studied; in Psycholinguistics, for instance, we have a variety of competing studies for the human disambiguation processes. These studies are empirical and based on eye-tracking measurements. Here we take first steps towards formalizing these processes for semantic ambiguities where we identified the presence of two features: (1) joint plausibility degrees of different possible interpretations, (2) causal structures according to which certain words play a more substantial role in the processes. The novel sheaf-theoretic model of definite causality developed by Gogioso and Pinzani in QPL 2021 offers tools to model and reason about these features. We applied this theory to a dataset of ambiguous phrases extracted from Psycholinguistics literature and their human plausibility judgements collected by us using the Amazon Mechanical Turk engine. We measured the causal fractions of different disambiguation orders within the phrases and discovered two prominent orders: from subject to verb in the subject-verb and from object to verb in the verb object phrases. We also found evidence for delay in the disambiguation of polysemous vs homonymous verbs, again compatible with Psycholinguistic findings.

Semi-supervised learning (SSL) has been proven to be a powerful method for leveraging unlabelled data to alleviate models' dependence on large labelled datasets. The common framework among recent approaches is to train the model on a large amount of unlabelled data with consistency regularization to constrain the model predictions to be invariant to input perturbation. However, the existing SSL frameworks still have room for improvement in the consistency regularization method. Instead of regularizing category predictions in the label space as in existing frameworks, this paper proposes a feature space renormalization (FSR) mechanism for SSL. First, we propose a feature space renormalization mechanism to substitute for the commonly used consistency regularization mechanism to learn better discriminative features. To apply this mechanism, we start by building a basic model and an empirical model and then introduce our mechanism to renormalize the feature learning of the basic model with the guidance of the empirical model. Second, we combine the proposed mechanism with pseudo-labelling to obtain a novel effective SSL model named FreMatch. The experimental results show that our method can achieve better performance on a variety of standard SSL benchmark datasets, and the proposed feature space renormalization mechanism can also enhance the performance of other SSL approaches.