AI for Science

Tetraphenylpyrazine (TPP) and 2,3,4,5-tetraphenyl-1H-pyrrole (TePP) are closely related heterocycles bearing four phenyl substituents, whose structural similarity makes them a useful pair for comparing how intramolecular flexibility influences excited-state relaxation and emission in the gas phase and in the solid state. TPP is a prototypical solid-state luminescence enhancement (SLE) emitter, exhibiting a markedly increased quantum yield upon molecular aggregation. In contrast, TePP displays similar quantum yields in solution and solid state, characteristic of dual-state emission (DSE). This behaviour indicates that intramolecular rotations are already significantly hindered in the isolated-molecule regime, consistent with our previous observations for TPP and other solid-state emitters (Hernández-Rodríguez et al., ChemPhysChem, 2024, 25, e202400563). To unravel the excited-state dynamics underlying this contrasting behaviour, we performed mixed quantum-classical trajectory simulations on a single molecule of TPP and TePP employing the surface-hopping method. Twelve singlet states were included at the TD-B3LYP-D3/def2-SVP level, which were previously benchmarked against coupled cluster methods. Simulated observables such as gas phase ultrafast electron diffraction (GUED) and time-resolved fluorescence (TR-FL) signals allow us to dissect the distinct deactivation pathways operating in both systems in the gas phase, while also providing mechanistic insight into how these pathways are expected to evolve in solution and solid-state environments.

Neutrons are important final-state particles in neutrino interactions, yet they are not considered or reconstructed in most current neutrino LArTPC physics analyses. In this paper, we present a simulation-based proof-of-concept study of neutron reconstruction in a generic LArTPC detector. Leveraging isolated, MeV-scale energy deposits, or blips, from neutron inelastic scattering, and using realistic blip response from published experimental results, we demonstrate the capability to identify neutrons and to reconstruct the direction and energy of the final-state neutron system in sub-GeV neutrino interactions. We then explore how neutron-related blip attributes can be used to improve physics studies of neutrino interactions, such as enhancing neutrino-antineutrino separation in atmospheric neutrinos and reverse-horn-current beam neutrinos. This simple study provides an initial quantification of LArTPC neutron reconstruction capabilities, which we expect to improve with future advancements in blip reconstruction, identification, and classification algorithms, as well as the modeling of neutrons.

We propose a neural network-based model capable of learning the broad landscape of working regimes in quantum dot simulators, and using this knowledge to autotune these devices - based on transport measurements - toward obtaining Majorana modes in the structure. The model is trained in an unsupervised manner on synthetic data in the form of conductance maps, using a physics-informed loss that incorporates key properties of Majorana zero modes. We show that, with appropriate training, a deep vision-transformer network can efficiently memorize relation between Hamiltonian parameters and structures on conductance maps and use it to propose parameters update for a quantum dot chain that drive the system toward topological phase. Starting from a broad range of initial detunings in parameter space, a single update step is sufficient to generate nontrivial zero modes. Moreover, by enabling an iterative tuning procedure - where the system acquires updated conductance maps at each step - we demonstrate that the method can address a much larger region of the parameter space.

Efficiently solving the Fokker-Planck equation (FPE) is central to analyzing complex parameterized stochastic systems. However, current numerical methods lack parallel computation capabilities across varying conditions, severely limiting comprehensive parameter exploration and transient analysis. This paper introduces a deep learning-based pseudo-analytical probability solution (PAPS) that, via a single training process, simultaneously resolves transient FPE solutions for arbitrary multi-modal initial distributions, system parameters, and time points. The core idea is to unify initial, transient, and stationary distributions via Gaussian mixture distributions (GMDs) and develop a constraint-preserving autoencoder that bijectively maps constrained GMD parameters to unconstrained, low-dimensional latent representations. In this representation space, the panoramic transient dynamics across varying initial conditions and system parameters can be modeled by a single evolution network. Extensive experiments on paradigmatic systems demonstrate that the proposed PAPS maintains high accuracy while achieving inference speeds four orders of magnitude faster than GPU-accelerated Monte Carlo simulations. This efficiency leap enables previously intractable real-time parameter sweeps and systematic investigations of stochastic bifurcations. By decoupling representation learning from physics-informed transient dynamics, our work establishes a scalable paradigm for probabilistic modeling of multi-dimensional, parameterized stochastic systems.

This paper is the second and final part of a two-part study. We construct positive-energy relativistic spatial localization observables in Minkowski spacetime within standard quantum field theory, using the stress--energy--momentum tensor smeared with suitable test functions. For each fixed timelike direction, the construction gives positive operator-valued measures (POVMs) on spacelike hypersurfaces, well defined on every $n$-particle sector and satisfying a relativistic causality condition excluding superluminal propagation of detection probabilities. The observables are built from local or quasi-local field-theoretic quantities, thus providing a rigorous version of earlier heuristic proposals. In the one-particle sector, the construction reduces to the observable previously introduced by the author, and its first moment gives the Newton--Wigner position operator under appropriate normalization and centering assumptions. Because the Reeh--Schlieder theorem prevents the normally ordered stress--energy--momentum tensor from being positive on the full Fock space, we use quantum energy inequalities to obtain lower bounds controlling deviations from positivity. This leads to regularized operator families, bounded from below, which approximate the localization effects. Finally, we define conditional localization observables for finite laboratories through modified local energy operators. By Haag duality, the corresponding conditional POVMs belong to local von Neumann algebras and commute for causally separated regions, in accordance with the Araki--Haag--Kastler framework. The results show how commutativity of localization observables is recovered for conditional measurements in finite spacetime regions.

In this paper we present a numerical scheme to solve coupled mean field forward-backward stochastic differential equations driven by monotone vector fields. This is based on an adaptation of so called extragradient methods by characterizing solutions as zeros of monotone variational inequalities in a Hilbert space. We first introduce the procedure in the context of mean field games of controls and highlight its connection to the fictitious play. Under sufficiently strong monotonicity assumptions, we demonstrate that the sequence of approximate solutions converges exponentially fast. Then we extend the method and main results to general forward backward systems of stochastic differential equations that do not necessarily stem from optimal control.

Mean field games (MFGs) describe the limiting behavior of large populations of strategically interacting agents. This paper addresses two numerical challenges for MFGs: globally convergent forward solvers and solver-agnostic methods for inverse problems. For the forward problem, we extend the Hessian--Riemannian flow (HRF), previously developed for stationary MFGs, to time-dependent MFGs. We first discretize the system in space and time and then construct the flow directly on the resulting finite-dimensional problem. The proposed flow exploits Lasry--Lions monotonicity, preserves the initial density and terminal value function, and maintains positivity and mass of the density. Under standard assumptions, we prove global convergence of the HRF and show how to recover a solution of the full discretized time-dependent MFG system from its limit. For the inverse problem, we formulate parameter estimation as a bilevel problem in which the outer problem updates unknown coefficients and the inner problem solves the discretized MFG system. Gradients of the outer objective are obtained by differentiating the discretized MFG system at the inner solution, rather than differentiating through the iterations of a particular forward solver. This yields a solver-agnostic framework with adjoint-based gradient descent and Gauss--Newton acceleration. Numerical experiments on stationary and time-dependent MFGs demonstrate the effectiveness of the proposed methods.

The origin of recently observed spontaneous chiral symmetry breaking in polar fluids is an unsolved problem, and poses fundamental questions as to how heliconical structures emerge in systems composed of achiral molecules. We report on the softening of bend elasticity close to such phase transition, showing that flexoelectric coupling between the electric polarization and the bend deformation is the responsible mechanism, presumably arising from the bent shape of the constituent highly polar molecules.

The variational quantum eigen solver (VQE), has been widely used to find the ground state energy of different Hamiltonians with no analytical solutions and are classically difficult to compute. In our work, we have used VQE to identify the phase transition boundary for an infinite order phase transition. We use long-range XXZ (LRXXZ) chain for our study. In order to probe infinite order phase transition, we propose to utilise the ground state energy obtained from VQE. The idea rests on the argument that VQE requires an ansatz circuit; therefore, the accuracy of the VQE will rely on this ansatz circuit. We have designed this circuit such that the estimated ground state energy is sensitive to the phase it is evaluated in. It is achieved by applying the constraint that the net spin remains constant throughout the optimisation process. Consequently, the ansatz works in a certain phase where it gives relatively small random error, as it should, when compared to the error in ground state energy calculations of the other phases, where the ansatz fails. By identifying these changes in the behaviour of the error in ground state energy using VQE, we were able to determine the phase boundaries. Using exact diagonalisation, we also compare the behaviour of the energy gradient and energy gap across both the phase transition boundaries for this model. Further, by increasing the depth of the optimisation circuit, we also accurately evaluate the ground energy of the LRXXZ chain for the value of coupling constant, J equal to -1

The rapid scaling of deep neural networks comes at the cost of unsustainable power consumption. While optical neural networks offer an alternative, their capabilities remain constrained by the lack of efficient optical nonlinearities. To address this, we propose an optical neural computing architecture by embedding quantum emitters in inverse-designed nanophotonic structures. Due to their saturability, quantum emitters exhibit exceptionally strong nonlinearity compared with conventional materials. Using physics-aware training, we numerically demonstrate that the proposed architecture can solve complex tasks, including nonlinear classification and reinforcement learning, within all-optical neural networks. To enable fair comparison across different platforms, we introduce a framework that quantitatively links nonlinearity to a network's expressive power. Analysis shows that our quantum activation operates at $\text{nW}/μ\text{m}^2$ intensity, which is seven orders of magnitude below the nonlinearity threshold of conventional optical materials. Looking ahead to large language models, we estimate the nonlinearity-limited optical power, which scales sublinearly with model size. Our results indicate that quantum nanophotonics may provide a route toward sustainable AI inference.

Estimating molecular ground-state energies is a central application of quantum computing, requiring both the preparation of accurate quantum states and efficient energy readout. Understanding the effect of hardware noise on these experiments is crucial to distinguish errors that have low impact, errors that can be mitigated, and errors that must be reduced at the hardware level. We ran a state preparation and energy measurement protocol on an ion-trap quantum computer, without any non-scalable off-loading of computational tasks to classical computers, and show that leakage errors are the main obstacle to chemical accuracy. More specifically, we apply adiabatic state preparation to prepare the ground state of a six-qubit encoding of the H3+ molecule and extract its energy using a noise-resilient variant of iterative quantum phase estimation. Our results improve upon the classical Hartree-Fock energy. Analyzing the effect of hardware noise on the result, we find that while coherent and incoherent noise have little influence, the hardware results are mainly impacted by leakage errors. Absent leakage errors, noisy numerical simulations show that with our experimental settings we would have achieved close to chemical accuracy, even shot noise included. These insights highlight the importance of targeting leakage suppression in future algorithm and hardware development.

Partial Differential Equations (PDEs) are fundamental mathematical models for describing physical phenomena, yet most PDEs of practical interest require numerical approximations. The feasibility of such methods is constrained by existing computational models. Since digital computers are the primary realizations of numerical computations, and Turing machines define their theoretical limits, computability of PDE solutions is of fundamental significance. It provides a rigorous framework to distinguish equations that are effectively solvable from those that encode undecidable or non-computable behavior. Once computability is established, complexity theory quantifies the resources required to approximate PDE solutions. In this work, we present a novel framework based on least-squares variational formulations and associated gradient flows to analyze the computability and complexity of PDE solutions from an optimization perspective. Our approach approximates PDE solution operators via discrete gradient flows, linking PDE properties, such as coercivity, ellipticity, and convexity, to solution complexity. Within this setting, we characterize representation- and discretization-dependent sufficient conditions for regimes where PDEs admit polynomial-time approximations, as well as regimes exhibiting complexity blowup, where polynomial-time input data produce solutions with super-polynomial complexity. In summary, this paper develops a variational framework for analyzing computability and computational complexity of PDE solution classes. The results show how PDE structure and solution regularity influence their complexity, by establishing sufficient conditions for computability and complexity bounds. Beyond the theoretical characterization, the framework provides guidelines for effective numerical methods and contributes to understanding the limitations of digital computation for PDE problems.

In gravitational theories containing matter fields and higher-derivative corrections, the standard Smarr formula often fails unless all dimensionful couplings are incorporated consistently. Traditionally, parameters such as the cosmological constant or the coefficients of higher-derivative terms are regarded as immutable features of the theory and therefore excluded from the thermodynamic phase space. In our recent work, we developed a fully general framework that promotes every such coupling to a dynamical, freely varying parameter of black hole solutions. This is accomplished by introducing, for each coupling, an auxiliary scalar and gauge field, through which the coupling appears as a conserved charge associated with the global sector of an emergent gauge symmetry. The corresponding conjugate variables naturally arise as electric potentials evaluated at the black hole horizon. As a result, the first law and the Smarr relation acquire additional, systematically determined contributions, yielding a consistent and universal extension of black hole thermodynamics. We illustrate the validity of this construction by revisiting several black hole examples in the literature where the Smarr formula remains inconsistent even after treating the cosmological constant as a thermodynamic variable. Our analysis shows that only by including all dimensionful couplings in this generalized manner can one obtain an internally consistent Smarr relation, thereby providing the foundation for a truly universal formulation of black hole thermodynamics.

We investigate a one-dimensional tight-binding model in which onsite potentials $\{\varepsilon_i\}$ exhibit power-law spatialcorrelations (with exponent $α$) and the hopping amplitudes decay as $t_{ij}\sim |i-j|^{-β}$. This two-parameter family interpolates continuously between short-range Anderson-like disorder, correlated disorder with conventional hopping, and long-range hopping models with nontrivial delocalization tendencies. Using large-scale exact diagonalization, we construct a comprehensive phase map in the $(α,β)$ plane by combining spectral statistics, density-of-states analysis, and energy-resolved localization indicators such as the participation ratio, single-particle entanglement entropy, level-spacing ratio $r$, and the ratio of the geometric to arithmetic density of states. From these observables we define phase-indicator functions that compactly quantify localization behavior across the spectrum. Our analysis reveals robust mobility edges and multiple regimes of spectral coexistence between localized, extended, resonant, and critical states. Finite-size scaling, implemented via an explicit smoothness-based cost function, enables extraction of critical exponents and delineation of transition lines across the $(α,β)$ parameter space. To validate and complement these physics-based diagnostics, we employ a supervised autoencoder that learns high-level representations of eigenstate structure directly from raw features and reliably reproduces the phase classification defined by the indicator functions. Together, these approaches provide a coherent and internally consistent picture of the spectral transitions driven by correlated disorder and long-range hopping, establishing a unified framework for characterizing mobility edges in long-range one-dimensional systems.

We study an inverse boundary value problem for the nonlinear wave equation in $2 + 1$ dimensions. The objective is to recover an unknown potential $q(x, t)$ from the associated Dirichlet-to-Neumann map using real-valued waves. We propose a direct numerical reconstruction method for the Radon transform of $q$, which can then be inverted using standard X-ray tomography techniques to determine $q$. Our implementation introduces a spectral regularization procedure to stabilize the numerical differentiation step required in the reconstruction, improving robustness with respect to noise in the boundary data. We give rigorous justification and optimal stability estimates for the regularized spectral differentiation of noisy measurements, which may be of independent interest. Numerical experiments demonstrate the feasibility of recovering potentials from boundary measurements of nonlinear waves and illustrate the advantages of the Radon-based reconstruction.

Granular creep is the slow, sub-yield movement of constituents in a granular packing due to the disordered nature of its grain-scale interactions. Despite the ubiquity of creep in disordered materials, it is still not understood how to best predict the creep-to-failure regime based on the forces and interactions among constituents. To address this gap, we perform experiments to explore creep and failure in quasi two-dimensional piles of photoelastic disks, allowing the quantification of both grain movements and grain-scale contact force networks. Through controlled external disturbances, we investigate the emergence and evolution of grain rearrangements, force networks, and voids to illuminate signatures of creep and failure. Surprisingly, the force chain structure remains dynamic even in the absence of observable particle motion. We find that shifts in force chains provide an indication to larger, avalanche-scale disruptions. We connect these force signatures with the geometry of the voids in the pile. Overall, our novel experiments and analyses deepen our mechanical and geometric understanding of the creep-to-failure transition in granular systems.

The emergence of neutral collective modes is a hallmark of correlated quantum phases but is often challenging to probe experimentally. In two-dimensional flatband systems, charge responses have been intensively investigated yet neutral excitations remain largely unexplored. In particular, intervalley coherent state (IVC) features a neutral Goldstone mode due to spontaneously broken valley U(1) symmetry. While IVC state has been proposed as a unifying theme across graphene and semiconductor based systems, its defining feature, the neutral Goldstone mode, remains elusive in experiment. Here we investigate space and time resolved transport of neutral modes in twisted WSe2 moire superlattices through a novel ultrafast imaging technique. We uncover two new propagating collective modes with very different velocities, which emerge near the van Hove singularity (VHS) in both intermediate (3.5 to 4 degree) and large (around 5 degree) angle twisted WSe2. The fast-propagating mode has a large speed of about 3 km/s and is consistent with a Goldstone mode for an IVC state, while the slow-moving mode is likely a gapped amplitude mode. They can be understood as the spin-valley analogues of collective modes of a superfluid, whose propagation is imaged for the first time in a condensed matter system. Our study demonstrates a powerful new approach for probing charge-neutral modes in quantum materials and offers key insights into the interplay between charge and spin-valley physics in moire superlattices.

The Doyle-Fuller-Newman (DFN) model resolves internal electrochemical states in lithium-ion batteries with high fidelity. However, the numerical solution of its governing equations is computationally prohibitive for real-time deployment, limiting scalability from individual cells to pack and fleet-scale applications. While machine learning surrogates can substantially reduce inference latency through GPU acceleration, most existing approaches learn solution approximations tied to specific operating conditions rather than learning generalizable state-evolution dynamics. This work presents a systematic comparison of four neural network architectures (MLP, ResNet, U-Net, FNO) formulated as autoregressive state-transition operators that predict full DFN internal states across a wide range of operating conditions. To ensure a controlled architectural comparison, all models are trained under a unified framework using multi-step unrolling and current-conditioning, isolating the impact of spatial inductive bias. Results demonstrate that the U-Net's multi-scale feature hierarchy achieves a mean final-step nRMSE of 3% averaged across all internal state variables after 300-step autoregressive rollouts, while providing a 5.38x speed-up over the numerical solver. These findings highlight spatial inductive bias as a critical determinant of surrogate performance, advancing the development of surrogates for internal state observability for next-generation battery management systems and digital twins.

Long-span roadway bridges exhibit highly localized structural responses under vehicular loading, making repeated FE analysis computationally expensive for applications such as influence surface generation and structural digital twins. Existing SciML approaches struggle to accurately capture these localized responses. To address this challenge, this study proposes an adaptive-trunk DeepONet for localized structural response prediction in large-scale bridge systems. The framework dynamically constructs a load-dependent learning domain using a KNN strategy, allowing the network to focus on structural influence zones. The trunk network is further enhanced using distance-aware features that encode the geometric relationship between the load and structural nodes. A physics-based full-field reconstruction is incorporated through a stiffness-informed Schur complement formulation, enabling predictions at adaptive nodes to be extended to the entire structural domain. To enable scalable training, response data are generated using a reduced-order equivalent shell model that preserves the dominant global behavior while significantly reducing computational cost. The proposed framework is validated on both a benchmark bridge model and the real-world Mussafah Bridge. Results show that the method achieves FEM-level accuracy with relative errors below 5%, while reducing the total response evaluation time (including full-field reconstruction) by approximately 60x; excluding the post-processing reconstruction step, the AD-DeepONet inference is up to four orders of magnitude faster than FEM. In addition, the framework enables rapid generation of full-field responses, influence lines, and influence surfaces under arbitrary vehicular loading configurations, demonstrating strong potential for large-scale bridge analysis and digital twin applications.

Identification of the particle interaction potential is a challenging and important task in dusty plasma, colloids, and smart materials as it allows the characterization of structure formation and helps predict phase transitions. With the advent of machine learning methods, this interaction can be extracted from particle position data, leading to a generalizable expression which is applicable in different systems. Methods such as sparse regression aim to provide a physically interpretable model that can generalize well, while avoiding unnecessary complexity due to overfitting. In this work, we present the use of the Sparse Identification of Nonlinear Dynamics (SINDy) with the weak formulation to learn equations of motion for noisy data from simple simulations of two dust particles interacting with a Yukawa (shielded Coulomb) potential. The application of these methods to experimental dusty plasma data is discussed, particularly in the case of simulation data and glass box experiments in RF discharge gravity environments and DC discharge microgravity environments, such as the Plasmakristall-4 (PK-4) experiment.

Molecules are often represented as SMILES strings, which can be readily converted to hand-crafted descriptors or fingerprints (FP) for molecular property prediction. Research has demonstrated that SMILES can be converted to molecular graphs $G = (V, E)$, with atoms as nodes $(V)$ and bonds as edges $(E)$. These molecular graphs can subsequently be used to train graph neural networks (GNN) models. Despite the recent surge in application of GNN (existing and novel architectures) for molecular property prediction, a rigorous benchmark is still lacking. We propose MolGraphBench, a comprehensive benchmark of four commonly used GNN models for molecular property prediction. Benchmarking results demonstrate graph convolutional network (GCN) and graph isomorphism networks (GIN) as the optimal GNN architectures for molecular graph regression tasks, based on absolute performance, training efficiency, transfer learning and prediction quality. The study also indicates the non-complementary nature of molecular fingerprints in the fusion (GNN-FP) framework. Furthermore, our GNN models achieved performance superior or comparable performance to current state-of-the-art GNN baselines across three datasets (GCN with RMSE of $0.518$ on B3DB, GIN-FP with RMSE of $1.022$ on FreeSolv and GIN with MAE of $63.783$ on RT datasets). Findings from this study indicate that type of GNN-layer, should be treated as a tunable hyperparameter rather than a fixed design choice to achieve superior performance.

While correlated phenomena of flat bands have been extensively studied in twisted systems, the ordered states that emerge from interactions in the intrinsic flat bands of kagome lattice materials remain largely unexplored. The newly discovered kagome metal CsCr3Sb5 offers a unique and rich platform for this research, as its multi-orbital flat bands at the Fermi surface result in a complex interplay of pressurized superconductivity, antiferromagnetism, a structural phase transition, and density wave orders. Here, using ultrafast optical techniques, we provide strong spectroscopic evidence for a charge density wave transition in CsCr3Sb5, resolving previous ambiguities. Crucially, we identify rotational symmetry breaking that manifests as a three-state Potts-type nematicity. Our elastoresistance measurements directly demonstrate the electronic origin of this order, as the rotational-symmetry-breaking E2g component of the elastoresistance shows a divergent behaviour around the transition temperature. This exotic nematicity results from the lifting of degeneracy of the multi-orbital flat bands, akin to phenomena seen in certain iron-based superconductors. Our study pioneers the investigation of ultrafast dynamics in flat-band systems at the Fermi surface, offering new insights into the interactions between multiple elementary excitations in strongly correlated systems.

Aliphatic hydrocarbons, such as normal alkanes, constitute a naturally abundant source of carbon atoms. Of special interest is the formation of cyclic and aromatic products from aliphatic reactants. Combining scanning tunneling microscopy and ab initio calculations, we investigate the thermal induced aromatization of linear n octane molecules on the catalytic Pt(111) surface and the reactions of intermolecular homocoupling between them at temperatures above 600 K. The cycloaromatization of individual n octane molecules requires bending the linear adsorbates prior to their dehydrogenation and the formation of an intramolecular C-C bond, yielding adsorbed benzene rings. In addition, the Pt(111) surface catalyzes a homocoupling reaction by initiating the formation of a C-C bond between the dehydrogenated methyl ends of the chemisorbed n octane molecules and then propagating along the carbon backbone in a zipper like fashion. Our findings provide molecular level insight into the heterogeneous catalytic processes underlying the generation of aromatic products and stable on surface polycyclic species.

While geostrophy remains the simplest and most practical balance to extract velocity information from sea-surface height anomaly (SSHa), confusions remain within the oceanographic community to what extent this balance can be applied to altimetric observations with the launch of the Surface Water and Ocean Topography (SWOT) satellite. Given the limited temporal resolution of SWOT, many studies have resorted to claiming that the spatially filtered SSHa fields correspond to the geostrophic component. This introduces the ambiguity of which spatial scale to choose. Here, we build upon the recent developments in internal tide (IT) corrections (Yadidya et al., 2025) and apply a dynamic mode decomposition (DMD)-based method introduced by Lapo et al. (2025) to robustly extract the geostrophic component associated with sub-inertial frequencies from the SWOT one-day-repeat orbit; we distribute the global dataset as a public good. We provide the joint probability density function (PDF) of vorticity and strain, and spectra of SSHa at a few cross-over regions.

We introduce a novel active-learning framework for failure probability estimation in structural reliability analysis that integrates Active Kriging Monte Carlo simulation with conformal prediction. The proposed approach employs an adaptive cross-conformal strategy specifically designed for small-sample settings and kriging surrogate models using the J+GP conformal estimator. Unlike standard AK-MCS methods, the proposed framework provides distribution-free guarantees on prediction errors, leading to more reliable classification of samples near the limit-state surface. This improved uncertainty quantification enhances both the accuracy and robustness of failure probability estimates, especially for rare-event regimes where such efficiency is crucial. Reproducible numerical results illustrate the effectiveness of the method and also compare it to classical approaches on well-established benchmarks.

Factor models are popular approaches for analyzing high-dimensional data to extract low-rank signals and estimate covariances. They decompose the covariance matrix as the sum of low-rank and diagonal components. A key issue is how to choose the latent dimension $k$, which is particularly challenging when the factor model only holds approximately and in low signal-to-noise scenarios. Bayesian overfitted factor models specify an upper bound on $k$ and rely on structured shrinkage priors to effectively remove extra components. Such approaches are popular and effective, but computationally expensive. We propose a much faster \texttt{EigenBayes} approach that provides valid uncertainty quantification, based on spectral estimation of latent factors and adaptive empirical Bayes calibration of key hyperparameters. The resulting posterior distribution factorizes across outcomes and is analytically tractable, bypassing Markov chain Monte Carlo. We show that \texttt{EigenBayes} adapts to the signal-to-noise ratio of each outcome and latent dimension, while shrinking superfluous latent components to zero. We establish favorable asymptotic properties and demonstrate strong empirical performance in numerical experiments and a genomics application, where EigenBayes outperforms state-of-the-art alternatives.

Brain network is commonly divided into modules for analyzing their functionally segregated roles for group-level analysis in neuroimaging studies. Here, we introduce stochastic modules within brain networks for a robust probabilistic measurement of structural-functional module consistency (SFMC) in a group of subjects. Specifically, a stochastic module can be regarded as the chance of a brain region across subjects potentially being assigned to a group-level sub-network, characterized as an assignment probability for this brain region. This novel method has two advantages for evaluating inhomogeneous modules in brain networks. The first is that it can robustly evaluate the consistency between brain structural and functional modules whose population sizes are not necessary the same, and the second is that it is able to take into account the inter-individual variability of the modules for the groups. Moreover, compared with the conventional structural-functional coupling approach, our stochastic module-based method reveals a more pronounced decline in the coupling between structure and function, indicating stronger developmental reorganization. Our results using the dataset from Baby Connectome Project (BCP) show that the SFMC decreases from 0 to 5 years old, and is greater in primary brain regions, such as visual areas, while lower in more advanced cognitive regions, including those related to attention, control, and default mode network.

Seasonal influenza infects millions of people and causes substantial morbidity and mortality in the United States each year, making accurate short-term forecasting a core public-health need. Reliable forecasts of epidemic time series can inform vaccination timing, hospital staffing, and resource allocation, yet the comparative behavior of modern forecasting architectures on infectious-disease surveillance data remains insufficiently characterized. We address this gap through a systematic evaluation of regional influenza forecasting using influenza-like illness surveillance and influenza-associated hospitalization time series under both temporal and spatial generalization settings for 1-4-week-ahead prediction. We compare classical neural network architectures, numerical transformer-based models, pretrained time series foundation models, and LLM-based forecasting approaches. Across tasks, we demonstrate that a mixture-of-experts model that fuses multiple pretrained forecasters achieves the strongest overall performance, indicating that heterogeneous pretrained representations provide complementary predictive information. Our results further show that numerical transformer-based models produce reliable forecasts, while pretraining provides the largest gains at longer horizons, particularly when the pretraining domain is mechanistically aligned with influenza dynamics. In contrast, LLM-based time series methods underperform relative to numerical forecasters in this setting. Finally, we examine hospitalization information as both an auxiliary covariate and a pretraining source. Hospitalization signals provide complementary improvements in selected settings and clarify when additional surveillance streams enhance the robustness of multi-horizon forecasting. These findings provide actionable guidance on model selection, pretraining strategy, and auxiliary-signal use for influenza preparedness.

Reliable benchmarking is critical for developing machine learning models for tandem mass spectrometry (MS/MS) based molecule discovery. Subtle issues in experimental design and model evaluation procedures can degrade the trustworthiness of such benchmarks and lead to erroneous conclusions. We conduct a thorough review of model evaluation issues in the recent MS/MS machine learning literature, using the standard MassSpecGym benchmark suite as a case study to illustrate the impact of these issues. We find evaluation issues in at least 17 of 26 papers reporting MassSpecGym benchmark results in the first year of its adoption. We isolate three classes of failures: (i) data leakage, (ii) shortcut learning, and (iii) implementation bugs and metric divergence. Through extensive experimentation and code replication, we quantify the impact of these issues and show how they corrupt the evaluation standards MassSpecGym was designed to enforce. We distill our findings into recommendations generalizable to MS/MS challenges, benchmarks, and custom evaluation setups. We also release MassSpecGym v1.5, an implementation of our recommendations in the MassSpecGym benchmarking suite which addresses the failure modes identified in this audit. MassSpecGym v1.5 is publicly available at https://github.com/pluskal-lab/MassSpecGym.

Generative models can produce individually plausible samples while deviating substantially from a target set in the distribution of key features. For example, a model pretrained on broad drug-like chemical space may generate molecules whose molecular features differ from those of a therapeutic class of interest, such as known antibiotics. Correcting such distributional miscalibration is challenging: direct finetuning on the target set can overfit and does not control which features are matched. To fill this gap, we introduce kernel Calibrating Generative Models (kCGM). kCGM minimizes a maximum mean discrepancy (MMD) between generated and target feature distributions using an unbiased score-function estimator, with KL regularization to remain close to the pretrained model. On a target set of 174 antibiotics, direct finetuning sacrifices chemical validity for feature-distribution matching, whereas kCGM improves target feature matching while increasing validity. We further demonstrate kCGM in protein and DNA generation tasks, showing it can adapt autoregressive, continuous-space diffusion, and discrete diffusion models using only feature-level supervision. Code is available at https://github.com/smithhenryd/cgm.