Papers

Many inverse problems in physics infer an unobserved field from measurements connected to it through a governing equation. We combine Fisher information with a differentiable solver to quantify uncertainty in both the inferred field and its predicted observables, using a local Gaussian approximation without sampling the full parameter posterior. Applied to nuclear optical potentials, the method distinguishes features constrained by scattering measurements from those whose uncertainty remains set by the prior. Our flexible model improves agreement with held-out cross sections and achieves nearly nominal coverage with narrower predictive intervals than an established Bayesian optical model.

Accurate digital maps are essential for Advanced Driver Assistance Systems (ADAS) or Autonomous Driving (AD), providing critical information such as road geometry, traffic signs and speed limits required by safety functions including Intelligent Speed Assistance (ISA). Maintaining these map layers using traditional surveying methods is costly and difficult to scale. Crowdsourced approaches based on fleets provide a promising alternative for continuously validating and updating map information. However, the relationship between the number of contributing vehicles and the quality of the resulting map remains poorly understood. To address this gap, this paper presents a simulation-based framework for evaluating crowdsourced traffic sign maintenance using a dissimilarity measure called GOSPAM (Generalized Optimal SubPattern Assignment for Maps), which combines localization errors with detection performance by accounting for False Positives (FP) and False Negatives (FN). The proposed system models multivehicle observations with representative sensor noise, detection errors, and semantic recognition uncertainties. Observations from multiple vehicles are aggregated using spatial clustering and semantic filtering to estimate traffic sign locations. Using simulated trajectories generated from data carried out by an experimental vehicle in an area containing ground-truth traffic signs, we assess the influence of fleet size on the performance of crowdsourced mapping. The number of vehicles ranges from 5 to 50, and performance is analyzed using standard evaluation metrics which are compared to the GOSPAM . The results show that GOSPAM can be used to effectively assess the quality of crowdsourced mapping, such as the contributions made by the first vehicles or the improvements made by numerous vehicles.

Raman preprocessing and enhancement methods are often assessed by comparing their output with a clean reference spectrum using measures such as mean squared error (MSE). Whether these spectral quality measures reflect downstream analytical performance is rarely tested. We propose a controlled-perturbation framework for this test. Five perturbation types (baseline distortion, independent noise, correlated noise, global wavenumber shift, and nonlinear axis warping) at eight strengths produce paired changes in a quality measure (metric harm) and in downstream performance (task harm). The alignment gap (AG) quantifies how much a single monotone metric-to-task relationship, fitted by isotonic regression, improves when each perturbation type receives its own relationship. Ordering concordance (OC), a clustered Kendall-type index, measures how often a measure ranks conditions of different perturbation types in the same order as their task harm. Cluster-bootstrap intervals and Holm-adjusted sign-flip tests compare twelve candidate measures with MSE. Three public datasets are used: bacterial classification by principal component analysis and logistic regression, sugar-mixture quantification by partial least squares regression, and mineral identification by cosine library matching. Models are fitted to unperturbed or to correspondingly perturbed training spectra. For bacterial classifiers fitted to unperturbed spectra, Wasserstein distance improved both statistics relative to MSE (Holm-adjusted p < 0.05), also after axis perturbations were removed or spectra were compared on a common grid; refitting to perturbed spectra reversed this advantage. Peak-based measures and a structure-to-noise ratio improved both statistics only for refitted sugar calibrations, and no candidate did so for mineral identification. Open code supports testing new measures.

Returning to a familiar location can help a searcher find its target—but how should the target move to avoid being found? We address this question for a resetting Brownian searcher and a mobile target fluctuating around a home location. Keeping the target's typical exploration range fixed, we find that the mean capture time is maximized at an intermediate correlation time: rapid motion promotes encounters, whereas slow motion leaves the target effectively stationary. Between these extremes, persistent excursions away from the searcher's reset point can substantially delay capture. Analytical limiting results explain this optimum, while numerical solutions reveal an approximately linear relation between the maximal mean capture time and the optimal correlation time across many decades. These findings identify temporal correlations as a resource for evasion, allowing a target to prolong survival by changing how it moves rather than where it roams.

The efficient operation of accelerator facilities increas- ingly relies on rapid access to heterogeneous operational knowledge, including logbooks, interlock reports, machine parameters, and historical archive data. At ELBE, we pro- posed a Retrieval-Augmented Generation (RAG) frame- work that integrates facility documentation and operational records into a unified AI-assisted support tool for operators. The system is expected to index electronic logbooks, ma- chine archive time-series data, and subsystem manuals using domain-adapted embeddings stored in a vector database. User queries will be expected to be processed through a large language model that retrieves the most relevant oper- ational context and generates structured, operator-oriented responses with traceable source references. This contribu- tion presents the system architecture, data integration strat- egy, and challenges toward real-time AI-assisted accelerator operation

Accurately predicting fast solar wind conditions is challenging, as uncertainties are large and unquantified by traditional single-value prediction models. In particular, the risks of high-speed solar wind streams (HSSs), which can cause damage to technological infrastructure, cannot be reliably assessed without probabilistic forecasts. We present PROSWIN, a probabilistic machine learning model that forecasts the hourly solar wind speed (SWS) at Earth with a four-day lead time. The approach combines solar images and magnetograms using a deep neural network coupled to a distributional regression algorithm. Because standard error metrics underweight the relevance of HSS peaks, we further introduce the prediction score, a model-selection metric that jointly rewards timeline and HSS peak accuracy. On 14 years of data, our forecast achieves very well-calibrated uncertainties (<1% average deviation). Using the continuous ranked probability score (CRPS), a metric that assesses distributional accuracy, we obtain a timeline CRPS of 41.0 km/s, an HSS peak CRPS of 45.3 km/s, and a prediction score of 42.3 km/s. We find that the 171 Å channel is an important complement to the typically used 193 Å and 211 Å channels and that the prediction score for model selection improves the applicability of the model. Compared to selected models from the literature, ours is the only one that is accurate for both timeline and HSS peak values, rather than trading one off against the other. These results support the advantages of probabilistic over single-value solar wind models. The introduced methods are also transferable to other forecasting problems.

Reconstructing the stress field of a planar viscoelastic flow from optical measurements loses its direct evidence wherever optical coverage is interrupted, and no improvement in optical precision restores an observation that was never made. We characterize what a second, velocity channel adds, and what neither channel can supply. Two calibrated optical components determine the local deviatoric stress pointwise, while velocity constrains spatial stress variation through momentum balance, so the two channels are complementary rather than redundant. The isotropic part of the stress is unobservable to both: the divergence of an isotropic field is a pure gradient, which the Leray projection annihilates, so every representable isotropic mode lies in the joint null space. That accounts for the null space exactly when the optical field is complete, and bounds it from below otherwise, since finite incomplete sampling and aperture zeros can remove further directions. We verify the count directly on three discretizations. In paired synthetic tests with finite measurement apertures, spatially correlated noise and optical stripe dropout, adding velocity reduces the mean whole-domain deviatoric error from 50.40% to 27.82% at 3% reference noise, and the improvement survives shared gaps, inverse-grid refinement at fixed physical sampling, and a constitutively generated stress field. The improvement does not rest on how the regularization parameter is chosen: it holds under both the expected-norm discrepancy rule and generalized cross-validation, and we report each selection with its position in the search interval, which is where the two rules differ.

When multiple differential cross-section measurements are extracted from a common event sample, the same events contribute simultaneously to multiple distributions. This event-sharing structure imposes exact linear constraints among the bin counts, reducing the effective dimensionality of the measurement below the total number of bins. Since the covariance matrix obeys these inter-distribution constraints, it contains a rank deficiency. While limited numerical precision may inadvertently restore invertibility, the $\chi^{2}$ contributions along constrained dimensions will be arbitrary, yielding unphysically inflated $\chi^{2}$ values in global goodness-of-fit tests. We present the range-projected $\chi^{2}$, a test statistic that restricts the goodness-of-fit test to the subspace carrying independent statistical information, yielding a $\chi^{2}$ with $N_\text{bins} - N_\text{null}$ degrees of freedom, where $N_\text{null}$ is the number of independent constraints. We show that this rank deficiency is a predictable consequence of the event-sharing structure, and that $N_\text{null}$ decomposes into a structural contribution determined a priori from the binning geometry and a kinematic contribution that depends on the phase-space occupancy. The method is validated with an analytical toy model and a simulated neutrino–argon cross-section measurement including unfolding and multi-source systematic uncertainties.

We report the experimental observation and characterization of Replica Symmetry Breaking (RSB) manifestation while analyzing the transverse intensity profile of pulses in filamentation experiments using sapphire crystal and distilled water, excited by a femtosecond laser centered at 800 nm. The RSB arises from the competition between self-focusing and plasma defocusing, subject to local fluctuations in the nonlinear refractive index generated by plasma via multiphoton excitation, which subsequently promotes frustration among modes. Our results confirm the existence of glassy-like photonic states not only in multifilamentation, as previously reported [W. Ettoumi, J. Kasparian, and J. Wolf, "Spin-glass model governs laser multiple filamentation," Phys. Rev. Lett., vol. 115, no. 3, pp. 033902, 2015], but also in the generation of a single filament and in filamentation accompanied by conical emission. These findings improve the understanding of statistical nonlinear optics by establishing connections with magnetism and highlighting the glassy-like behavior of light in the context of ultrafast optical phenomena.

Recent observations of replica symmetry breaking (RSB) in ytterbium-based mode-locked fiber lasers have revealed glassy behavior in the quasi-mode-locked (QML) regime. Here, we investigate whether this behavior is restricted to a specific laser implementation or represents a more general feature of mode-locked systems. By analyzing statistical correlations of spectral intensity fluctuations through the Parisi overlap and Pearson correlation parameters, we study two Titanium:sapphire laser systems: a homemade cavity and a commercial laser. In both cases, clear signatures of RSB are observed in the QML regime, while replica-symmetric behavior is recovered in the amplified spontaneous emission (ASE) and standard mode-locked (SML) regimes. These results demonstrate the occurrence of RSB in Titanium:sapphire lasers and support the interpretation of the QML regime as a photonic glassy phase. Together with previous observations in ytterbium-based fiber lasers, these findings suggest that the connection between QML dynamics and RSB may be a general feature of mode-locked laser systems.

An unresolved mixture of beta-decaying ground and isomeric states populates a common daughter nucleus through different excitation-energy and spin-parity distributions. A framework is developed to determine when such data admit conventional $\beta$-Oslo and Shape analyses and which quantities remain identifiable. The physical primary-$\gamma$ distribution is an average of separately normalized branching kernels; the global parent fraction does not, in general, equal the fraction in an excitation-energy bin or an accepted primary-$\gamma$ sample. Population invariance, Oslo factorization, and recovery of the total nuclear level density are separated. An exact log-linear compatibility test and a lower-cascade replacement identity isolate factorization and first-generation-subtraction effects. For Shape analysis, matched final-state spins and parities remove common angular-momentum factors but can retain excitation-dependent E1/M1 weights. A graph representation gives consistency conditions and exposes the information lost when only one fixed final-state separation is measured. Deterministic spin-parity-resolved cascade benchmarks reproduce the population-invariant limit and exhibit both exact factorization with an effective, rather than total, level density and small matrix residuals accompanied by appreciable shape errors. Evaluated $\rb\rightarrow\sr$ properties specify a relevant application, including two $2^+$ candidate final states and time-dependent parent mixing. The numerical examples are controlled synthetic tests, not an extraction from $^{90}$Rb data. The results provide criteria for interpreting unresolved-parent measurements and for identifying the additional observations required for population-aware inference.

A polarimeter does not report stress. It reports a retardance and an azimuth, and converting those to a stress pair fixes both the calibration that is required and the covariance that the subsequent inference must carry. We set out that observation chain for planar viscoelastic flow, combine it with velocimetry, and ask what the combined measurement can resolve. The calibration constant is fixed by three separately measurable quantities (path length, stress-optic coefficient and wavelength) rather than being fitted. Propagating the polarimetric errors to first order gives a stress covariance that is anisotropic and site dependent even for independent homoscedastic inputs, and whose conditioning degrades as the retardance approaches zero, where the linearization itself stops describing the measurement. Wrapping imposes a separate design bound. Two numerical studies follow, both in ideal calibrated stress coordinates under a prescribed covariance rather than the propagated polarimetric one. Holding the total scalar count fixed and varying the split between velocimetric and optical sites, an unequal allocation favoring optical sites outperforms either pure configuration. We then ask what the measurement resolves between constitutive models compatible with the same velocity data. In self-consistent pressure-driven flow of the finitely extensible nonlinear elastic Peterlin model, at extensibility L^2=50 and 3% noise, the optical channel rejects the velocity-compatible Oldroyd-B family in 78.1% of realizations at the Deborah number De=2, the ratio of the relaxation time to the flow timescale, and in 100% at De=4, while rejecting only about 5% below De=0.3. The resolving power of a design is therefore a strong function of Deborah number and must be quoted with it.

Molecular systems have many degrees of freedom, but their metastable behavior can often be described by a few collective variables. Identifying these variables and estimating free energies along them from limited simulation data remains a challenging, important problem. Separate short trajectories may sample different metastable states without capturing transitions or establishing their relative equilibrium populations. For unbiased trajectories generated with the same Hamiltonian at a single temperature, alternate methods based on histogram reweighting cannot correct this imbalance. Here we present SPIBER, which combines the State Predictive Information Bottleneck (SPIB) with Generative Flow Networks (GFlowNets). SPIB uses deep learning to approximate slow degrees of freedom through a past-future information bottleneck, retaining information needed to predict future metastable states. We show that this compression limits conditional entropy variations in populated regions, allowing conditional mean potential energies, which are much easier to calculate, to be used to approximate free energy differences. Given sufficient local sampling to estimate these energies, they define the target distribution for GFlowNets, energy-based generative samplers that sample according to estimated thermodynamic stability rather than observed populations. For a particle in a radial double-well potential, for alanine dipeptide, and for the nine-residue peptide AIB9, SPIBER recovers free energy differences between sampled metastable states to within one thermal energy unit of reference values. The method combines collective-variable learning and free energy estimation in up to four latent dimensions, without requiring converged state populations or additional molecular dynamics simulations.

Empirical regularities described by parametrized families of probability distributions can shape how complex systems are interpreted and explained. A recurring problem is to determine the extent to which these descriptions are supported by observations, and how they can be used to characterize the underlying system. Here, we introduce a general framework for constructing constrained surrogates capable of representing arbitrary families of continuous distributions. We demonstrate its utility by providing explicit algorithms for several canonical distributions in statistical physics, including continuous powerlaw, lognormal, exponential, and truncated Gaussian distributions. These constrained surrogates enable unbiased estimation and accurate tests of model validity based on arbitrary (physically meaningful) sample statistics, without requiring specification or estimation of model parameters. We show how these theoretical advantages translate into more informative and nuanced conclusions in applications ranging from bushfire magnitudes and word usage in texts to brain connectomes and city populations.

Context: We developed a probabilistic machine learning method with the aim of performing the O(10)-way classification of low- and high-resolution spectra of stellar and extragalactic targets for the upcoming 4MOST survey. In fulfilment of the survey requirements, this method should be able to express uncertainty in the input data as well as uncertainty introduced in its prediction. Aims: Four different methods are explored: (1) convolutional neural networks (CNNs), (2) the Dirichlet distribution, (3) Monte Carlo dropout (MCD), (4) Bayesian neural Networks (BNNs) + variational inference (VI). Training and validation was performed using labelled spectra from the SDSS database and a custom 4MOST mock dataset. All the methods were compared in terms of the same metrics: accuracy, area under the curve (AUC), expected calibration error (ECE), Shannon entropy, negative log-likelihood (NLL), Brier score, training time, and inference time. Methods: A CNN with simple architecture and about 20,000 parameters was trained to achieve classification accuracies of 91.5% on SDSS data and 92.8% on 4MOST mock data. The direct Dirichlet prediction and VI models tested provide uncertainties on class membership probabilities, but they confuse classes more often. The MCD on a CNN is found to be the most suitable; it boosts the point-estimate accuracies to 92.6% and 93.9%, while still providing fast training and sufficiently fast inference. Compared to a standard CNN, the method additionally provides well-calibrated uncertainties at marginal extra cost.

This paper introduces the mollified-sharp decomposition, a probabilistic regularization of moving shocks in parametric reduced-order models. Each detected shock location is treated as a random variable with a prescribed probability density. Averaging over this artificial distribution replaces the localized pressure change by a smooth transition whose spatial extent is set by the density width, rather than by direct filtering of the pressure field. Each snapshot is decomposed exactly into a regularized mollified field and a local sharp correction that restores the shock. This probabilistic construction and exact additive split define the general method; the detector, kernel, treatment of multiple shocks, alignment coordinates, and regression are implementation choices. In the present realization, a calibrated indicator detects shocks, a compactly supported Wendland kernel mollifies them, and a peak-normalized and, where necessary, partitioned weight derived from each shock-location probability density defines the centroid, principal axes, and scales of its local alignment domain. Separate POD-GPR models represent the mollified field and aligned corrections, with additional regressions for shock presence and alignment. The method is demonstrated on the transonic airfoil pressure data of Catalani et al. (2023) and compared with a standard POD-GPR model constructed from the same data and POD-energy criterion. The mollified-sharp model reduces the mean test-set relative $L^2$ pressure error by 31.2% and the mean test-set surface-pressure-coefficient error by 33.2%, while also improving the predicted shock locations and pressure changes; the trade-off is a median online evaluation time 2.24 times as long. The construction is applicable in principle to other parameter-dependent fields with moving sharp features, such as moving material interfaces in multiphase flows.

Existing aviation emissions inventories lack accurate trajectory data for high-resolution social cost and health impact assessment. This paper develops a 3-D emissions map by reconstructing flight trajectories for US west coast hubs to estimate regional environmental and near-airport health impacts. A physics-informed autoencoder (AE) is applied to ADS-B trajectory records for January 2025 covering US west coast hubs. The encoder combines a Convolutional Neural Network (CNN), a Bi-GRU, and a 3-D CNN with skip connection; the decoder is a Temporal Convolutional Network (TCN). It is benchmarked against a baseline-AE and cubic spline interpolation. Emissions are mapped via EUROCONTROL Base of Aircraft Data (BADA) performance tables and ICAO Engine Emissions Databank (EEDB) emission indices, with altitude corrections via Boeing Fuel Flow Method 2 (BFFM2). Social costs are quantified for all flight phases, with health impacts assessed for Landing and Takeoff cycles within 50 km of each hub. The proposed AE model outperforms both a TCN-AE and cubic spline interpolation across 5% to 50% missing rates. Monetizing the emissions inventory shows NOx produces a small net cooling effect in direct climate forcing, while accounting for 99.7% of monetized air-quality and health cost despite being under 0.4% of CO2 by mass, making it the dominant health-cost driver. To our knowledge, this is among the first studies combining AE-based trajectory reconstruction with separate spatial-temporal feature encoding and altitude-based emissions modeling to produce a regional aviation emissions inventory for air quality, climate impact and population exposure. The resulting emissions map and social cost estimates provide quantitative context for environmental impact assessment and near-airport health policy evaluation for US domestic aviation.

The most energetic coherent structure of a hovering full-scale quadcopter is associated with a self-organizing process in which the individual rotor vortices synchronize their frequencies while undergoing merging events, yielding a globally correlated structure. We identify and characterize this phenomenon by applying spectral modal and conditional analyses to assimilated three-dimensional velocity data acquired via Shake-The-Box Lagrangian particle tracking. The dataset captures a high-Re, turbulent flow further complicated by time-varying rotor speeds stemming from active flight control, low-frequency vehicle drift, finite spatio-temporal resolution, and measurement uncertainty. Most coherent structures recover established single-rotor features such as tip vortices and their subharmonic pairing. The globally synchronized vortex merging manifests as a spectral peak at an incommensurate frequency below the rotor band, which cannot be explained by single-rotor aerodynamics, subharmonic instabilities, or band-to-band triadic interactions. Instead, conditional averaging provides evidence of the aforementioned intermittent, distinctly non-subharmonic vortex-merging process involving all four rotor wakes. Establishing whether or not this phenomenon is observed across different flight conditions and configurations remains speculative; however, the consistent characterization of the globally synchronized vortex merging using complementary frequency- and time-domain analyses despite experimental complexities, in particular rotor speed variations, demonstrates its robustness.

We propose a new approach for analyzing Time-Dependent Perturbed Angular Distribution data. In this, a likelihood is constructed with the help of conditional probabilities of single events and binning of time data is avoided. This likelihood is used in a Bayesian framework to calculate the posterior probability density function for the $g$ factor of interest. This approach is compared to more traditional approaches that use binned data by analyzing simulated datasets. In many cases the resulting posterior probability densities are observed to be multimodal and the results can thus often not be summarized with a single Gaussian approximation. We find that results from the new approach are more reliable for low-statistics datasets.

The test error of a model plotted against its number of parameters $d$ falls, peaks when the model can just fit the training data, and falls again, exhibiting the double descent phenomenon. We explain the phenomenon with statistical mechanics. The training trajectory of a stochastic gradient-based method is a particle wandering over the energy landscape of the training loss at an induced temperature $T$, and a run that has equilibrated visits every parameter vector of a given training loss equally often, the fundamental postulate of statistical mechanics, with probability given by the Boltzmann distribution. Because training starts at an initial point and has only finite time to diffuse, it carries an effective weight decay, which makes every parameter a quadratic degree of freedom. The equipartition theorem then distributes the energy among the $d$ degrees of freedom in shares of $T/2$, so at a fixed training loss adding parameters lowers the temperature and drives the Boltzmann distribution toward the stationary path. Finally, adding parameters can only lower the $L^2$ norm of the stationary path, so a solution sampled at fixed loss is less likely to be large with increasing $d$, effectively increasing weight regularization.

Environmental systems are characterized by complex spatial interactions that cannot be fully described through pairwise relationships or local uncertainty measures. We propose a unified framework combining higher-order information theory and topological data analysis to characterize the organization and uncertainty of environmental networks. Spatial entities, represented by monitoring stations or municipalities, are embedded into a Delaunay simplicial complex, and O-information is used to quantify redundancy and synergy among neighboring triplets. The resulting field of higher-order interactions is analyzed through persistent homology, enabling the identification of topological structures that remain stable across interaction scales. The methodology is applied to both an air-quality monitoring network based on weekly \(\mathrm{NO_2}\) and \(\mathrm{O_3}\) observations and a multi-hazard territorial assessment. We show that regions exhibiting strong O-information and persistent topological structures correspond to robust environmental patterns, whereas areas characterized by heterogeneous regimes and rapidly varying interactions display increased uncertainty. Building on these results, we introduce a topological uncertainty framework that integrates simplex divergence, higher-order interactions, and topological uncertainty. Our results demonstrate that uncertainty can be interpreted not only as statistical variability but also as the instability of the underlying information topology. By integrating O-information and persistent homology within a common spatial framework, the proposed approach provides a new methodology for detecting robust higher-order structures and topologically uncertain regions in environmental and multi-hazard systems.

Large-amplitude entrywise corruption can distort flow-field data and contaminate extracted modes. Robust principal component analysis (RPCA) separates low-rank flow content from a sparse corruption component, but recovery deteriorates when corruption occupies a large fraction of measurements. We introduce library-learning-assisted robust principal component analysis (LLA-RPCA), which restricts the recovered spatial basis to combinations of functions from a fixed candidate library and prescribes the available modal capacity. Here, the library contains standard trigonometric functions and graph-Laplacian eigenfunctions. The decomposition is solved via augmented-Lagrangian alternating minimization. The method is evaluated on a post-stall NACA0012 wake, oscillating-cylinder wake video data, and particle image velocimetry (PIV) measurements of a flat plate undergoing a transverse gust encounter. For the first two cases, synthetic large-amplitude entrywise corruption is imposed over fractions from 0% to 90%. LLA-RPCA retains coherent wake structures and recovers dominant linear modes at corruption levels where standard RPCA retains residual corruption, attenuates the reconstructed field, or collapses to a one-dimensional reconstruction. For the experimental gust-encounter case, standard RPCA exhibits a trade-off between attenuating coherent flow content and retaining naturally occurring PIV artifacts as its tuning factor increases. Conversely, LLA-RPCA suppresses artifacts while consistently preserving coherent velocity and derived-vorticity structures. These results indicate that a library-constrained reconstruction with prescribed modal capacity improves denoising and modal recovery when the prescribed representation adequately captures the relevant spatial content.

Most molecular transitions occur on timescales far beyond direct molecular dynamics simulations. The committor, the probability that a configuration reaches a product state before a reactant state, is a central kinetic statistic, providing a mechanism-independent reaction coordinate and a foundation for transition path theory and the calculation of rates. This review surveys modern approaches for estimating the committor and related kinetic statistics from molecular simulations, with an emphasis on self-supervised methods that learn solutions of their defining dynamical equations rather than relying on labeled shooting data. We develop a common operator viewpoint connecting generator-based partial differential equations, variational principles, Markov state models, dynamical Galerkin approximation, and neural networks. Empirical and theoretical evidence points to the efficiency of these methods. We provide theoretical and practical guidance for realizing their full potential in applications, including strategies for treating non-Markovian effects and for sampling. We conclude by identifying opportunities for further research, including connections to reinforcement learning and generative modeling.

Muon-spin rotation/relaxation is one of the most powerful microscopic probes for understanding magnetic order, spin dynamics, superconductivity, and complex magnetic phases in emerging quantum materials. Quantitative interpretation depends critically on the accurate identification of the muon stopping site, a problem traditionally addressed using density functional theory-based structural relaxation. However, conventional DFT approaches are computationally demanding, time-consuming, and require extensive calculations. Here, we develop MEOWN (Muon Engine for Optimized Weighted Networks), a machine-learning-based, physics-informed computational framework that combines a Polarizable Unperturbed Electrostatic Potential (P-UEP) model with machine-learning-guided optimization and symmetry-driven relaxation to predict energetically favorable muon stopping sites in crystalline solids. MEOWN explicitly incorporates electrostatic interactions, electronic screening, polarization effects, and zero-point motion into the learning workflow, providing physically interpretable predictions with substantially reduced computational cost while maintaining physical consistency and scientific rigor. To validate the framework, we investigated several well-established benchmark materials, including MnSi, CoF2, CaF2, LiF, and NaF. The predicted muon stopping sites and dipolar fields are in close agreement with previously reported DFT+mu results, demonstrating the reliability and transferability of the approach across chemically diverse systems. Notably, MEOWN predicts the equilibrium muon stopping site within a few minutes, offering a significant speedup over conventional DFT-based calculations. This manuscript presents the theoretical foundations, computational methodology, and validation of MEOWN as a general-purpose software for rapid and reliable muon stopping-site prediction in crystalline materials.

SpectraFit XPS is a free web application for the analysis of X-ray photoelectron spectroscopy (XPS) data that runs entirely in the browser, with no installation and no server-side processing: spectra never leave the user's computer. It combines an interactive Levenberg–Marquardt fitting engine with true Voigt, Doniach–Šunjić, and summed Gaussian–Lorentzian line shapes; Shirley (static and dynamic), linear, and Tougaard (two- and four-parameter) backgrounds; spin–orbit doublet generation; and expression-based inter-peak constraints. Quantitative analysis supports ten relative-sensitivity-factor sets, several kinetic-energy correction schemes including TPP-2M inelastic mean free paths, angular correction, and atomic and weight percentages, with the underlying database and algorithms adapted from the open-source KherveFitting project. The application reads and writes ISO~14976 (VAMAS) files—including multi-region and depth-profile data and load-time transmission-function correction—and imports common vendor and spreadsheet formats. A publication plotter exports journal-ready SVG/PNG figures. The quantification pipeline reproduces KherveFitting reference values exactly in a 30-case regression suite, part of an automated test set of 100 tests. The application, an illustrated bilingual user guide, and a synthetic demonstration dataset are freely available at https://spectrafit-xps.web.app/.

We investigate how unsupervised machine-learning methods can characterize the active-absorbing phase transition in the contact process in one and two spatial dimensions. Our analysis focuses on principal component analysis (PCA) and variational autoencoders (VAEs), and we show that direct applications of these methods encounter a central difficulty: contact process configurations are intrinsically positive-definite. In the PCA case, standard centering procedures fail to isolate the order parameter in the leading component. To address this, we augment the data with sign-reversed configurations, creating a balanced dataset with zero mean while preserving the density information required to describe the transition. This preprocessing allows the dominant principal component to recover the order parameter and reproduce the expected finite-size scaling near criticality. For VAEs, we find a related limitation: a fixed Gaussian prior does not provide sufficient latent regularization across the full range of control parameters and system sizes for positive-definite data. We overcome this by adopting a heteroscedastic Gaussian prior that adapts to the control parameter, leading to a substantial improvement in the finite-size scaling of reconstruction-based observables near the critical threshold. Taken together, these results highlight a key lesson: the success of machine learning in phase-transition problems does not rely on algorithmic complexity alone, but on tailoring the representation to respect the physical structure of the system, including its intrinsic constraints and symmetries.

The hulusi is a wind instrument that was invented in Yunnan Province, China, and has become tremendously popular in recent years. It consists of a mouthpiece, a gourd, and three bamboo tubes, all with free reeds made of copper. The main bamboo tube in the middle has seven finger holes. In this instrument, the pipe length, not the free reed's eigenfrequency, determines the instrument's pitch, unlike, for example, with the Western accordion or the blues harp. In this study, a machine learning model implemented in the COMSAR framework (https://github.com/ifsm) was used to investigate the timbre characteristics of the hulusi to cluster different instruments and pitches. The measured hulusi pitches C, B, A, G, and F were analyzed according to seven psychoacoustic features, among which only the spectral centroid, sharpness, and fractal correlation dimension are shown to form pitch clusters. These timbre features were used to train Kohonen self-organizing maps (SOMs) for clustering. Brightness and sharpness analysis revealed that the highest pitches were less bright and less sharp than mid- and low-range pitches were. Furthermore, the fractal correlation dimension, which mainly determines the chaoticity of the initial transients, was the best-clustering timbre feature for the hulusi, with the highest pitches showing the least chaoticity. This result is supported by defining a cluster quality index for the SOMs.

The efficiency of a machine at the scale of thermal fluctuations is random, and the conventional ratio $-W/Q_h$ has no moment of any order: its input heat fluctuates through zero. We work instead with the exergetic ratio $\eta=W/(W+T_0S)$, which lies in $[0,1]$ pointwise for non-negative dissipation, and ask what the energy budget alone determines about its mean. With $\alpha=T_0\langle S\rangle/W$ and $\sigma^2$ the relative variance of the dissipation, $1/(1+\alpha)<\langle\eta\rangle\le\sigma^2/(1+\sigma^2)+1/\{(1+\sigma^2)[1+\alpha(1+\sigma^2)]\}$, both ends sharp, with no distributional assumption. The floor is Jensen's inequality: fluctuating dissipation raises the mean efficiency above its deterministic value, and the mean alone gives nothing more. The ceiling is attained by an intermittently reversible law, dissipating nothing in a fraction $\sigma^2/(1+\sigma^2)$ of realisations, a prediction testable on trajectories. A third moment lifts the floor. Fixed delivered work is not required: when it too fluctuates, the bounds hold with the moments taken on $T_0S/W$, and the thermodynamic uncertainty relation on the work current converts the ceiling into a precision-efficiency frontier, whose zero-variance member is the known bound on a motor's ratio-of-means efficiency, shown here to be unsafe for the mean of the fluctuating ratio. Inside the interval lies the maximum-entropy benchmark $\alpha^{-1}e^{1/\alpha}E_1(1/\alpha)$. Finally the bounds are worked out for a motor with futile cycles, observed until a fixed number of steps is delivered. There the dissipation cannot fall below the reversible cost of that work, and this floor $b$ sharpens the ceiling to $q/(1+\alpha b)+(1-q)/(1+\alpha c)$, $q=\sigma^2/[\sigma^2+(1-b)^2]$, $c=1+\sigma^2/(1-b)$, removing 40-67 per cent of the width. It is saturated when slips are rare: the extremal law is an operating regime, not an idealisation.

Generative thermodynamic computers turn thermal noise into structured data through Langevin dynamics. We train these systems with a local update at each integration step. The reverse-path Onsager-Machlup objective yields a coupling gradient that is a symmetric sum of local residual-state correlations. We apply this gradient immediately rather than accumulating it over a full trajectory. In digital simulations using MNIST prototypes, online and trajectory-batch training reach similar validation losses on fixed noising paths. Models trained online release less heat on average in all five independently seeded pairs, with both models' parameters held fixed during sampling. Auxiliary classifier and nearest-prototype measures change modestly, while pairwise diversity decreases. The response to noise depends strongly on where the errors enter: independent zero-mean errors in the formed updates produce little heat change over a finite range of noise amplitudes, whereas residual offset and temporal correlation have much larger effects. Storing trained couplings requires substantially less precision than resolving deterministic updates during training. Together, these results establish a local online training method and show how update timing, noise structure, and precision affect generative thermodynamic computing.

We develop and implement a two-step location-scale analysis for repeated physical measurements when the underlying distribution is not known. For a chosen substitute distribution, stationarity of population Kullback-Leibler information loss at fixed scale motivates the location score, which we apply to the observed measurements through empirical cross-entropy. Steiner's curvature rule then defines a companion scale separately. We place Gaussian, Cauchy, and logistic substitutes in one common construction and implement them reproducibly on a physics benchmark. For the logistic substitute, we pair the established bounded location score with a scale defined by the curvature rule rather than by a fitted tuning constant or a scale-likelihood equation. For Gaussian measurements with different quoted uncertainties, an experiment-level curvature convention and a stated variance mapping give an exact algebraic connection to a standard residual-based variance estimate for a weighted fit. Applied to a published 21-measurement neutron-lifetime compilation, the inverse-variance weighted, most frequent value, and logistic locations are 878.689, 881.164, and 882.835 s, respectively. These values are benchmark results of the compared constructions and are not proposed as a new recommended neutron lifetime.