Papers

Earthquake sequence forecasting requires models that can learn nonlinear history dependence while retaining robust statistical structure. We develop a scaling-law-informed neural marked point process, termed Fusion, that combines neural representations of catalog history with temporal features derived from the Epidemic-Type Aftershock Sequence model and magnitude information derived from the Gutenberg–Richter law. The model separates the magnitude cutoff applied to the input catalog from the fixed target-event threshold, allowing lower-magnitude earthquakes to inform forecasts without changing the target-event set. For the 2016–2017 Amatrice–Visso–Norcia sequence, Fusion achieves the highest target-event temporal likelihood when lower-magnitude events are retained, outperforming both ETAS and a purely neural point-process baseline. Event-wise and cumulative analyses show sustained timing gains through substantial portions of the Visso and Norcia sequences. Across five benchmark catalogs, catalog-specific neural training with a fixed ETAS prior yields the highest temporal likelihood at the minimum evaluated magnitude cutoff. Magnitude likelihood shows no consistent predictive gain beyond the Gutenberg–Richter-based ETAS reference, indicating that the additional information captured by Fusion is primarily temporal. These results show that lower-magnitude catalog histories and empirical scaling-law information complement neural sequence learning for target-event timing.

Delayed-coincidence searches identify a rare prompt-delayed signal, but their accidental background is not a simple product of marginal rates: muon vetoes, event dead time, and delayed events created before the current window condition which event sequences can be recorded. We derive exact ordered coincidence rates, within a stated stochastic model, for a recorded stream of uncorrelated prompt-like singles and correlated prompt-delayed sources subject to Poisson reset boundaries and event dead time. The calculation separates two tasks: a Markov history chain carries the delayed events still pending at reset boundaries across windows, and a current-window propagator evaluates the ordered within-window integrals in closed form with block-matrix exponentials, the matrix-analytic toolkit of applied probability. The construction extends to any prescribed finite multiplicity by increasing the block-chain depth. Here we report every ordered one-, two-, and three-fold rate formed from uncorrelated singles, correlated prompts, and recorded delayed events, together with the genuine/accidental split of prompt-delayed pairs, multiplicity efficiencies, and the aggregate rate for multiplicity four or more. For the default window-close convention, we derive a three-term a posteriori error bound for the finite pending-population truncation. An independent streaming toy Monte Carlo validates the ordered rates, two-fold time densities, matched dead-time conventions, and aggregate high multiplicity. Within the stated assumptions, the construction is exact on the retained finite state spaces and provides explicit, computable truncation-error bounds.

The Nearest Neighbors estimation of likelihood is implemented for the multivariate amplitude analysis of the cascades of particle decays. In this approach Monte Carlo simulated events that are used to describe data are assigned weights dependent on the parameters of the theoretical fitting model. Each of such weighted events is considered as contributing to N-dimensional probability density function in it's neighborhood in the parameter space. No analytic p.d.f. or cpu-intensive re-generation of N-dimensional p.d.f. at each fit step are required. The method allows accurate accounting for reconstruction effects, demands modest cpu resources and can be effectively multi-threaded. General setup of the fit as well as toy example of the amplitude analysis of B-meson decays are demonstrated.

Domain adaptation is widely used to make neural networks trained on simulations applicable to experimental data. Its premise is that the two domains differ only in nuisances, and that the quantity of interest is distributed identically in both. In physics neither assumption holds: simulations can be wrong about the physics, and the distribution of the target quantity - an energy spectrum, a redshift distribution - is often the measurement itself. We study the consequences of such mismatches on a toy air-shower benchmark in which a detector-response nuisance, a physical simulation shift, and an energy-spectrum shift can be switched on separately or together. Standard adversarial adaptation handles the conditional shifts, but once the two spectra differ it aligns them, replacing an uncontrolled bias by one anchored on the simulation prior. We present adaptive domain adaptation, which reweights the simulated events so as to focus domain adaptation on the genuine physical mismatch alone. Since the predicted spectrum depends on model training configuration, we provide a label-free model selection rule for selecting the near-the-best operation point.

Modern machine learning is leading to substantial gains in precision, flexibility, and computational efficiency in fundamental physics. Statistical validation, uncertainty quantification, and robustness assessment are less systematically addressed. The VERaiPHY initiative (Validation & Evaluation for Robust AI in PHYsics) is a series of articles developed within the PHYSTAT programme, aimed at establishing statistical standards for the development, evaluation, and deployment of ML techniques. Each article focuses on a specific methodological domain from a statistics perspective and clarifies statistical questions, tests, and the interpretation of results. This opening article establishes the probabilistic, statistical, and machine learning foundations that the later contributions assume, together with the notation used throughout.

Whole-pattern fitting methods, such as Rietveld refinement, excel at extracting detailed structural, chemical, and microstructural information from powder diffraction data. Obtaining reliable results requires both considerable expertise and software-specific knowledge, and applying these methods at scale typically relies on custom scripts written for each application. High-throughput experiments and autonomous self-driving laboratories increasingly utilize powder diffraction analysis to proceed programmatically and to return structured, machine-readable results. Here, we introduce PowderLine, a Python application that encapsulates a complete refinement into a single declarative recipe, validates that recipe against a versioned schema, and executes it through refinement software to return structured results. The refinement recipe is an all-inclusive, machine-readable and -writable description of either Rietveld or single peak analysis that users, scripts, and automated agents can specify and run in the same way. As a result of PowderLine's composability, it naturally fits into interactive, scripted, and autonomous workflows alike.

Thermal-aware optimization of multi-die 3D integrated circuits evaluates many designs, each a costly heat-equation solve. Operator-learning surrogates replace this solve with a fast forward pass, ideally trained from physics alone, without labeled data. DeepOHeat-v1 made such surrogates fast and trustworthy, but only on low-contrast geometries. High-contrast multi-die stacks break it in two ways: discontinuous conductivities make the continuous physics loss ill-defined at material interfaces, and ill-conditioning ($\kappa_2(A_h) \approx 6 \times 10^4$) puts the discretized strong-form loss beyond first-order optimization. We propose DeepOHeat-v2 to overcome both. First, we train on a discretized physics loss that handles the discontinuities natively; its energy form reduces the prediction-space loss-Hessian conditioning from $\kappa^2$ to $\kappa$, and a matrix-preconditioned optimizer cuts the mean peak temperature error from over 30 K to 0.55 K. Second, because optimization leaves the training distribution, we propose a self-improving framework: a hotspot trust gate sends flagged placements to a reference solver, and the surrogate incrementally retrains on the refined solutions, keeping an update only when it improves held-out validation error. On a multi-die benchmark, the surrogate-true peak gap on the returned design falls from 1.12 K to 0.11 K, matching a solve-at-every-step optimizer while running $56\times$ faster.

Air-quality and climate monitoring routinely convert native-resolution measurements into exceedance counts before testing whether high values cluster in time. A surrogate null can be imposed on the derived index or on the native series and then propagated through the same thresholding and aggregation. We show that the two placements can encode different scientific hypotheses and lead to opposite conclusions. In 31 Chilean PM2.5 monitoring stations (2018–2025), weekly clustering of days above the 50 ug m^-3 national 24-hour standard was significant at all stations under an index-level IAAFT null but at only two under a daily native-resolution null; a native generative null with seasonal marginals and short-memory Gaussian-copula dependence agreed with the native surrogate at 30 of 31 stations. Across thresholds spanning the WHO guideline (15 ug m^-3) to the Chilean episode-alert level (80 ug m^-3), index-only rejections increased from 8 of 31 to all eligible stations as monthly event probabilities became more seasonally concentrated, and equalizing monthly event probabilities at the 50 ug m^-3 level reduced index-only decisions from 29 to five. We formalize the issue as null transport through a lossy observation map: an exact aggregate-level equivalent of a native null exists if and only if the randomization kernel is lumpable with respect to that map. A within-fiber diagnostic, which perturbs native amplitudes while keeping the observed index exactly fixed, shows that this condition fails in the monitoring data: the native null distribution moved by a median of 18 times its Monte Carlo variability. Weekly clustering of PM2.5 exceedances in Chile is therefore fully compatible with seasonality plus short-memory daily persistence, and index-level surrogate rejections should not be read as evidence about daily concentration dynamics.

Spatial early warning signals (EWSs) seek evidence of an approaching tipping point from a single snapshot of many interacting elements. Existing theory largely assumes spatial homogeneity, whereas networks introduce systematic differences among nodes that may obscure fluctuation-based warning signals. We develop a mathematical framework for spatial EWSs in stochastic dynamical systems on networks. We find that the expected spatial variance, a popular spatial EWS, decomposes exactly into a structural contribution from heterogeneity in the equilibrium state and a fluctuation contribution determined by the stationary covariance. Near a simple steady-state bifurcation, the potentially divergent covariance concentrates along the critical eigendirection: the left eigenvector determines how strongly noise excites the critical fluctuation, while the right eigenvector determines its spatial pattern. Consequently, the spatial variance has a divergent fluctuation contribution when the limiting critical eigendirection is noise-excited and spatially nonuniform after centering. In contrast, the spatial coefficient of variation generally saturates, while skewness, kurtosis, and Moran's $I$ approach network-dependent limits without a universal warning direction. We also derive results for homogeneous networks, node-wise baseline subtraction as preprocessing, and Hopf bifurcations, for which the limiting distributions are qualitatively different. These results clarify when spatial EWSs provide reliable warnings and why their performance depends on network structure, noise, and preprocessing.

Acoustic mode frequencies in the Sun and Sun-like stars change due to magnetic activity, on time-scales much larger than the star's rotation and much smaller than its evolution. Given the poor S/N of the observed stellar p-modes, it is challenging to measure the changes of individual mode frequencies. Typically, power spectra of different time series segments are cross-correlated to estimate a mean p-mode frequency change, which ends up averaging over the individual mode contributions. We seek to enhance the cross-correlation method, by introducing a novel and computationally cheap method, thus enabling us to disentangle p-mode frequency changes for different spherical harmonic degree $\ell$. Assuming that the inclination angle and rotation rate are already measured, filters are designed, which enable the isolation of $\delta\omega_\ell$, frequency changes of modes with a given $\ell$, while preventing bias creeping in from neighbouring modes. Monte-Carlo simulations are performed to quantify uncertainty in the estimation of $\delta\omega_\ell$. We validate our method against well-studied solar data (SOHO/VIRGO and BiSON) and demonstrate its applicability to the solar-like Kepler star KIC 8006161.

Uncertainty decompositions in profile-likelihood fits are commonly reported through nuisance-parameter impacts, although shifting a fitted parameter and fluctuating the observation that constrains it answer different questions. Recently, Pinto et al. provided an explicit construction for uncertainty decomposition based on fluctuating the observations and argued that such a construction allows for a cleaner interpretation of systematic uncertainties in terms of physical sources. We provide a geometric description of the distinction between the two methods by using a coupled pair of fiber bundles. The geometrical approach clarifies the relationship between several methods traditionally used to estimate systematic uncertainties in high-energy physics. By describing the profiling as an information-orthogonal horizontal lift and the Schur complement as the induced metric on the parameter-of-interest manifold, physical-source uncertainties arise by mapping observation fluctuations to score covectors, raising them with the inverse total information, and pushing the resulting estimator covariance forward to the parameters of interest. This construction clarifies why nuisance-parameter impacts do not generally coincide with repeated-experiment source variances.

Localized detector inefficiencies produce incomplete calorimeter data that limit the ability to perform precision measurements. We address this problem in relativistic heavy-ion collisions from a Bayesian perspective using pretrained calorimeter diffusion models as priors to reconstruct the missing signal conditioned on surrounding measurements. In this work, we conduct a systematic comparison of several diffusion-based inpainting algorithms, whose performance is evaluated using Bayesian posterior diagnostics of energy response, spatial bias, and uncertainty calibration. The reconstruction fidelity is also analyzed across collision centralities and masked region sizes. This study establishes a general validation strategy for probabilistic reconstruction of missing detector information.

We propose the Inference-driven Participant Determination (IPD) method, a Bayesian framework for inferring event-by-event posterior distributions of the number of participants ($N_{\text{part}}$) and binary collisions ($N_{\text{coll}}$) from final-state charged-particle multiplicities in relativistic heavy-ion collisions. The joint distribution of $(N_{\text{part}}, N_{\text{coll}})$ obtained from the Monte-Carlo Glauber model is used as the prior, while negative binomial distributions calibrated to charged-particle multiplicity fluctuations define the likelihood. This approach replaces conventional hard-cut centrality classification with a probabilistic assignment based on $N_{\text{part}}$, making the multiplicity–geometry smearing explicit and reducing the impact of volume fluctuations on downstream observables. A closure test using an UrQMD-MCG hybrid model at $\sqrt{s_{NN}} = 19.6$~GeV shows that the method yields well-calibrated posterior distributions with negligible bias and improves the reconstruction of net-proton cumulants relative to conventional multiplicity-based centrality selection.

We present the first application of simulation-based inference to resonant inelastic X-ray scattering spectroscopy. Using truncated marginal neural ratio estimation to efficiently restrict the prior and conditional flow matching as the joint density estimator, we infer full posteriors with a modest simulation budget for two Ni$^{2+}$ compounds—NiPS$_3$ as a representative covalent case and K$_2$NiF$_4$ as a more atomic one. We demonstrate that a vision transformer encoder whose tokenization matches the physical layout of the RIXS map yields better-covered and sharper posteriors than generic image encoders. Applying the validated method to experimental NiPS$_3$ and K$_2$NiF$_4$ data, we recover a joint posterior that reveals parameter correlations invisible to point estimators, and a posterior predictive distribution that closely matches the observed spectrum. The amortized posterior unlocks a class of analyses not previously available to the field such as nuisance-marginalized uncertainty quantification, multi-measurement posterior fusion and active experimental design.

Machine learning is now a central tool for solving inverse problems in particle physics and astronomy. Models are trained on simulation and deployed on real data, raising the question not just of whether they fit, but of whether they are wrong in ways we did not anticipate: the unknown unknowns. This challenge of model misspecification is not unique to machine learning. In physics, misspecification is sometimes exactly what we want to find: new discoveries appear as failures of existing models. At other times, we want such effects absorbed into the analysis without biasing the measurement. A robust analysis is one that absorbs the misspecifications we are not interested in, while preserving sensitivity to the ones we are. Machine learning can both amplify misspecification and provide new tools to address it. We discuss the challenges of model misspecification, diagnostics for detecting it, and strategies for mitigation. No single diagnostic can confirm that a model is correctly specified: detection and mitigation are two halves of an iterative loop, in which a battery of complementary diagnostics is applied, the model is updated, and the process repeated. Robustness against unknown unknowns is ultimately less about any single technique than about a disposition: a willingness to suspect one's own model, and to design analyses that can survive being wrong in ways one did not anticipate.

Satellite precipitation products such as IMERG exhibit biases that vary with terrain, season, and precipitation regime, leaving the applicability boundaries of machine learning correction unclear. This study proposes the Terrain-Moisture-Intensity (TMI) framework, centered on mechanism purity, extending the correction problem from purely algorithmic optimization to physical consistency diagnosis. A proof-of-concept study in Hunan Province employs IMERG V07, SRTM DEM, and ERA5 variables (tcwv, u10, v10). Ablation results indicate that, under the conditions of this study, terrain-moisture relationships are predominantly additive: RF-Full yields merely +0.001 R^2 gain over LR-Full, while bias rises to 1.282 mm d^-1; MAE decreases by approximately 14%, reflecting a trade-off between tail-fitting improvement and mean shift. SHAP diagnostics identify three categories of boundaries. Spatially, Central Hunan exhibits significant degradation (R^2=0.133) despite strong variable activation, consistent with mechanism fragmentation induced by mixed terrain. Temporally, u10 undergoes directional reversal between summer and spring (+0.096 to -0.156), presenting "silent failure." Extreme precipitation (>=50 mm d^-1) approximates a mechanism saturation frontier rather than isolated out-of-distribution samples, with DEM showing the largest relative amplification in SHAP disorder (+150%). The results demonstrate that machine learning correction performance is primarily constrained by mechanism purity. A pre-registered cross-regional test (Hunan, Guangxi, Guangdong) confirms this screening capability out of sample: a priori coherence proxies predict correction efficiency with a mean absolute error of 2.6 percentage points, while the transfer-versus-retraining contrast separates mechanism mismatch (coastal Guangdong) from portability (Guangxi), establishing the framework as a validated applicability screen.

Calibrating computational models to experimental data is a core task in applied statistics, especially in scientific domains, where physical experiments are costly and simulations play a central role in design and inference. Motivated by uncertainty quantification challenges in particle accelerator experiments, we develop and evaluate a Hierarchical Bayesian Calibration framework. In contrast to standard Bayesian calibration, certain inputs - such as beam injection amplitude - must be estimated separately for each experiment. We adopt the Kennedy-O'Hagan formulation and extend it with a hierarchical prior structure to model the distribution of experiment-specific calibration parameters, thus borrowing strength and improving generalisation across repeated experiments. A key methodological challenge arises from the need to evaluate a large number of forward simulations, which renders conventional Markov chain Monte Carlo approaches computationally prohibitive. To address this, we leverage the Bayesian Committee Machine as a scalable modelling strategy for Gaussian Process emulators. The BCM provides a principled divide-and-conquer approach, enabling parallel inference and reducing computational cost without requiring problem-specific tuning of the emulator approximation. Posterior sampling is performed using the No-U-Turn Sampler, supported by automatic differentiation in Julia, which removes the need for analytic gradient derivation and facilitates flexible model specification. We assess the proposed framework using established benchmark problems and simulated data from the Argonne Wakefield Accelerator. The results demonstrate substantial computational savings and robust calibration performance, highlighting the applicability of the method to large-scale scientific modelling problems.

Is it possible to find an objective classification criterion that organizes the complexity of gust-induced loads across many flight conditions? And one that remains as interpretable as a labelling based on coarse parameters, such as the flight attitude? Our approach encodes a large number of experimental observations through a machine-learned representation and applies a summarization procedure to select a minimal subset of highly significant exemplars. The exemplars provide a similarity-based objective classification criterion of all the observations, they can be more conveniently inspected by experts and can become subject of more refined experiments. We demonstrate the approach on a database of 3480 pressure-load measurements induced by random gusts on a flying-wing model across six flight attitudes. We find nine fundamental response types that recur across multiple attitudes; analysis of a type's transient response enables physical intuition into the underlying fluid mechanics.

The proposed formulation establishes a formal correspondence between the Heisenberg representation and the Bayesian formulation of inverse problems. The likelihood function is first expressed in Hilbert space through a quadratic norm of the difference between the noisy observations and the response of a forward model depending on the unknown parameters, weighted by the inverse of the observational noise covariance. Based on the common mathematical structure of this quadratic form and the observable operator in the Heisenberg representation, the inverse observational noise covariance operator is identified with the initial observable. To establish this correspondence, a stochastic field with Matérn covariance is considered and represented through the Karhunen-Loève expansion. The eigenvalues and eigenfunctions of this expansion are then used to define the state $|\Psi\rangle$ within the proposed formalism. The main results are summarized by four theorems: the unitarity of the evolution operator, the self-adjointness of the Hamiltonian, the conservation of the trace of the observable, and the formal correspondence between the Bayesian likelihood and the Heisenberg observable structure. Limiting cases of the Matérn covariance are analyzed. Finally, numerical examples illustrate the analytical results.

Track seeding strongly affects both the quality and computational cost of charged-particle reconstruction, yet its many configuration parameters are commonly tuned through expert intuition and repeated trial and error. ACTS reduces this burden with an Optuna Tree-structured Parzen Estimator auto-tuner, but expensive evaluations, a restricted search space, and a scalarized objective can limit evaluation efficiency, exclude promising configurations, and obscure performance trade-offs. We investigate whether Bayesian optimization can address these limitations using ACTS with the Open Data Detector (ODD). Under identical search ranges and a common 100-trial budget, we compare Expected Improvement and Upper Confidence Bound with TPE and random search on the existing eight-parameter problem, extend the best-performing Bayesian method to fifteen parameters, and apply Expected Hypervolume Improvement to optimize efficiency, fake rate, duplicate rate, and runtime without fixed scalar weights. Candidate configurations are evaluated through the full ACTS reconstruction chain and validated on disjoint held-out events. The Bayesian acquisition methods identify strong configurations earlier than TPE, and their advantage persists in held-out validation. Expanding the search further improves performance, while multi-objective optimization reveals competitive non-dominated solutions spanning distinct trade-offs. These results indicate that Bayesian optimization can strengthen ACTS auto-tuning through efficient evaluation, broader parameter searches, and post-hoc expert selection among non-dominated alternatives.

Forward and inverse modeling of parametric dynamical systems requires surrogate models that are not only accurate for state prediction, but also informative for parameter calibration. However, a systematic end-to-end differentiable formulation for coupling deep-learning-based reduced-order surrogates with variational parameter estimation remains underdeveloped. In this work, we introduce a physics-aware neural-network-based latent-space framework for reduced-order forward modeling and variational parameter estimation. The proposed autoencoder-based approach yields a differentiable surrogate that maps physical parameters to predicted flow fields through a latent representation. The observable supervision is used during offline training to encourage the latent variables to retain information correlated with system parameters, while the online inverse problem is solved in the parameter space through the surrogate-induced observation operator. The method is evaluated on two computational-fluid-dynamics benchmarks. The results show that reconstruction accuracy alone is insufficient for inverse modeling, owing to the lack of end-to-end differentiability or physics awareness for variational parameter calibration. Quantitative latent-space analysis further shows that observable supervision improves case-level separability and temporal organization of latent representations. Experiments with realistic measurement settings, including noisy, low-resolution, randomly masked, and block-wise partial observations, demonstrate the robustness of the proposed framework and show that it generally reduces calibration error and variability compared with the standard surrogate models.

Accurate physical-layer modeling is increasingly essential for reliable ultra-wideband operation and capacity optimization, especially under the intensified inter-channel stimulated Raman scattering (ISRS) effect. This paper proposes the link-adaptive digital twin (LA-DT) for hybrid-amplified ultra-wideband links to overcome the generalization and speed limitations of existing methods, achieving accurate modeling and robust generalized signal-to-noise ratio (GSNR) estimation across diverse links. First, to address EDFA heterogeneity, the GSNR modeling task is decomposed into three key power predictions: ASE, NLI, and signal powers before EDFA entry. Second, to enhance cross-scenario generalization, three dedicated DT models are developed using a novel neural architecture with linear modulation layers (LMLs). Third, for rapid adaptation to unseen scenarios with limited data, three domain discriminators guide few-shot fine-tuning of the LMLs. Fourth, the LA-DT explicitly accounts for Raman amplifier (RA) insertion loss, improving practical deployment reliability. Results across 35 scenarios show that LA-DT reduces RMSE for NLI, ASE, and signal power predictions to 0.151, 0.111, and 0.113 dBm with improvements of 56.0%, 58.4%, and 52.7% over the baseline,and achieves an average GSNR estimation RMSE of 0.114 dBm (55.8% improvement). For 12 unseen scenarios, the LA-DT maintains high accuracy through few-shot fine-tuning with only 20 samples per scenario, achieving an average GSNR RMSE of 0.159 dB and demonstrating strong adaptability and robustness.

While conventional rogue wave statistical models rely on linear or weakly nonlinear descriptions of random seas, we demonstrate experimentally that moderately or strongly nonlinear wave fields can be represented by sparse ensembles of coherent soliton-like packets. These packets exhibit log-normal amplitude distributions together with uniformly distributed phases and peak emergence times. This sparse coherent structure framework naturally leads to an extreme value description in which the probability of exceedance is governed by the tail of the coherent-structure amplitude distribution. The prediction is validated against laboratory hydrodynamic experiments across a variety of unidirectional sea states, showing good agreement with the experimental observations and comparing favourably with conventional statistical prediction models while retaining analytical simplicity. Our results provide a direct physics-based link between sparse coherent structures and rogue wave probabilities, with broader implications for nonlinear wave physics in optics, cold gases, and plasmas.

We started the Living Review of Machine Learning for Particle Physics (HEP-ML Living Review) in 2020 as a community-maintained, near-comprehensive bibliography of machine learning in particle physics. The field was then growing faster than any single researcher could follow, finding the relevant papers was hard, and a structured, continuously updated reference paid off immediately. Since then the literature has grown by more than an order of magnitude, the methods reach far beyond the classification and generation tasks of the early years, and the community has built its own ecosystem of topic-specific reviews, benchmark papers, and software frameworks. The original model no longer serves this field well, and we can no longer sustain it. We therefore change direction. We freeze the Living Review as an archival reference covering the literature up to 1 June 2026, where it remains a stable record of the first phase of HEP-ML. A new resource, the HEP-ML Living Guide, replaces it. It does not list everything. It curates, it annotates, and it points readers to foundational and representative work, so that researchers can find their way into a mature and rapidly diversifying field. In this article we explain why we make this change and how the new resource works.

Reconstructing the analytic structure of a function from finite datasets is a fundamental problem across theoretical, numerical, and experimental physics. While Padé approximants provide a natural framework, finite-information effects, as well as statistical and systematic uncertainties, may obscure the underlying analytic structure and limit reconstruction reliability. In this work, we reinterpret the appearance of Froissart doublets not merely as numerical artifacts but as diagnostic objects carrying information about the analytic consistency of the input data. Accordingly, we develop a general Padé-based algorithm that exploits the dynamics of Froissart doublets along Padé sequences to identify localized inconsistencies and iteratively reconstruct the analytic structure most compatible with the data. The method requires no model for the origin of the inconsistencies and distinguishes genuine analytic features from spurious structures induced by finite-information effects. We validate it using Stieltjes functions, realistic pseudo-experimental datasets with statistical and systematic uncertainties, and general holomorphic functions. The complete algorithm is provided as a supplementary Mathematica notebook in an open GitLab repository.

Molecular motion within living cells provides a window into the physical principles underlying intracellular organization and transport. Yet a fundamental limitation remains: measured trajectories are often short, noisy, and randomly oriented, rendering spatial anisotropies inaccessible to conventional analyses. We show that turning-angle statistics provide a robust approach for uncovering anisotropies in anomalous diffusion. Using a two-dimensional anisotropic fractional Brownian motion model with random orientations, we show theoretically and through simulations that turning-angle distributions preserve signatures of anisotropy. We apply this approach to single-particle tracking data, including quantum dots in the cytoplasm of HeLa cells and membrane proteins in hippocampal neurons. Turning angles reveal hidden anisotropies in the motion of quantum dots and Nav 1.6 channels, and in specific dynamical states of glycoprotein CD4. These results establish turning-angle analysis as a powerful strategy for detecting organization in complex environments and reveal that anisotropic anomalous diffusion is an overlooked feature of intracellular dynamics.

Accurate and robust time series forecasting is essential in many applications involving physical processes, such as manufacturing monitoring and astrophysical event detection. In these settings, predictive models must remain reliable under noise, variability, and measurement uncertainty while capturing temporally localized structures corresponding to physically meaningful events. Convolutional neural networks (CNNs) are widely used for such tasks due to their computational efficiency and strong representational capacity. However, their learned temporal representations often exhibit unstable or physically inconsistent attention patterns, reducing robustness, generalization, and interpretability. This paper introduces PhysAttNet, a physics-informed attention framework for time series forecasting. PhysAttNet augments a lightweight CNN forecaster with an attention head guided by domain-informed regularization reflecting the structural properties of physical signals. Specifically, three complementary constraints are imposed during training: an alignment regularization that encourages attention to follow smooth, peak-centered temporal structures derived from the input signal, a smoothness regularization that enforces continuous temporal evolution, and a sparsity regularization that promotes selective focus on informative intervals. These differentiable regularization terms introduce physics-guided inductive bias without requiring annotated explanations or manual supervision. Experiments on two distinct applications, namely predicting cutting forces during milling and forecasting flares in blazar time series, demonstrate that PhysAttNet improves forecasting accuracy, generalization, and prediction performance on structurally important events.

Equilibrium climate sensitivity (ECS) is a zero-frequency susceptibility, whereas historical globalmean temperature variability samples a finite, forced projection of the climate system. We test whether information missed by a scalar fluctuation-memory coordinate reappears in a finite CO2 response. After conditioning both ECS and the finite response on {\Psi}, CMIP5 residuals are nearly uncoupled (C5 = 0.154), whereas CMIP6 shows strong complementarity (C6 = 0.593, p = 0.00288). A two-mode stochastic response model attributes this contrast to hidden-response spread that is visible in the finite response but poorly projected onto {\Psi}. The CMIP6 residual direction defines a first-order correction and yields a HadCRUT5 conditional ECS estimate centered at 3.00 K. Thus the weakened CMIP6 fluctuation constraint does not imply that susceptibility information is lost: part of it is recovered through a complementary finite-response projection.

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

Many of the smooth functions that matter most in physics are precisely the ones that standard neural network methods struggle to fit accurately. Here we present NestyNet, a coupled model-and-optimizer framework capable of fitting such targets to high accuracy while also delivering their gradients, Hessians, Laplacians, and antiderivatives analytically and at low cost. This makes it a natural substrate for scientific machine learning tasks. The model is a deterministic segmented analytic surrogate, and its optimizer is a second-order Levenberg–Marquardt scheme whose damping and linear solves are tailored to the stiff, strongly correlated parameter geometries induced by multiscale and sharply structured targets typical in physics and other scientific applications. On the AI Feynman benchmark of 120 physics equations, NestyNet achieves median improvement factors of $2\,100\times$ for function values, $1\,400\times$ for first derivatives, and $780\times$ for second derivatives relative to standard neural networks trained with first-order optimization (Adam). Even after refining those fits with quasi-Newton (L-BFGS) optimization, the corresponding improvements are $540\times$, $450\times$, and $250\times$. Owing to the analytic design it is up to $\approx 44\times$ faster than vectorized automatic-differentiation (autograd) baselines, with a margin growing with model size. The same analytic-derivative framework also supports vector- and complex-valued targets, measurement uncertainties in both inputs and outputs, and constraints, and its modules can be composed flexibly to build scientifically useful model architectures, all without reverting to autograd. Together, these components provide a practical modular framework for fitting difficult scientific surrogates while delivering accurate differential operators for subsequent analysis.