This work presents a finite element formulation for coupled chemo-mechano-thermodynamical large deformation contact. The formulation is based on the contact theory of Sauer et al. (2022) that contains six coupled (but separate) fields: the deformation and temperature of the two contacting bodies, as well as an interfacial bonding field and interfacial temperature. The latter is governed by the chemical and mechanical energy dissipation at the interface. Here the focus is placed on the evolution of bonding and debonding, and how it is coupled to the mechanical and thermal contact state. Several elementary models are proposed for this based on a quadratic contact potential. The resulting contact formulation becomes very general and versatile, which is illustrated by several challenging examples. They include pressure- and gap- depended bonding, exothermic bonding reactions, thermal hardening and thermal expansion, as well as simultaneous bonding and debonding. They are based on a monolithic finite element implementation using classical and isogeometric shape functions together with implicit time integration. Its full linearization, required for the Newton-Raphson solution method, is also provided. If bonding sites are material points, the bonding variable can be condensed-out locally.

Kinetic collisionless plasma equations are commonly solved via spectral methods in velocity space. The most commonly used spectral method is based on Hermite polynomials with a Maxwellian weight, as this basis efficiently represents near-Maxwellian distributions with relatively few degrees of freedom. An alternative approach uses Legendre polynomials, which are better suited for resolving strongly non-Maxwellian features. In this paper, we propose a mixed method that combines the Hermite and Legendre expansions. The mixed method is particularly advantageous for problems in which non-Maxwellian features are localized in velocity space, such as beams and plateaus. We demonstrate analytically and numerically that the mixed method conserves total mass, momentum, and energy by imposing certain constraints. The numerical results show that, for the same number of degrees of freedom, the proposed mixed method can achieve improved accuracy in comparison to the individual Hermite or Legendre methods, while maintaining comparable computational cost.

Positron annihilation lifetime spectroscopy (PALS) spectra are commonly analyzed by fitting multi-exponential lifetime models convoluted with the detector resolution function. In practice, this inverse problem is sensitive to initial parameter choices, parameter bounds, source corrections, and correlations between lifetime and intensity parameters. This paper presents fitPALSpectra, an open-source Python workflow for configurable PALS spectrum simulation, fitting, visualization, and reporting. The implementation uses an analytically integrated exponential--Gaussian response model, configurable source and sample components, constrained optimization, optional least-squares refinement, and machine-readable output of fit results, correlation matrices, and fitted curves. Validation on fully synthetic spectra with known ground-truth parameters shows accurate recovery of the simulated lifetimes, intensities, detector full width at half maximum, prompt shift, and background.

Elastically accommodated grain-boundary sliding (EAGBS) is a plausible source of upper-mantle seismic attenuation and dispersion, yet classical theory predicts a localized Debye-like peak that is absent or only weakly expressed in dry olivine experiments. Here we test whether microstructural heterogeneity can explain this discrepancy using 2-D finite-element simulations on periodic Voronoi tessellations. We find that irregular grain geometry changes the baseline EAGBS response relative to the regular hexagonal benchmark, but increasing grain-size variance alone produces only modest changes in modulus and peak height, with little spectral broadening. In contrast, a broad distribution of grain-boundary viscosities progressively suppresses and broadens the Debye-like loss peak into a weak background spanning a wide frequency interval. This broadening arises from the superposition of many localized relaxation processes with distinct characteristic timescales and motivates a reduced-order 0-D description of the aggregate response. These results suggest that the absence of a pronounced EAGBS peak in dry olivine does not necessarily imply the absence of EAGBS mechanism itself. If grain boundaries sample a sufficiently broad viscosity distribution, the macroscopic EAGBS contribution may appear experimentally only as part of a broad attenuation background, while still remaining relevant for upper-mantle seismic attenuation and velocity dispersion.

The combinatorial design space of multilayer perovskite solar cells is vast, yet exhaustive experimental or computational screening of all possible material combinations remains impractical. Here, we integrate SCAPS-1D device simulations with machine learning to systematically explore 125 device architectures constructed from five electron transport layers (ETL), five absorbers (including lead-free double perovskites), and five hole transport layers (HTL). A representative subset of configurations is used to train a machine learning (ML) model, which predicts the power conversion efficiency (PCE) of the remaining unexplored structures. Leave-One-Group-Out cross-validation yields a Spearman rank correlation, demonstrating reliable ranking capability. SHAP (SHapley Additive exPlanations) analysis reveals that the HTL band gap, absorber band gap, and ETL electron affinity are the most influential descriptors, providing physical insights into interfacial recombination and charge extraction. The machine learning model identifies several high-performance configurations that are subsequently verified by full SCAPS-1D simulations. Among them, the device FTO/TiO$_2$/Cs$_2$AgBiBr$_6$/NiO/Ag achieves a PCE of 28.85%, and the ML-suggested structure FTO/SnO$_2$/Cs$_2$AgInBr$_6$/NiO/Ag exhibits 28.62%, outperforming a closely related literature architecture by approximately 4% absolute. Notably, eight of the top-11 structures employ the lead-free double perovskite Cs$_2$AgInBr$_6$. This work demonstrates that a physics-based, data-driven workflow combining SCAPS-1D, ML, and SHAP can accelerate the discovery of high-efficiency, environmentally friendly perovskite solar cells while providing transparent design rules. The approach is generalizable to other multilayer optoelectronic systems.

Neural operators provide a powerful framework for learning solution mappings of partial differential equations directly in function space. However, many existing architectures still struggle to represent nonlinear time-dependent systems that involve multi-scale structures, long-range interactions, and stable long-time evolution. In this work, we introduce the Hierarchical Adaptive Multi-scale Neural Operator (HAMNO), a neural-operator architecture that combines local convolutional representations, global spectral operators, and hierarchical encoder-decoder processing. The central component of HAMNO is a data-dependent gating mechanism that adaptively balances local and global information at each spatial location, allowing the model to resolve fine-scale features while preserving long-range dependencies. We further develop a physics-informed extension, PI-HAMNO, based on a multi-objective loss strategy that combines data fitting with strong- and weak-form physics constraints. The strong-form term penalizes the domain-integrated squared PDE residual in physical coordinates, while the weak-form term is constructed by multiplying the governing residual by finite-element test functions and evaluating the resulting element integrals using centroid-based tetrahedral quadrature. The framework is evaluated on non-periodic Allen-Cahn (AC), Cahn-Hilliard (CH), and Swift-Hohenberg (SH) equations defined on cubic domains. Across long-horizon rollout, data-limited training, out-of-distribution initial-condition shifts, and random-seed variations, HAMNO improves predictive accuracy over standard neural-operator baselines, while PI-HAMNO further enhances stability, physical consistency, and data efficiency. The implementation is publicly available at this https URL.

We characterize the quasi-stationary distribution (QSD) of the bond directed-percolation line of the Domany--Kinzel automaton using a matrix-product-state representation of the probability distribution, obtained by projecting out the absorbing state and iterating the transfer matrix. Unlike moment- or sampling-based methods, this yields the full conditional distribution and direct access to information-theoretic diagnostics. The spatial structure of the QSD changes sharply across the transition: the active phase is bulk-like with finite density, whereas in the inactive phase the surviving activity collapses into a single flock occupying a vanishing fraction of the chain, with an internal filling that ranges from a single cluster deep in the inactive phase to a loose, partially filled group near criticality. This picture carries a sharp information-theoretic signature: throughout the inactive phase the bipartite mutual information of the QSD equals the entropy of a single binary choice -- whether the flock lies to the left or right of the cut -- so the surviving clusters together encode just one bit of positional information, corresponding to a single effective cluster. The approach extends matrix-product-state techniques to the projected eigenvector defining a QSD, opening information-theoretic diagnostics for absorbing-state systems that bulk-observable methods cannot reach.

Traditional wildfire models rely on rigid, low-dimensional parameters and static fuel maps, frequently underpredicting fire spread. To address this weakness, we introduce a hybrid deep-learning parameterized Probabilistic Cellular Automata (CA) framework implemented in JAX. Our approach employs a Multi-Scale Convolutional Neural Network to dynamically generate spatially varying parameters that govern fire-spread probability, wind alignment, and slope influence. This hybrid design captures complex, nonlinear environmental interactions while preserving the physical interpretability of the underlying three-state CA. The JAX implementation enables hardware acceleration and gradient-based parameter calibration. Evaluated on six large-scale wildfires in the western United States, the model maintains IoU > 0.6 over 72-hour forecast horizons after a 10-day data assimilation window during which the model is fitted incrementally to observed perimeters; the resulting forecast is a conditional projection of fire growth under the suppression regime already ncoded in those observations.

Recent advances in scientific machine learning provide a means of near-real-time solution to partial differential equations (PDEs), but lack the theoretical underpinnings of conventional simulators that support contemporary verification and validation. In this work, we construct data-driven reduced-order models that serve as structure-preserving, real-time surrogates. Remarkably, the exterior calculus that imposes physical conservation structure also exposes topological structure that we use to build a Gaussian process (GP) representation of uncertainty in state-flux relationships, ultimately yielding a Dirichlet-to-Neumann map for quantities of interest with closed-form expressions for posterior uncertainty. We specifically propose structure-preserving $H(\mathrm{div})$--$L^2$ subspaces of conventional Raviart--Thomas and $dgP_0$ elements prescribed by a lightweight transformer. Reduced-order dynamics consistent with this subspace are learned by posing a conservation law in which a GP describes the fluxes between volumes. This work hinges on a novel interface between mixed FEM spaces and GP regression; when training is posed as the optimal recovery problem (ORP), the resulting GP regression can be written as an optimization problem with equality constraints that impose a conservation structure, amenable to a fast Schur-complement training strategy. The trained model can then be solved in real time with closed-form estimators for boundary fluxes driven by prescribed Dirichlet data. The paper includes RKHS posterior error bounds for linear functionals to support uncertainty quantification, as well as numerical experiments demonstrating the accuracy of the posterior distribution as a surrogate for error estimation.

Large language models (LLMs) can translate and modify source code, and have been shown to do so for codes of different complexity. Whether they can port a complete, production geophysical model to a different language without degrading its physics has not been established. We demonstrate that LLM-assisted code translation can preserve the physics of a complete production ocean model while moving it into a modern performance-portable form. We report our experience using an agentic LLM coding assistant, directed by domain experts, to port the FESOM2 unstructured mesh ocean--sea-ice model (about 74000 lines of core Fortran) first to C and then to C++/Kokkos for performance portability across CPUs and GPUs. We describe the practices that proved necessary, what worked and what did not, and the failure modes that we encountered. Three practices mattered most: translating in two stages that separate reproducing the numerics (Fortran to a clean C reference) from introducing parallelism (C to Kokkos); requiring a strictly literal translation in which the assistant was not permitted to ``improve'' the source; and validating each stage against an acceptance criterion suited to it. The C port reproduces the original Fortran at the level of long-term simulation statistics over five years. The Kokkos port is bit-for-bit identical to the C reference on CPU and statistically close on GPU over multi-year runs. On eddy-rich meshes up to 7.4 million surface vertices a single A100 GPU node runs 1.6--3.7 times faster than a CPU node, reaching the 1-2 simulated-years-per-day required for production integrations. The result is more than a single GPU port: by following a clear validation procedure, an LLM moved a full Fortran ocean model into another language and onto accelerators while preserving its physics in a matter of weeks.

Reliable extrapolation remains a central challenge for generative models in computational physics, because models trained over finite ranges of time, parameters, or geometries may produce physically inconsistent predictions outside the training distribution. We introduce a least-action-principle-guided diffusion, LAPG, a framework that promotes physical consistency during inference rather than relying solely on constraints imposed during training. The method combines a conditional score-based diffusion model with an action-derived physical guidance score. In the first stage, the learned score model generates an in-distribution proposal; in the second, an action-based variational prior refines this proposal toward the target out-of-distribution condition. This formulation turns the principle of least action into a differentiable inference-time correction mechanism and provides an alternative to pointwise residual penalties that often require empirical loss balancing. We evaluate LAPG on representative ordinary- and partial-differential-equation systems, including free fall, conservative and dissipative spring-mass dynamics, interacting point vortices, and potential flow over parameterized airfoils. In temporal, parameter, and geometric extrapolation tests, LAPG reduces phase drift, preserves dissipative decay, captures vortex motion, and improves the lift response of airfoil flows compared with training-time physics-informed baselines.

Gradient-based inversion of reaction-diffusion systems is typically approached via surrogate models or physics-informed neural networks (PINNs), while the most direct route, backpropagation through the PDE's structure itself, has largely been avoided. We pursue this direct route as a diagnostic probe, backpropagating a steady-state loss through unrolled Gray-Scott simulation to recover its parameters, with no surrogate or neural-network augmentation. Optimization fails to converge, and plotting the landscape directly locates the failure in its geometry -- flat plateaus with no gradient signal, bounded by sharp cliffs that align with bifurcation boundaries -- a structure that recurs across loss functions and is inherited however the gradients are routed to parameters. Reading this minimal setup as an ablation of PINN, we disentangle each component's role: with the neural network fixed, the residual loss is quadratic in the PDE parameters and yields a smooth landscape, so it alone already avoids the pathology, by implicitly encoding the full PDE dynamics across all initial conditions. The neural network, for its part, cannot repair an ill-posed parameter subspace, and so serves only to complete the observed data -- a division of labor not previously made explicit. These findings carry concrete design implications for PINN-type methods and a broader heuristic on when added dimensions actually help.

Accurate modeling of quantum many-body systems often requires computationally expensive simulations such as Density Matrix Renormalization Group (DMRG) or Quantum Monte Carlo (QMC) calculations. These methods, while precise, impose significant time and resource constraints, limiting their use in exhaustive parameter exploration. Moreover, these expensive simulations can contain variable errors over the large unknown parameter space, which needs to be quantified and propagated. Thus, predictive modelling is required to estimate the functional space accurately over scarcely sampled data with heteroskedastic noise, while preserving the physical relevance of the estimation. Therefore, we present a Physically Constrained Ensemble Gaussian Process (pc-EGP) framework designed to efficiently model complex and noisy quantum systems under physical consistency constraints. The proposed method first enforces physical constraints as a user controlled weighted penalty to the data-driven loss function of the Gaussian Process (GP) surrogates. Then an ensemble of such GP models is trained with variable noisy simulations via numerical quadrature method where these multiple GP(s) at different nodes is integrated as a quadrature weighted average. We first demonstrate the framework on synthetically generated data before applying to quantum systems. In the first case study, we leverage DMRG simulations of the Bose-Hubbard Model to predict the critical interaction parameter Uc governing the superfluid-to-Mott-insulator transition. In the second case study, we demonstrate our method on QMC simulations, of a quantum liquid confined inside a nanoporous silicate with the goal of optimizing a chemical environment to realize a one-dimensional superfluid. Compared to conventional GP, pc-EGP achieves a better balance of accuracy and physically meaningful predictions.

Second Harmonic Generation (SHG) in nonlinear crystals has been extensively investigated, but most existing models still rely on simplifying assumptions. In realistic settings, thermal effects introduce complications that are difficult to capture analytically because the governing equations are highly coupled and nonlinear. Direct experimental characterization is also limited, since studying thermal effects would require spatiotemporal temperature data at every point in the crystal, which is not experimentally accessible. To address these limitations, we have developed a SHG Computational Toolkit Suite, a coordinated collection of independent modeling toolkits that cover different SHG scenarios under various physical conditions. Each toolkit focuses on a particular configuration or coupling mechanism, while the suite as a whole provides well-documented numerical implementations, reproducible workflows, and illustrative examples. Together, this article and the Toolkit Suite provide a coherent infrastructure for computational studies of SHG. It enables researchers to replicate, adapt, and extend our methods without duplicating foundational development efforts, thereby accelerating SHG research and promoting reproducibility.

In this work, we investigate the use of a quantum circuit as a binary classification model in the context of quantum machine learning. We call this model, binary quantum classifier. First, we describe fundamental concepts of quantum computing and introduce the computational tool used: Qibo, an open-source framework for efficient quantum simulations and quantum hardware control. Then, we describe how to design a binary quantum classifier for the classification of images and small arrays of variables by showing how to input data in the circuit, defining a quantum circuit model Ansatz with trainable parameters and a loss function, and implementing multiple minimizers. We test our quantum classifier with two data sets. The first one is the MNIST data set which is composed of handwritten digits (reduced to only handwritten zeros and handwritten ones for binary classification). We study the behavior of different minimizers by increasing the number of layers of the Ansatz. The second data set represents two different high energy collisions that can occur at colliders such as LHC (CERN). Due to in-time proton-proton interactions known as pile-up, we distinguish two different data sets: "without pile-up" and "with pile-up". These collisions can be represented by images of size 32x32 or by six high-level variables that we call features. By increasing the size of the training data set and the number of layers of the Ansatz, we search for the best minimizer. Splitting the data set in training set and test set, we compute: ROC curve, AUC score, confusion matrices and test set accuracy. For "with pile-up" images, we compare the results obtained with the quantum classifier with a small convolutional neural network. We conclude that is possible to build a binary quantum classifier with a quantum circuit and we highlight its performances and limitations in comparison with classical technologies.

Machine-learned interatomic potentials (MLIPs) have had a profound impact on molecular modelling in recent years, promising to resolve the long-standing tension between the scale and accuracy of simulations. There has been a proliferation of new models and designs, and recently the paradigm of ``foundational'' MLIPs has become prevalent. Broadly speaking, foundation models are trained on large diverse datasets and promise to work well for new systems with minimal updates required. However, in such a new and fast moving field, there are many unanswered questions. In this article, we set out to articulate and explore what we see as the most important among these questions. We start by developing a working definition for foundational MLIPs and use this definition to frame the subsequent open questions. Despite the rapid progress in the field of MLIP models, we believe that these are fundamental questions which will continue to define cutting edge research in MLIPs in the years to come.

Machine-learning interatomic potentials now approach quantum-mechanical accuracy on standard benchmarks, but the training cost of the most expressive equivariant architectures has become a serious bottleneck. We introduce DPA4, an SE(3)-equivariant interatomic-potential architecture with an EMFA (Edge-conditioned, Multi-Focus, Attention) SO(2)-equivariant convolution that combines a low-rank edge-node SO(2)-equivariant product, a multi-focus design for message nonlinearity, and envelope-gated attention for message aggregation. A Lebedev-grid projection further preserves SO(3)-equivariance in the nonlinearity to machine precision. A compiler-friendly conservative energy-gradient training path provides up to $\sim$3 times wall-clock speedup under torch compile. On the compliant Matbench Discovery benchmark, DPA4-Pro attains the best Combined Performance Score (CPS) on the leaderboard, while the 2.76M-parameter DPA4-Air exceeds the accuracy of the 30.1M-parameter eSEN-30M-MP baseline with 10.9$\times$ fewer parameters and 42.9$\times$ less training compute. On SPICE-MACE-OFF, the 5.4M-parameter DPA4-Plus lowers the aggregate molecular energy and force errors of the 6.5M-parameter eSEN baseline by 29% and 30%, while the 2.7M-parameter DPA4-Air still surpasses that baseline with $\sim$2.4$\times$ fewer parameters. Together these results place DPA4 on a new accuracy-cost Pareto frontier on Matbench Discovery and position it as a strong candidate backbone for future multi-task large atomistic model (LAM) pretraining.

Phononic crystals can confine elastic waves through localized defect states within bandgaps, offering promising opportunities for vibration control and energy localization. However, designing defect states at prescribed frequencies while maintaining adequate separation from other in-gap modes remains a significant challenge. Existing optimization approaches generally treat the target mode indirectly and provide limited control over competing localized modes. This study presents a gradient-based two-stage topology optimization framework for the frequency placement of localized defect modes in periodic elastic media. First, a host unit cell is optimized to create a bandgap around a prescribed frequency. Subsequently, only the defect cell is modified to attract a selected localized mode toward the target frequency while repelling non-target modes away from the central region of the bandgap. The formulation incorporates a smooth mode-selection function that combines mode attraction and repulsion within a unified objective, enabling automatic tracking of the relevant modes throughout the optimization process. Because the localized defect branches of interest are nearly flat, the optimization is performed using only the $\Gamma$-point eigenspectrum, while the corresponding dispersion relations over a reduced irreducible Brillouin zone are evaluated afterwards for verification. Numerical examples involving two material systems and two supercell sizes demonstrate accurate placement of localized resonances, clear separation from competing in-gap modes, and substantial preservation of the host bandgap. The resulting structures exhibit strong elastic-wave localization, highlighting the potential of the proposed approach for the design of phononic devices for vibration confinement and energy trapping.

We propose a deep learning framework based on an encoder-decoder architecture for the design and evaluation of cloaking devices, demonstrated in this work for two-dimensional wave propagation governed by the Helmholtz equation. The cloaks under consideration are concentric layered media surrounding the object, whose geometry and material parameters determine the scattering response. We consider circular and object-fitted layer configurations and parameterize all designs by the layer thicknesses, enabling a unified representation for direct comparison of different cloaks for the same object. Training data are generated using a boundary element formulation suitable for geometries where analytic solutions are not available, and neural networks are trained with standard hyperparameters on geometry-specific datasets. The proposed approach is applied to circular, star-shaped, and kite-shaped objects. Results show that object-fitted configurations consistently outperform simpler circular-layer designs in scattering reduction, highlighting the importance of geometry in cloaking performance. Overall, we present a flexible, data-driven approach for systematic comparison of cloaking strategies, with potential extension to more complex geometries and broadband settings.

The differentiable physics paradigm may be leveraged as an a-posteriori approach for discovering turbulence closure models by embedding a neural network parameterization directly inside the solver and optimizing it given potentially sparse target data. This addresses a key limitation of a-priori learning where direct numerical simulation (DNS) data is used to approximate the subgrid stress with the assumption of a low-pass filter. Closures trained in this a-priori manner frequently lead to unstable deployments due to the mismatch between the assumed filter and the effect of numerical discretizations and coarse-graining. In comparison, while typically stable during deployment, a-posteriori learning incurs high computational costs due to the need to backpropagate through a large eddy simulation (LES) solver. Furthermore, a-posteriori methods are challenging to apply broadly since they require significant modification of existing solvers. Finally, both approaches are limited when generalization is desired across different numerical schemes with their implicit filtering characteristics. In this work, we present a deep-learning approach for turbulence closure modeling built on the continuous data assimilation framework. Our approach enables the a-priori training of closures using sparsely observed DNS data without modifying or differentiating through the LES solver, while preserving stability during deployment for the recovery of invariant statistics. We focus on the model's ability to adapt to different discretizations by explicitly conditioning it on the numerical scheme. We use two- and three-dimensional canonical cases to test our framework and show that the learned correction systematically tracks the discretization error of the coarse solver.

As a powerful theoretical construct, the entanglement Hamiltonian (EH) encapsulates the essential entanglement properties of a quantum many-body system. From the EH, one can extract a variety of entanglement quantities, such as entanglement entropies, negativity, and the entanglement spectrum. However, its general analytical form remains largely unknown. While the Bisognano-Wichmann theorem gives an exact EH form for Lorentz-invariant field theories, its validity on lattice systems is limited, especially when Lorentz invariance is absent. In this work, we propose a general scheme based on the lattice-Bisognano-Wichmann (LBW) ansatz and multi-replica-trick quantum Monte Carlo methods to numerically reconstruct the entanglement Hamiltonian in two-dimensional systems and systematically explore its applicability to systems without translational invariance, going beyond the original scope of the primordial Bisognano-Wichmann theorem. Various quantum phases--including gapped and gapless phases, critical points, and phases with either discrete or continuous symmetry breaking--are investigated, demonstrating the versatility of our method in reconstructing entanglement Hamiltonians. Furthermore, we find that when the entanglement boundary of a system is ordinary (i.e., free from surface anomalies), the LBW ansatz provides an accurate approximation well beyond Lorentz-invariant cases. Our work thus establishes a general framework for investigating the analytical structure of entanglement in the complex quantum many-body systems.

We present a hardware demonstration and resource analysis of split-evolution quantum phase estimation (SE-QPE) on a Quantinuum System Model H2 quantum computer. SE-QPE is a modification to canonical QPE for particle-conserving Hamiltonians in which controlled time evolution is replaced by CSWAP-based interference between a target register and a reference register. For factorizations of time evolution with a shared eigenbasis, SE-QPE preserves the phase-register outcome distribution of canonical QPE and, unlike with compute--uncompute substitutions, it remains compatible with non-exact eigenstates. The substitution removes controlled-simulation overhead and enables parallel evolution on two registers, reducing the depth of each phase-kickback block. Resource analysis for Trotterized double-factorized chemistry Hamiltonians shows that the substitution becomes increasingly favorable at higher phase powers and combining QPE and SE-QPE implementations can be a useful option. Over a range of FeMoco active spaces, SE-QPE reduces time evolution resources, with asymptotic reductions of about 33% in CX count, 25% in $T$ count, and an asymptotic depth ratio of $3/N$ for CX layers. On Quantinuum H2-2, a four-qubit model ethylene demonstration with explicit inverse QFT and repeated phase-kickback steps up to 8 phase bits yields distinct energies and shows the auxiliary registers provide useful error detection filters.

Accurate mode tracking is essential for elastic waveguide dispersion analysis in ultrasonic nondestructive evaluation and structural health monitoring. Its reliability, however, deteriorates near mode veering and closely spaced eigenvalues, where rapid eigenvector exchange causes mode misidentification. Although widely observed, the quantitative relationship between veering, eigenvector evolution, and tracking robustness has not been systematically established. By specializing classical perturbation theory to the single-parametric Hermitian SAFE eigenproblem--exemplified by conservative elastic waveguides--we obtain explicit expressions for eigenvector derivatives and modal coupling strength. This yields a unified, quantitative interpretation of mode veering, symmetry-protected crossings, and degeneracies, and clarifies their distinct tracking implications: eigenvector sensitivity scales inversely with the eigengap, explaining modal repulsion and the degradation of correlation-based tracking near avoided crossings, whereas symmetry-protected crossings remain benign because symmetry-induced decoupling preserves smooth eigenvector evolution, and symmetry-protected degeneracies require rotation-invariant subspace tracking. A numerical consistency condition and an existence result for a critical step size are then derived, motivating a two-level adaptive strategy with an a posteriori error indicator that separates numerical tracking consistency from symmetry-based physical correctness. Numerical examples validate the theoretical predictions and demonstrate improved robustness in regions of strong modal interaction, providing practical guidance for reliable dispersion calculations and ultrasonic inspection.

Accurately predicting the Curie temperature ($T_c$) of ferroelectrics from first principles remains a major challenge, as theoretical estimates often fall significantly below experimental values. In this work, we investigate the origin of these discrepancies in the prototypical ferroelectric PbTiO$_3$ by performing extensive constant-pressure ab initio molecular dynamics (AIMD) simulations and benchmarking them against classical molecular dynamics (MD) using machine learning force fields (MLFFs) derived from first-principles data. Our results show that the underestimation of $T_c$ primarily stems from the limitations of the exchange-correlation functional, rather than inaccuracies in the MLFF fitting. We uncover a critical interplay between finite-size effects and the range of interatomic interactions: although short-range MLFFs appear to yield better agreement with experimental $T_c$, this improvement results from a fortuitous cancellation of errors. Incorporating explicit long-range interactions improves accuracy for larger supercells but ultimately leads to lower predicted $T_c$ values. These findings highlight that accurate finite-temperature predictions require not only high-quality training data and sufficiently large simulation cells, but also the explicit treatment of long-range interactions and improved exchange-correlation functionals.

This work presents a survey of mechanical models describing van der Waals interactions between 2D materials, encompassing both continuous elastomer-like materials and discrete (crystalline) 2D materials such as graphene. These interactions give rise to a range of physical phenomena, including contact instabilities, Moiré patterns, surface reconstructions, and superlubricity. The underlying contact forces follow from the variation of an interfacial interaction potential. The presentation first discusses normal contact models, and then tangential contact models. Both atomistic and continuum approaches are considered. In addition, the influence of external loading and changes in length scale on the ground state configuration and frictional contact behavior are analyzed. A particular emphasis is placed on discussing strategies that reduce computational cost in multiscale modeling.

Thermodynamic stability of N$_2$ clathrate hydrates in the sI and sII structures is investigated using density functional theory with several exchange-correlation functionals, explicitly accounting for composition (cage occupancies) and pressure at T = 0 K. Among the tested functionals, revPBE-D3(0) best reproduces experimental lattice parameters and bulk moduli B$_0$ . Energetic analyses confirm the strong impact of large cage double occupancy on sI, whereas the convex-hull results show that sI with single occupancy remains thermodynamically stable up to $\sim$ 0.8 GPa alongside sII with single occupancy. Increasing pressure then stabilizes sII with double occupancy, consistent with its larger large-cage volume and lower framework strain. These results provide a coherent, first-principles thermodynamic framework for N$_2$ hydrate stability and a baseline for finite-temperature extension.

Many complex physical systems naturally decompose into an exactly solvable component augmented by a perturbative correction. Rather than directly employing neural networks to analyze complex physical systems, we introduce Neural Network Perturbation Theory (NNPT)--a correction learning approach that predicts residual perturbations after analytically subtracting known exact solutions. Using the gravitational three-body problem as testbed, we vary Jovian mass from f=0.05 to 30 times its physical value while holding network architecture fixed. An equalized-accuracy protocol with 1% tolerance reveals an unexpected non-monotonic capacity profile: capacity peaks at f=5 in the late integrable regime (3x32, 2242 parameters), remains elevated through the transition region (f~15-17), then decreases in the fully chaotic regime (f>=17, requiring only 2x32 with 1186 parameters)--a 47% reduction from peak. With symplectic integrator energy conservation below 2x10^{-4}, this counterintuitive phenomenon reflects genuine physical structure rather than numerical artifacts. Sequential correction experiments show negligible refinement (||y2||/||y1||~0.997), confirming single-stage networks capture dominant perturbative features without hierarchical decomposition. The capacity transition at f_c=16.6+-2.8 aligns with Chirikov's resonance-overlap criterion. Intermediate-complexity regimes impose maximal capacity requirements, while fully chaotic dynamics undergo ergodic smoothing--trajectory-specific fluctuations become irreducible noise, leaving only statistically smooth corrections requiring fewer parameters.

In this paper we introduce an electron ptychography reconstruction framework, CAVIAR -- Correlated Atomic Vibration Imaging with sub-Angstrom Resolution -- that reveals an entirely new channel of information: spatial correlations in atomic displacements at the atomic scale. We show reconstructions of a symmetric $Σ$9 grain boundary in silicon from realistically simulated data and experimental data for hexagonal boron nitride. By reconstructing the object as an ensemble of multiple states we are able to observe correlations between movements of atoms in the range of 10-20 pm at room temperature in agreement with the expectation. Moreover, using only the masses of the atomic species and the temperature as input, we obtain average frequencies of $10.8\pm0.1$, $13.6\pm0.6$, $18.0\pm0.2$, $25.5\pm1.5$ THz for the longitudinal and transversal acoustic and optic phonons, respectively, in agreement with inelastic neutron scattering, albeit from just a few nm$^3$ volume. This ability to spatially resolve correlated atomic motion makes CAVIAR a unique tool to explore atom dynamics at the finest scale with the potential to be instrumental in the development of phononic devices, in studying phonon-based decoherence in quantum systems, or other emerging phonon-based applications.

Partial Differential Equations (PDEs) describe phenomena ranging from turbulence and epidemics to quantum mechanics and financial markets. Despite recent advances in computational science, solving such PDEs for real-world applications remains prohibitively expensive because of the necessity of resolving a broad range of spatiotemporal scales. In turn, practitioners often rely on coarse-grained approximations of the original PDEs, trading off accuracy for reduced computational resources. To mitigate the loss of detail inherent in such approximations, closure models are employed to represent unresolved spatiotemporal interactions. We present a framework for developing closure models for PDEs using synthetic data acquired through the method of manufactured solutions. These data are used in conjunction with reinforcement learning to provide closures for coarse-grained PDEs. We illustrate the efficacy of our method using the one-dimensional and two-dimensional Burgers' equations and the two-dimensional advection equation. Moreover, we demonstrate that closure models trained for inhomogeneous PDEs can be effectively generalized to homogeneous PDEs. The results demonstrate the potential for developing accurate and computationally efficient closure models for systems with scarce data.

Modeling and simulation of complex fluid flows with dynamics that span multiple spatio-temporal scales is a fundamental challenge in many scientific and engineering domains. Full-scale resolving simulations for systems such as highly turbulent flows are not feasible in the foreseeable future, and reduced-order models must capture dynamics that involve interactions across scales. In the present work, we propose a novel framework, Graph-based Learning of Effective Dynamics (Graph-LED), that leverages graph neural networks (GNNs), as well as an attention-based autoregressive model, to extract the effective dynamics from a small amount of simulation data. GNNs represent flow fields on unstructured meshes as graphs and effectively handle complex geometries and non-uniform grids. The proposed method combines a GNN based, dimensionality reduction for variable-size unstructured meshes with an autoregressive temporal attention model that can learn temporal dependencies automatically. We evaluated the proposed approach on a suite of fluid dynamics problems, including flow past a cylinder and flow over a backward-facing step over a range of Reynolds numbers. The results demonstrate robust and effective forecasting of spatio-temporal physics; in the case of the flow past a cylinder, both small-scale effects that occur close to the cylinder as well as its wake are accurately captured.