Papers

A structural simulation needs a constitutive law, and experiments rarely determine one uniquely: several laws may fit the same data and satisfy the same physical constraints, yet differ where the structure is loaded in ways the tests never were. Constitutive-Set Mechanics (CSM) keeps all of those laws. It replaces the single law in the variational formulation by the admissible set, and lets the mechanics itself decide which members of the set affect the structural prediction. The framework rests on one observation: a finite element assembly consults the law only at the strains the structure reaches, so the incremental energy depends on the law through a weighted record of those strains, the occupation measure of the state. The energy of a state under the set is a support function on that measure, and the equilibrium solve one performs anyway supplies the information needed to bound the worst case. Equilibrium states become certificates on the robust response, rigorous on the upper side for any mechanics solver and two-sided under global minimisation; the certificate has at most one more state than the number of constitutive directions the structure interrogates; a coherence theorem identifies when the pointwise-worst material is one no single material can be; and constitutive inference acts on the same support function. The method is demonstrated on linear elasticity, a data-constrained constitutive function, phase-field fracture, an assembled finite-strain composite shell, and a membrane characterised by one-mode tests alone. On the shell the structure interrogates four of 226 constitutive directions; on the membrane the certified worst-case energy exceeds the reference more than fourfold, and the experiment that most contracts the certified prediction is not the one where the constitutive uncertainty is largest.

Nonreciprocal mechanical response is usually associated with built-in directional couplings, structural chirality, or external driving. Whether an achiral active body can instead generate and reverse such directionality through its own motion remains less clear. Here we show that spontaneous rotation makes an active elastic ring with reciprocal passive interactions mechanically nonreciprocal. Off-center elastic forces reorient propulsion, coupling deformation back to motion. Reversing the rotation reverses the antisymmetric response, while a compensating control preserves finite directionality but strongly suppresses the near-Hopf resonance. Approaching Hopf, the selected response grows inversely with distance to onset and becomes a self-sustained traveling deformation above threshold. Thus nonreciprocity is selected by the dynamical state, while active feedback controls its critical amplification.

Phase-field models of fracture in fibre-reinforced shells are usually formulated against a single closed-form stored energy, so that the stress, consistent tangent and plane-stress condensation are derived and verified for that expression alone. Here the constitutive law enters instead as a replaceable operator. The Green-Lagrange strain of a geometrically exact Reissner-Mindlin shell is pulled back through the Cholesky factor of the reference metric and resolved on four mutually orthogonal invariants with an exact closure identity, making the separation into fibre, inter-fibre and interaction channels a change of basis rather than a modelling assumption. On a curved midsurface, the metric, Cholesky factor and fibre direction vary through the thickness through the shifter I - zeta b, and the invariants inherit that dependence. The tension-compression split, channel degradation, plane-stress condensation, consistent tangent and finite-element assembly are all expressed in the channel potentials and their derivatives, allowing either closed-form or learned operators. The fibre-transverse interaction energy is stored once and degraded by the product of the fields whose mechanisms it couples. Six conditions define admissible operators; the two linear invariants are proved convex in the deformation gradient, the geometric tangent is shown independent of the material tangent, and the plane-stress condensation is regular wherever the residual stiffness is positive. A three-tier protocol certifies the algebra, solver state and admission of a state as training data. Numerical studies on notched IM7/8552 shells verify the discretisation in thin and curved regimes and show that fibre orientation governs the damage envelope and load capacity, while curvature drives a through-thickness fracture asymmetry that a single midsurface field cannot represent.

Starting from the robust foundation of the peculiar velocity based upwind (PVU) Boltzmann scheme, which fails to recognize contact discontinuities, this paper introduces new variants for the numerical solutions of equations of gas dynamics. A modified partial differential equation (MPDE) analysis of the original scheme reveals that the numerical diffusion coefficient corresponding to the peculiar velocity part does not vanish as the Mach number goes to zero. The numerical discretization of the peculiar velocity term is redesigned so that the numerical diffusion depends only on the bulk fluid velocity across the stationary contact discontinuities, enabling its exact capture in 1D and exact capture of slip surfaces in 2D. The resulting variants achieve low numerical diffusion while preserving the robustness of the original scheme, as demonstrated through several 1D and 2D benchmark compressible flow test cases.

GPU-based optimization faces two communication bottlenecks: coordinating frequent requests and delivering dense models that exceed device memory. We present a discrete simulated bifurcation (dSB) architecture that addresses both through NVIDIA DOCA GPUNetIO. For resident models, a persistent service receives field updates, executes each solve within one GPU thread block, and returns the result. Exact integer coupling sums, GPU work queues, and batched transmission keep the receive–solve–reply path on the device without a dedicated CPU data-path core. In comparisons with socket-based servers using the same solver, the largest latency gains occur under concurrent load. As the offered load increases from 400 to 800 thousand requests per second, median round-trip latency rises by only 6%. At the highest tested load, median and 99th-percentile latencies are 189 and 218~$\mu$s, compared with 288 and 609~$\mu$s for the tuned persistent CPU proxy across repeated runs. For models larger than device memory, a streaming solver retains dynamical state on the GPU and reuses incoming coupling tiles across replicas. It evaluates ten-million-variable dense binary matrices at approximately 307~Gb/s, consuming a 12.5-TB logical matrix through a 64-MiB packet buffer. Ground-state recovery on planted instances and agreement with reference executions verify the computation. Together, the two modes scale dSB to concurrent requests and dense models beyond GPU memory.

Compact, reliable, and cost-effective gas sensors have become a highly demanding subject for safety management in the medical sector, chemical manufacturing, food quality monitoring, agriculture, and industrial safety. Hazardous gas emissions need to be controlled and monitored with fast-responsive and highly sensitive sensing devices. A first-principles study employing density functional theory (DFT) was used to investigate the adsorption behavior of Cl2, CO, CO2, NO, NO2, and HCN gas molecules with our proposed alloys, which consisted of hexagonal boron nitride (hBN) and graphene (Gr). The alloy consisting of 22% carbon (BNGr-2) was found to be most competent for sensing Cl2, CO, CO2, and HCN with sufficient adsorption energy, charge transfer, and bandgap alteration. However, NO and NO2 gas molecules showed more engagement with 33% carbon-proportioned alloy (BNGr-3) in terms of adequate gas sensing properties. NOx gases exhibited the most chemiresistive sensitivity towards the adsorbents. Other gases also showed significant chemiresistive sensitivity and distinct selectivity ratios, which would facilitate these alloys as chemiresistive sensors. Besides, noticeable work function variation (~20%) of these systems manifested potential as work function based sensors. Cl2 and NO2 showed strong physical adsorption, while the rest of the gases were weakly to moderately physisorbed, resulting in very short recovery times (10-1 ~ 10-6 seconds). Additionally, the distinctive absorption spectra observed for the gas analyte systems highlighted the potential of the proposed alloys as optical gas sensors. Temperature variation revealed that all gas molecules can be freed from the adsorbent BNGr-2 at 425 K. These findings imply hBN-Gr alloys as promising gas sensors for pollution auditing.

This study combines a stochastic renormalization group (RG) in space with a path-integral description of the time evolution, giving a spatial hierarchy of coarse-grained dynamics together with the distribution over spatiotemporal paths. The RG is defined as a diffusion process that applies scale-dependent Laplacian damping together with additive Gaussian noise. The time evolution at each spatial scale is formulated as an Onsager–Machlup action, with a drift (i.e., the predictor) and white noise whose amplitude is fixed by the RG. The predictor of these dynamics is optimized by minimizing the Kullback–Leibler divergence between the path distributions from the RG and from the path-integral description. The optimal predictor contains the score function that connects the spatial scales, so the predictor and the score are two aspects of the same multiscale path formulation. The formulation unifies simulation using the predictor, unconditional generation using the score, and super-resolution using both. The predictor has no closed form, so it is computed by a neural network in two realizations that differ only in how the score is computed. The first realization obtains the score by automatic differentiation of the path distribution, remaining faithful to that formulation. The second obtains the score as an additional network output trained by denoising, at a lower computational cost. These two realizations are validated through numerical experiments on two representative multiscale systems, the Kolmogorov flow and the two-timescale Lorenz-96 model.

Preparing quantum states from classical data can cost more than the computation they serve; most loaders tailor a circuit to each input. Here we show that the signals of a real dataset share structure that can be learned once and reused. Our quantum-native loader learns a low-dimensional description of a dataset and prepares every signal with one fixed circuit set by a few numbers. Across seven views of five public datasets it meets the targets of the strongest structured loader at equal gate cost with several times fewer numbers per signal. These numbers can be inferred from a random subset: in a preregistered blind replication the subset needed to come within ten per cent of full-signal accuracy stayed constant within a prespecified margin as signals grew sixteenfold, whereas the structured loader needed ever more. It declines what it cannot represent, covering fewer cases than that baseline and no electrocardiogram.

Superionic conductors enable exceptionally fast ion transport in solids and offer broad technological potential. However, their highly conductive states are typically accessed only above the order-disorder transition of the mobile-ion sublattice, which limits low-temperature operation. Here, electric-field-responsive machine-learning molecular dynamics reveals a nonequilibrium route to superionic transport in quasi-two-dimensional AgCrSe2 driven by an out-of-plane oscillating electric field. At 300 K, far below the transition temperature near 475 K, the field activates fast in-plane Ag+ transport with an ionic conductivity reaching ~1.7 S/cm. This originates from field-driven dynamic disorder of Ag+ across two equivalent sublattices rather than thermally induced disordering. With increasing frequency, the Ag occupation evolves from complete switching to a highly conductive dynamically disordered state and finally to an ordered state with weak field response. These regimes shift to higher frequencies with increasing temperature or field amplitude, consistent with competition between the driving period and Ag-sublattice response time. At strong fields, this timescale is consistent with field-assisted thermal activation, while weak-field deviations suggest additional dynamics beyond single-ion activation. These results suggest timescale-matched periodic driving as a route to transport-active ionic disorder far below an equilibrium superionic transition.

We develop structure-preserving methods for the compressible Euler equations with gravity in vector-invariant form and potential temperature as a prognostic variable within the flux-differencing discontinuous Galerkin spectral element method (DGSEM) framework. By discretizing the nonconservative terms as symmetric and antisymmetric products, we derive two-point numerical fluxes that conserve both the thermodynamic entropy and the total energy. Moreover, we design an entropy-stable numerical flux that is well-balanced for both isothermal and isentropic background states. All properties are shown to carry over to the high-order DGSEM on general curvilinear meshes. Several numerical examples confirm the theoretical findings and show the robustness and accuracy of the scheme for use in modern dynamical cores for atmospheric flows.

Design-dependent wall velocities are difficult to treat in density-based fluid topology optimization. This difficulty arises because the fluid-solid interface is represented implicitly and evolves with the design. This paper proposes a diffuse-interface formulation for topology optimization of steady incompressible Navier-Stokes flows with design-dependent wall actuation. A continuous topological description field parameterized by compactly supported radial basis functions (CS-RBFs) provides the local interface orientation, and its regularized projection defines the pseudo-density for Brinkman flow analysis. The wall velocity is imposed on a fixed mesh through an equivalent volumetric momentum source, which is localized by a diffuse-interface measure constructed from the pseudo-density and the gradient of the description field. Assuming a locally planar interface and uniformly distributed Wendland radial basis functions, the source coefficient is determined analytically by balancing the equivalent momentum input with the Brinkman resistance at the interface center. These assumptions also yield a characteristic transition-width estimate in terms of the projection steepness and support radius. Continuous adjoint analysis is performed to derive the design sensitivities. Two- and three-dimensional examples formulated using the analogy equation demonstrate the effectiveness of the proposed topology optimization method for flow-rate maximization. Body-fitted re-simulations verify the flow fields and transport performance of the optimized designs. The formulation is further extended to electroosmotic transport under the thin electric double layer (EDL) assumption using the Helmholtz-Smoluchowski relation.

Atomistic foundation models screen hypothetical crystals by thresholding predicted energies, an output that states neither how likely a candidate is to be stable nor whether more computation would change the decision. CrystalJev reads one forward pass of a frozen potential on the unrelaxed structure and returns calibrated probabilities, conformal guarantees and a rule for escalating candidates to relaxation or density-functional theory (DFT). Across 65 Matbench Discovery models, threshold calls hide cost assumptions, and ordering slower computation by its value for the decision, rather than by probability, recovers most of its benefit at a tenth of its cost. In a registered prospective test with 2,100 DFT calculations on ionic substitutions, forecasts calibrated on existing data over-stated the stable fraction of new candidates by 0.9–2.2 percentage points, because the population had shifted, not the labelling protocol; a few hundred labels from the new pool removed this bias more reliably than label-free corrections.

We develop and analyze several families of fully discrete, high-order methods in the finite difference time domain (FDTD) framework for a nonlinear dispersive electromagnetic model for ultrashort pulse propagation in a nonlinear optical medium. The model consists of the time domain Maxwell's equations coupled to two ordinary differential equations; the nonlinear Kerr-Debye equation and the linear dispersive Lorentz equation, in one space dimension. The proposed methods combine staggered spatial discretizations of $2M$th-order, for integer $M>0$, with second-order explicit leapfrog or implicit trapezoidal time integrators. To handle the stiff relaxation in the nonlinear Kerr-Debye equation, we adopt a modified exponential integrator, introduced in \cite{PengJCP2020}, which ensures asymptotic-preserving (AP) behavior in the limit of vanishing relaxation time. We prove that the resulting schemes satisfy a discrete analogue of the continuous energy identity and preserve the positivity (PP) of the nonlinear susceptibility. For the schemes based on the leapfrog time integrator, we establish energy stability under a CFL condition, while the schemes based on the trapezoidal time integrator are unconditionally energy stable. High-order temporal accuracy in the trapezoidal time integrator based schemes is further achieved via Richardson extrapolation yielding $2M$th-order accurate methods in both space and time. Numerical experiments demonstrate the theoretical convergence rates and the ability of the proposed schemes to capture nonlinear wave phenomena such as soliton propagation, self-steepening, and odd harmonic generation. This work extends previous AP-PP and energy stable approaches in a discontinuous Galerkin framework to the FDTD setting, offering a computationally efficient, flexible and robust tool for simulating electromagnetic wave propagation in nonlinear dispersive optical media.

We present a qualitative case study of a human-supervised team of specialized AI agents supporting an astronomy research project. The Bot Spectroscopist team, described in the project record as operating through Grok Bot powered by xAI Grok, divided work among orchestration, numerical implementation, data curation, spectroscopy critique, literature search, figure preparation, manuscript editing, and review. Human decisions determined scientific scope, model changes, and manuscript inclusion. The scientific application is CondGen, a deterministic label-to-spectrum network extending our previous work to five individual elemental abundances. The reported baseline assessment achieved a mean absolute error (MAE) of 0.003681 in continuum-normalized flux on 21,657 synthetic test spectra. Existing binned diagnostics show that reconstruction error varies with effective temperature and abundance. The bots also flagged a non-monotonic cool-star magnesium response for further investigation; a matched SYNSPEC abundance sweep is needed to assess its physical fidelity. Building on a pre-existing spectral database, notebooks, and research program, the authors estimate that the reported analysis, diagnostics, figure preparation, and initial manuscript drafting were assembled in less than a week through human prompting and exchanges among agents. No comparison with a human team starting from the same resources was performed, so this elapsed-time account does not establish a productivity or labor saving. The study illustrates task delegation, artifact exchange, critique, and correction under human supervision.

A geometrically-exact planar beam finite-element framework is developed for the analysis of beams with hyperelastic constitutive models. A conventional three-field beam model is first formulated with full geometrical nonlinearity and a linear elastic material law. The kinematics are then enriched by an additional global field that permits deformation through the in-plane thickness. The out-of-plane direction is incorporated separately through plane-strain and plane-stress constitutive reductions, allowing the cross-sectional deformation assumptions and constitutive behaviour to be formulated independently. Numerical results for the present benchmarks show that the plane-stress condition gives essentially coincident centreline deformations for the Poisson's ratio values considered. In contrast, the plane-strain condition, which is widely employed in the literature, makes the formulation sensitive to Poisson's ratio coupling, with the beam becoming significantly stiffer at higher Poisson's ratios. Comparisons between Saint Venant-Kirchhoff and Neo-Hookean hyperelastic models further demonstrate close agreement in the global deformation and in-plane thickness response, with small constitutive differences becoming more apparent in the local out-of-plane stretch. The proposed approach offers a simple and consistent framework to integrate hyperelastic material models into planar geometrically-exact beam models.

An electromagnetic inversion scheme that integrates stochastic optimization (STO) and plug-and-play (PNP) regularization into contrast-source inversion (CSI), termed STO-PNP-CSI, is developed. Standard CSI solves for the contrast source vector of every transmitter at each iteration, which is expensive in a multi-transmitter configuration. STO instead solves for only one randomly selected contrast source vector per iteration, which reduces the per-iteration cost and can help the inversion escape poor local minima and saddle points. The resulting loss of information, however, increases the ill-posedness of the inversion. To counter this, the Swin-Conv-UNet (SCUNet) denoiser is plugged into the CSI scheme as an implicit regularizer, supplying a learned prior that is stronger than conventional hand-crafted ones and stabilizes the reconstruction. The proposed STO-PNP-CSI is applied to both synthetic and experimental data. The results show that it yields accurate reconstructions at substantially lower computational cost than CSI, including under strong nonlinearity and measurement noise.

We present two complementary neural routes for microscopic neutron-star EOS inference: truncated sequential neural posterior estimation with mixture importance sampling (TSNPE+MIS), which targets one observation, and amortized neural posterior estimation with importance sampling (A-NET+IS), which is reused across nuclear inputs and NICER sources. Both are corrected against the original prior and full likelihood, with the effective sample size as a diagnostic. We test nucleonic and hyperonic relativistic mean-field models with nuclear data, NICER, GW170817, and pQCD. For the fiducial analyses, both agree with UltraNest in the parameter posteriors and 90% mass-radius and tidal-deformability bands. TSNPE+MIS band-edge differences are only 0.024-0.033 km and 1.02-1.03%, while A-NET+IS differences are 0.019-0.050 km and 0.86-1.13%. TSNPE+MIS reduces the computing time by factors of 1.6-2.3; after training, A-NET+IS is 15-240 times faster per configuration. The frozen A-NET also analyzes three NICER sources absent from training, including the newly reported high-mass, compact PSR J1614-2230 posterior. For this source, the inferred $R_{1.4}$ agrees with UltraNest within 0.010 km for nucleonic matter and 0.009 km for hyperonic matter. We also introduce a Green-function Evidence Network (EN), a regression-based variant of Evidence Networks and, to our knowledge, the first Evidence Network applied to neutron-star EOS inference. After a one-time cost, its network queries return absolute evidences in about 0.03 s for new nuclear data and 3.5 s for a new NICER source; all 16 differences from UltraNest are below $1\sigma$, and independent importance-sampling evidences agree within the quoted EN uncertainties. Under the adopted likelihood, both evidence calculations favor nucleonic matter by Bayes factors of about 22:1-27:1.

We study the recently introduced SWAP ensemble for Ising spin-glasses, where the spins obtain varying lengths, with length scale $\Delta \in [0, 2]$. The lengths can be exchanged in the spirit of the SWAP algorithm for glassy poly-disperse hard-sphere systems. Using an annealing schedule, if the annealing is slow enough, ground states of the corresponding Ising Hamiltonian, where the spin lengths are incorporated into the bonds, can be obtained with high probability. We prove this statement for two-dimensional systems with sizes of up to $L^2=1024^2$ spins by comparison with exact ground states obtained by using graph matching algorithms. In particular, we analyze the nature of the obtained realizations of the disorder by calculating exact zero-temperature domain-wall energies, from exact ground state calculations using periodic and anti-periodic boundary conditions. For medium or large values of $\Delta$, e.g. $\Delta=1$, the realizations turn ferromagnetic if the annealing is slow enough, i.e., they lose their zero-temperature spin-glass property. If $\Delta$ is small, the realizations remain glassy, but the SWAP annealing does not easily find a true ground state.

Metasurfaces are ultrathin optical elements that control light through carefully engineered structures smaller than the wavelength of light, enabling compact devices with functionalities that are difficult to achieve with conventional optics. However, exploiting their full design freedom over large areas has been prohibited by the large computational cost of repeated electromagnetic simulations required for inverse design. Here we introduce a physics-tailored deep-learning surrogate model that exploits the locality and symmetries of electromagnetic interactions to generalize from small-scale simulations to metasurfaces orders of magnitude larger. The model captures nonlocal interactions while predicting optical fields more than four orders of magnitude faster than the conventional electromagnetic solver it is trained on, enabling gradient-based topology optimization under arbitrary illumination. We validate the approach through the inverse design and experimental realization of free-form metagratings with diffraction angles up to 75 degrees, as well as a millimeter-scale free-form holographic metasurface more than 1,000 wavelengths across and comprising 1.6 billion degrees of freedom. By decoupling the scale of electromagnetic simulation from the scale of inverse design, our approach enables system-scale free-form photonic devices that retain nanoscale design freedom.

Full-wave electromagnetic (EM) simulation enables accurate patch-antenna analysis but is computationally expensive for large-scale forward prediction and inverse design. We present a mesh-native, physics-augmented graph-learning framework that treats radiation-pattern prediction as signal reconstruction on an irregular surface mesh. For the forward problem, a GPS graph transformer is trained with Physics-Augmented Intermediate Supervision (PAIS), an auxiliary node-level objective that predicts complex surface currents, the physical intermediate linking geometry to radiation. PAIS improves multiple GNN backbones at no inference-time cost, while shuffled-current and non-physical controls show the gain comes from physical correspondence. Direction-conditioned decoding and a differentiable radiation-integral consistency loss further exploit this structure. On an 80,000-sample CST benchmark, GPS+PAIS reaches MSE 0.17 / PSNR 19.67, generalizes to a PCA split, and transfers zero-shot to canonical patches. For inverse design, surrogate-filtered diffusion beats nearest-neighbor retrieval by 32% relative MSE.

We develop a high-order discontinuous Galerkin formulation of the general synthetic iterative scheme (GSIS) for steady rarefied gas mixture flows. The resulting GSIS-DG discretizes the mesoscopic kinetic equations for monatomic gas mixtures and the macroscopic synthetic equations with the same polynomial degree and solves them alternately. The kinetic solution supplies nonequilibrium corrections to the stress and heat flux, while the synthetic equations accelerate the convergence toward the steady state. Asymptotic analysis shows that GSIS-DG recovers the continuum limit without requiring the spatial mesh to resolve the molecular mean free path. Numerical results over a wide range of Knudsen numbers demonstrate high-order spatial accuracy and rapid steady-state convergence, with more than an order-of-magnitude reduction in computational cost relative to conventional kinetic iteration in the near-continuum regime. Comparisons with second-order finite-volume GSIS further demonstrate that GSIS-DG achieves comparable or better accuracy on coarser physical meshes with fewer total spatial degrees of freedom.

The quasi-static Biot system, which governs coupled fluid-solid interactions in poroelastic media, poses significant computational challenges due to its strong coupling and multiscale nature. To address these, we propose a hybrid fixed-stress transferable neural network (HFS-TransNet) method. In HFS-TransNet, a data-driven TransNet module first approximates observed data on an initialization domain to supply a high-quality starting point for the subsequent physics-informed stage, which then drives fixed-stress splitting iterations via TransNet and admits an error bound. After each iteration, a greedy update strategy on a validation domain prevents model degradation and a relative tolerance criterion governs convergence termination. HFS-TransNet thereby inherits the robustness of the fixed-stress splitting scheme, the flexibility of data-driven modeling, and the transferability of TransNet, effectively overcoming the strong coupling and locking instability inherent in the Biot system. Ablation studies and comparisons with FS-FEM and FS-PINN confirm HFS-TransNet's superior performance in capturing multiscale coupled physics across varying physical parameters and boundary conditions. By bridging classical decoupled iterative schemes with hybrid scientific machine learning, HFS-TransNet offers a novel perspective for complex poroelastic simulations, as demonstrated by its successful application to brain edema simulations.

Random layer rotations are ubiquitous in layered matter, from turbostratic films to rotationally disordered crystals, and strongly suppress transport across the layers. Generated by a symmetry operation, this disorder is absent on the rotation axis, so the thickness laws of conduction are set by how fast backscattering vanishes there. We show that a time-reversal selection rule decides this: each twist harmonic of the interlayer bond is either a frame rotation, whose backscattering cancels, or a coupling change, which scatters. A zero-set theorem turns the rule into universal thickness laws for electrons and phonons, fixed by band-edge symmetry; random twist increments rescale the backscattering but keep its order. Where the axis is unprotected, band nodes provide a second route: a transparent energy with heavy-tailed disorder and an $N^{-3}$ law. A first-principles forward-channel model of black phosphorus shows both routes; its random-twist films act as a symmetry filter that, relative to aligned stacks, retains a hundred times more of the electron than of the hole conductance at 64 layers. The symmetry of band edges and phonon branches thus decides what crosses a disordered stack, making stacking disorder a design element.

Many physical inverse problems are mediated by expensive stochastic simulators for which response gradients, adjoint sensitivities, or a differentiable simulator interface are unavailable. We introduce Multiple Target-based Confident Acquisition (MUTACO), an uncertainty-aware sequential-design method for response matching that requires only noisy forward evaluations and learns the multicomponent response together with its predictive uncertainty. We develop and evaluate MUTACO for a disordered network of stochastic phase oscillators. The inverse task is to infer statistical properties of the local potential and interactions from macroscopic rotation and synchronization curves under multiple driving conditions. Rather than requiring unique recovery of these statistical properties, MUTACO searches for parameter configurations whose predicted rotation and synchronization responses are compatible with the target response while accounting for predictive uncertainty. This response-centered formulation is appropriate when experimentally accessible observables characterize ensemble statistics rather than a particular microscopic realization. Under strictly limited simulation budgets, MUTACO achieves the lowest held-out response error among the tested adaptive-search, space-filling, and simulation-based inference methods, while also yielding lower parameter-recovery error than the compared methods. These results demonstrate that response-targeted sequential design is a simulator-efficient approach to inverse modeling from finite noisy forward evaluations and suggest broader applicability to stochastic physical systems with correlated multicomponent responses and weakly constrained parameter directions.

This work studies the Riemann $\zeta$ numerically with emphasis on its physical manifestations. Three areas are examined: (i) the spectral statistics of the non-trivial zeros, which we compare with the Gaussian Unitary Ensemble predictions, obtaining $\chi^2/\text{dof} = 1.2$; (ii) the role of $\zeta(\frac{3}{2})$ in determining the critical temperature for Bose-Einstein condensation, where we find $T_c = 0.13$ K for an ideal gas; and (iii) the application of $\zeta$-function regularisation to the Casimir effect, yielding the standard Casimir energy density $-\frac{\pi^2 \hbar c}{720 a^3}$, which for $a=1\,\mathrm{nm}$ gives $\sim -4.33\times10^{-4}\,\mathrm{J\,m^{-2}}$. The numerical results are consistent with the Montgomery-Odlyzko conjecture and with spectral approaches motivated by the Hilbert-Pólya conjecture, within the statistical limitations of the analysis.

Differentiable programming connects scientific computation with gradient-based inference, learning and design. Extending these capabilities across a heterogeneous software ecosystem requires specialized effort to implement derivatives, integrate interfaces and evaluate quality. AI coding agents can accelerate this transformation, but translating their capabilities into useful scientific software requires identifying research needs and evaluating how well implementations meet them. We present an environment for agent-driven evolution of differentiable scientific software that connects demand identification, development and quality evaluation. A unified differentiation interface exposes reusable derivative rules alongside existing numerical routines, allowing research tasks to share these capabilities. Research requirements guide development, with implementations assessed through independent derivative checks, workflow tests and performance evaluation. Validated software, research programs and tests become shared resources for subsequent studies. We construct and validate automatic differentiation extensions across 20 packages spanning physical, chemical and biological modeling, with research workflows demonstrating reuse across tasks. Benchmarks demonstrate computational savings over finite differences in gradient evaluation and complete parameter estimation. Research-driven revisions make previously unsupported workflows differentiable, correct derivatives of scientific observables and eliminate redundant computation. Quantum-control and thermal-design studies revise objectives in response to physical evaluation, improving designs while reusing existing derivatives. This work provides a practical approach to expanding differentiable programming across established scientific software and organizing AI agents around the recursive improvement of a shared computational ecosystem.

Recent advances in generative world models have increased interest in digital models that reproduce both the appearance of real objects and their response to physical interaction. Three-dimensional reconstruction techniques, including 3D Gaussian Splatting, capture detailed surface geometry and appearance from images and videos. However, extending these representations beyond plausible animation to mechanically interpretable models for constitutive behavior, boundary conditions, and inverse parameter identification remains less explored. In this work, a differentiable Lagrangian-coupled 3DGS-smoothed particle hydrodynamics (SPH) model is proposed for forward simulation and inverse analysis of deformable solids. The observed object is first reconstructed from multi-view calibrated visual dataset as a 3DGS rendering model. An envelope-based procedure then generates an independent SPH support for the solid-mechanics model, avoiding the direct use of rendering primitives as mechanical particles. A reference-configuration Lagrangian transfer maps SPH deformation to Gaussian positions and covariances, thereby coupling the physical model and the image observation model while preserving a differentiable computational path. The SPH formulation supports linear elastic, hyperelastic, and Kelvin–Voigt viscoelastic responses, together with fixed, free, and Robin-type boundary conditions. Numerical studies validate the SPH response against finite-element results, assess accuracy and efficiency against a conventional model using Gaussian centers as surface SPH particles, and demonstrate forward simulations on beam, bridge, and liver-shaped examples. Inverse analyses further estimate constitutive and boundary parameters from rendered deformation observations, including noisy cases, demonstrating the feasibility of the proposed model for mechanics-based parameter identification from image data.

Additive friction stir deposition (AFSD) involves coupled thermal and material-flow fields governed by frictional heating, plastic deformation, and tool-imposed boundary conditions. High-fidelity finite-volume methods (FVMs) can resolve these fields but are computationally expensive, while constant-property approximations can distort the predicted thermo-mechanical response. This work develops a steady-state multi-task coupled physics-informed neural network (MCoPINN) to predict three-dimensional temperature and material-flow fields while reconstructing temperature-dependent thermal conductivity, density, and specific heat from sparse property measurements. A theoretical analysis decomposes prediction error into property reconstruction and neural field-solver contributions and characterizes the discrepancy associated with constant-property models. A controlled one-dimensional nonlinear-conduction study evaluates property reconstruction under sparse measurements. The framework is then evaluated for AFSD against a temperature-dependent FVM benchmark and experimental thermocouple measurements. MCoPINN reproduces the reference thermal and material-flow fields and reduces average temperature root-mean-square error from 50.13 K for the constant-property CoPINN to 30.28 K across four traverse speeds. MCoPINN requires approximately 8.5 hours of training per condition, compared with 52 hours for the FVM benchmark. These results demonstrate computationally efficient, physics-coupled prediction with temperature-dependent material properties.

Extreme values of a physical system are rare by definition, yet they can govern some of its most consequential and anomalous behavior. Their sparsity makes them particularly costly to identify in large data sets. Quantum computation offers a potential way to reduce this cost. The challenge is that quantum amplitudes cannot simply be read, copied, compared, or marked using conventional search oracles. Here we introduce an algorithm for searching amplitude-encoded quantum signals that exploits their underlying structure. Through a nonlinear amplitude transformation, the algorithm identifies and certifies a global extremum while exponentially reducing the effective search space for structured signals. We establish a polylogarithmic query complexity in the data size $N$, together with global completeness, efficient classical verification, and a measurable criterion for quantifying exploitable structure. We demonstrate the framework using computational turbulence data. Applied to line cuts of velocity gradients from a $1024^3$ simulation containing more than one billion grid points, the algorithm consistently isolates the extreme tail and reduces the median search space to $O(\log N)$. The clustered structure characteristic of turbulence further accelerates the search. These results establish a direct connection between physical structure and quantum advantage in extreme-value search. For accessibility, the main text emphasizes the central ideas and results, while the theoretical derivations are provided in the Appendices.

Amorphous materials are statistical ensembles rather than definitive structures, and conventional density-functional (DFT) and machine-learned-potential simulations sample only a small part of that ensemble. We present an $SE(3)$-equivariant denoising-diffusion model that learns the configurational distribution of amorphous oxides, so the model itself is the structure database. The learning is data efficient. A model trained on $1{,}781$ DFT configurations suffices to reproduce partial radial distribution functions, coordination statistics and bond-angle distributions, and to generate models of over $3\times10^{5}$ atoms at a cost comparable to that of the cheapest classical pair potentials. The trained model can propose amorphous atomic structures for first-principles relaxation to explore the configuration space. For example, it locates an amorphous Zr-Ta-O structure $36$ meV/atom below the previously known minimum. Generation can also extend beyond trained conditions to non-stoichiometric compositions, other mass densities, interfaces, and doping. First-principles verification confirms that generation can be steered to a requested energy, and shows that the denoising training loss does not rank generative quality, because the two measure different things.