Papers

Modeling electrochemical interfaces under operational non-equilibrium conditions is vital for energy technologies but remains bottlenecked by the expensive cost of ab initio methods. Current machine learning potentials, largely designed for closed systems under homogeneous electric fields, are limited in open quantum transport applications. To overcome this, we present an E(3)-equivariant graph neural network that embeds voltage bias for open-system simulations. Our approach decouples the system energy and forces into zero-bias and bias-dependent contributions, assigning distinct vector encodings to electrode and scattering-region atoms to capture non-equilibrium conditions. Trained on limited discrete bias data, the model achieves high predictive accuracy and robust extrapolation transferability. When applied to a lithium/water interface, our model successfully captures the field-induced dynamic reorientation of water molecules and reproduces asymmetric electrochemical behavior at different electrodes.

We propose a novel framework for deriving semi-discrete discontinuous-Galerkin (DG) methods using operator semigroups for scalar conservation laws, then apply it to construct a class of high-order OFDG-type schemes [13] satisfying infinitely many local entropy inequalities with general E-fluxes on non-uniform meshes. Such schemes are further generalized to systems of conservation laws in any number of space dimensions by using entropy stable numerical fluxes in the sense of [1]. Finally, we prove optimal error estimates for smooth solutions to nonlinear scalar conservation laws, and prove strong convergence for discontinuous solutions to strictly convex conservation laws via compensated compactness.

We develop an energy-based reduced-order model for micromagnetic magnetization dynamics that couples a convolutional autoencoder to a structured latent neural ordinary differential equation. Motivated by the precessional-dissipative structure of the Landau-Lifshitz-Gilbert equation, the latent vector field is generated from the gradient of a learned scalar potential through an antisymmetric operator and a symmetric positive-semidefinite dissipative operator. This potential is learned in nonunique latent coordinates and is not identified with the Gibbs free energy, but decreases monotonically along autonomous continuous-time solutions, while the antisymmetric component permits motion along its level sets. The encoder, decoder, latent energy, and operators are trained jointly on short trajectory windows using latent and decoded-rollout losses alone, without time-derivative supervision, physical-energy labels, or dissipation penalties. At inference, an initial state is encoded once, evolved in latent space, and decoded only at the requested output times, enabling substantially cheaper trajectory prediction than the micromagnetic solver used to generate the training data. We compare quadratic, deep, and additive deep-quadratic latent energies on two datasets parameterized by field amplitude and generated for the two applied-field directions of the NIST $\mu$MAG Standard Problem 4. Dissipative-only and antisymmetric-dissipative models achieve comparable accuracy on short training-style windows but differ substantially on uninterrupted rollouts, for which the antisymmetric-dissipative models provide markedly more accurate trajectory predictions. The deep-quadratic energy gives the best overall accuracy for both field directions and exhibits slower error growth when rollouts are extended to twice the training horizon.

Time-dependent density functional theory, though exact in theory, is in practice applied in an adiabatic approximation using exchange-correlation functionals with only local temporal dependence. Simultaneously, the exact correlation potential formally depends on, among other quantities, the time-history of electron densities. Here we develop a framework to learn neural network models of correlation functionals that feature explicit memory-dependence. Our framework includes two different approaches, both linked through their use of adjoint-based optimization. One approach decouples the learning of the functional from inversion to find ground truth values of the correlation potential. The other approach learns the functional directly without requiring inversion. We apply these methods to modeling the electron dynamics of two-electron systems in two spatial dimensions. In both cases, our methods yield correlation functionals with low test set propagation error, outperforming standard local density and generalized gradient approximation functionals by one to two orders of magnitude. Overall, our framework points at one strategy to move beyond the adiabatic approximation and develop memory-dependent correlation functionals that yield accurate propagation for excited state and/or non-equilibrium dynamics.

Fast solution times in production discrete ordinates transport codes often require the use of diffusion synthetic acceleration (DSA). A good implementation of DSA will substantially reduce the number of iterations to converge the transport solution at the cost of solving a diffusion-like linear system at each iteration. Often fewer transport iterations will lead to smaller times to solution. Recent work has shown the promise of reduced precision preconditioning. Time and memory cost can be decreased as long as the reduced precision does not substantially degrade the convergence behavior of the higher precision linear system being solved. In this paper, we discuss the algorithmic implications of accelerating transport iterations in double precision (64 bit) while using a reduced precision (32 bit) DSA solve. We initially implement a stand alone code to investigate any theoretical limitations of reduced precision DSA in slabs. Then we implement reduced precision DSA in ARDRA, Lawrence Livermore National Laboratory's (LLNL) discrete ordinance neutral particle transport code, coupled with hypre, LLNL's scalable linear solver and multigrid methods library capable of mixed precision linear solves Then we solve various neutron transport problems of interest. We find that in most circumstances, DSA acceleration in reduced precision has little to no impact on the acceleration properties of DSA when used with source iteration in most circumstances. However, as tighter tolerances are required, reduced precision DSA may fail to successfully accelerate the transport solve and increase time to solution.

The long-time dynamics of complex molecular systems often involves rare transitions across networks of metastable states. Building on transition-path theory, which provides a rigorous framework for describing rare transitions between two metastable states, we introduce the variational multistate committor network (VMCN), a neural framework that learns the probabilities of reaching each metastable state directly from molecular simulation data. From this representation, VMCN identifies state-specific commitment, candidate transition regions and committor-consistent pathways between state pairs, and an effective kinetic network characterized by transition rates. The model is trained using finite time-lag trajectory data together with boundary conditions defined on conservative state cores. Applications to a triple-well potential, trialanine isomerization, and the $c$–ring rotation in the V$_{\rm o}$ domain of a vacuolar ATPase show that VMCN recovers metastable organization, provides committor-consistent descriptions of transition mechanisms, and estimates state-to-state kinetics. VMCN further provides diagnostics for incomplete state decompositions and enables adaptive exploration of candidate metastable states and their connecting regions. By integrating VMCN with generative committor-guided path sampling (Gen-COMPAS) for chignolin, we start from two end point structures, identify a misfolded state and a candidate folding intermediate, and we direct subsequent sampling toward the resulting multistate transition network.

We study the spectral and eigenvector properties of random mixed graphs, combining undirected and directed interactions, using random matrix theory (RMT). The network is represented by a Hermitian adjacency matrix, with undirected links as real entries and directed links as purely imaginary conjugate pairs, ensuring a real spectrum. Network density is controlled by the connection probability, while directionality sets the fraction of directed edges. We focus on the GOE-to-GUE crossover: at fixed connectivity, increasing directionality breaks time-reversal symmetry and drives spectral statistics from GOE to GUE. We show that this transition requires sufficient connectivity. In sparse networks, weak level repulsion produces Poisson statistics regardless of directionality. At fixed directionality, increasing connectivity drives a Poisson-to-GUE crossover; only above a sparsity threshold does the directionality-induced GOE-to-GUE transition emerge. In the dense regime, where the spectral density follows the Wigner semicircle law, the crossover is characterized using spacing distributions, spacing ratios, and spectral rigidity. In sparse networks, where unfolding is unreliable, spacing-ratio statistics provide an unfolding-free characterization. Eigenvector structure is examined through multifractal dimensions and component distributions, while Kullback–Leibler divergence confirms the robustness of the transitions. Applied to S&P 500 mixed graphs, the framework reveals a GOE-to-GUE crossover across four major market crashes. Denser crisis periods show sharper crossovers than sparser recovery periods. The results provide a unified picture of how connectivity and symmetry breaking govern spectral and eigenvector universality, while providing a transparent probe of changing financial-market organization.

A discrete time crystal is an out-of-equilibrium phase of matter characterized by the spontaneous breaking of discrete time-translation symmetry. Using extensive numerical simulations based on matrix-product-state methods, we provide evidence for discrete time-crystalline behavior in strongly disordered spin chains with Heisenberg interactions, including the isotropic point, subject to periodic driving. Starting from a many-body localized regime, we observe that rotations induced by delta kicks produce a pronounced subharmonic response at half the drive frequency in spin observables. We investigate the stability of this response against rotation-angle errors through entanglement entropy, quantum Fisher information, short-range spin correlations, and restricted-control ergotropy. Increasing the rotation error reveals an intermediate dynamical regime separating the time-crystalline and Floquet-localized responses. In this regime, most observables exhibit signatures of weakly correlated dynamics reminiscent of Anderson localization.

Modeling complex physical phenomena directly from experimental data poses fundamental challenges: measurement devices introduce noise and biases into the data, the governing equations are often unknown or intractable, and the dynamics observed experimentally may exhibit stochastic behavior. In this paper, we consider capillary wave turbulence—an example of nonlinear wave interactions at a microfluidic interface—measured by ultra-high-speed digital holographic microscopy. With the goal to learn an efficient model directly from these data, we adapt a stochastic extension of Operator Inference to learn low-dimensional stochastic differential equation representations of the microscale wave dynamics from experimental measurements. Each experiment is repeated 16 times, and 10 different conditions are created by changing the nondimensional acoustic capillary number through an excitation device. In addition, we propose a new strategy to select the reduced-order model dimension, based on both mean and covariance errors. We further add Tikhonov regularization to the stochastic Operator Inference framework and show that, beyond its conventional role as a numerical stabilization technique in deterministic settings, it has a physically meaningful interpretation as controlling the spectral content of the learned stochastic dynamics. We demonstrate that the resulting stochastic reduced-order models faithfully capture salient physical features of capillary wave turbulence across a range of experimental conditions.

Metallic nanoring networks can serve as promising flexible transparent electrodes. These materials are crucial components in a wide range of applications, including solar cells, touchscreens and displays. In this work, a computational investigation considers in detail (i) the electrical conductance and optical performance of nanoring networks and (ii) the breakdown of these networks due to electrical damage. The electrical resistance of both the nanorings and the contacts between the rings (junctions) is taken into account. In part (i), the effects of 5 parameters on the electrical sheet resistance and optical transparency are presented. It is shown that several parameter combinations achieve better performance in comparison to indium tin oxide, currently the most widely used transparent electrode. In part (ii), due to electrical damage, the nanoring systems display the formation of a crack, running parallel to the vertical terminals, where a voltage difference is applied. The network degradation is measured by its sheet resistance, and a universal effect is observed: networks with varying filling factors exhibit the same degradation profile.

Rare-event search experiments demand ever-lower backgrounds, and the resulting radio-pure materials and suppressive shielding make related background simulations computationally expensive without event biasing. We present a method for optimising the widely used importance splitting and Russian roulette technique for rare-event searches, in which a whole number of equal-width importance layers fill the shielding geometry. Balancing relative uncertainty against execution time, we optimise the layer thickness for both $\gamma$-rays and neutrons, and across different shielding materials and thicknesses. Expressed as a multiple of the primary particle's mean free path, the optimal thickness generalises across energies for a given particle type and yields a physics-based prediction applicable to any shielding design. The same trend reveals that over-biasing is possible, with relative uncertainty worsening at high layer counts for fixed execution time. The optimal configuration gives an $\mathcal{O}$(20) gain in computational efficiency over the unbiased case.

Physics-informed neural networks for high-order partial differential equations require mixed input derivatives and their gradients with respect to the network parameters. Standard implementations obtain an order-$K$ derivative by repeated automatic differentiation. We instead organize the forward recursion of the multivariate Faà di Bruno formula and its explicit backpropagation over a prescribed downward-closed set of multi-indices, with the Bell-polynomial convolutions tabulated once. The forward pass carries only the derivatives the differential operator requires. The backward pass propagates gradients from losses formed from any subset of them, including nonlinear products and coupled fields. Both recursions are exact up to roundoff and avoid nested computational graphs. An independent Taylor-jet implementation, symbolic checks of the test problems, and finite differences verify derivatives and loss gradients through order seven. On one CPU core, the method evaluates 330 mixed derivatives with respect to four inputs through order seven and the corresponding loss gradient without the memory failures observed for several nested implementations. Numerical tests include third-, fifth-, and seventh-order dispersive equations, incompressible flow, and a manufactured five-field electrohydrodynamic system. The seventh-order Zakharov-Kuznetsov test in $3+1$ dimensions has a relative solution error of $6\times10^{-4}$.

Computer-aided engineering (CAE) simulation is among the largest and most demanding areas of engineering, where setting up a solver such as OpenFOAM, FEniCS, or COMSOL takes real expertise. Large language model (LLM) agents promise to turn a natural-language request into a working simulation, and recent CAE agents add simulation-specific machinery: multi-agent decomposition, domain retrieval, and scripted reflection. That machinery suited weak base models; modern harnesses already supply multi-turn reasoning, tool use, and execution feedback. We ask what a CAE simulation agent still needs beyond a generic harness. With information access and repair budget held fixed, a single-agent harness matches or beats multi-agent specialized systems (FoamBench 96.4% vs.\ 88.2%). Ablations trace this to capabilities the harness already provides: execution-feedback repair lifts FoamBench from 71.8% with no repair round to 96.4%, while scripted reflection adds nothing. The one input that still helps is domain knowledge supplied as solver tutorials, our largest measured gain (80.9% to 96.4%).

Accurate numerical models of sound propagation through biological media are an important tool for many applications, from medical physics to studying the auditory system of humans or other animals. We model high-frequency elastic and acoustic wave propagation through the head anatomy of a common bottlenose dolphin (Tursiops truncatus), by means of the open-source software packages specfem3d, based on the spectral-element method, and \textsc{k-wave}, based on the pseudospectral method. To achieve sufficiently high performance, we ported the latter solver to C++, for Multi-GPU CUDA support via the slab-decomposition of three-dimensional Fast Fourier Transform approach. Because the two schemes differ fundamentally in how the propagation medium is discretized and internal (in particular fluid-solid) interfaces are treated, similarity between modeled signals across methods is a legitimate measure of model accuracy. Plane waves, depending on time like four-cycle sinusoidal bursts of varying central frequency (20–100 kHz), are numerically propagated through a computed-tomography-based anatomy model using both solvers. The sound is “recorded” in front of the rostrum and at the right inner-ear locations for comparison. We successfully cross-validate both solvers on high-fidelity High-Performance Computing (HPC) clusters. We find that the stability of results from both solvers grows as the corresponding spatial resolution is refined. At their highest resolutions, the two methods show excellent agreement, with normalized correlation exceeding 0.99 across the entire 20–100 kHz frequency range. Together, our results provide a validated HPC-simulation framework for wave propagation in biological media, with broader implications, e.g., for biosonar research, auditory biomechanics, and medical ultrasound.

Numerical integration with Monte Carlo methods is a central computational task in many scientific and industrial applications, including financial derivative pricing and risk management. Classical Monte Carlo algorithms are computationally demanding: achieving an accuracy $\epsilon$ typically requires a number of function evaluations scaling as $O(1/\epsilon^2)$. Quantum-accelerated Monte Carlo methods based on quantum amplitude estimation can in principle quadratically improve this dependence. However, quasi-Monte Carlo methods have not been explored in the quantum context. In this work, we introduce a quantum quasi-Monte Carlo algorithm that combines low-discrepancy nets with quantum amplitude estimation. The proposed method prepares the quasi-random point set coherently in superposition. The method does not yield an asymptotic improvement over classical quasi-Monte Carlo, since the total error separates into a discretization error, determined by the finite net, and a quantum estimation error. Instead, we explore a pre-asymptotic advantage window: for a target accuracy that would classically require $2^q$ low discrepancy points, one can prepare a higher-resolution net of size $2^Q$, with $Q>q$, in superposition and reach the same accuracy using significantly fewer function queries. This window can be controlled by tuning the circuit resolution and amplitude-estimation parameters, making the approach relevant for practical regimes where the number of queries is finite rather than asymptotically large.

For a simple model fluid, the Yukawa fluid, the condition for dynamic crossover, known as the Frenkel line, is defined. The condition is related to the fact that the roton minimum in the dispersion relation of longitudinal acoustic-like excitations exists only when the collective vibrational dynamics of particles dominates in the liquid. Based on the self-consistent relaxation theory for the Yukawa fluid, thermodynamic states are determined in which the roton minimum disappears. The obtained values of the state parameters for the Frenkel line are consistent with the results of studies in which the position of this line on the phase diagram of the Yukawa fluid was determined using molecular dynamics simulations. It is shown that the Frenkel line in this system can be determined directly from the structural characteristic – the static structure factor. A physical interpretation of the roton minimum frequency for the simple liquids near the Frenkel line is proposed.

The multi-state Bennett acceptance ratio (MBAR) equations combine the data collected under different thermodynamic conditions in a statistically optimal way. Due to their practical importance, several solution strategies have been devised to optimize the convergence of the resulting set of coupled equations. However, even with graphics processing unit (GPU) acceleration, the convergence of these methods can still be either unstable or slow. We propose a new approach where the equations are interpreted as the limit of infinitesimal bin width of the respective weighted histogram analysis method (WHAM). In the proposed binned-to-unbinned MBAR (BU-MBAR) method, the bin width is adapted dynamically to ensure a stable and efficient convergence to the asymptotic solution.

In this paper, a conservative sharp-interface and diffuse-interface coupling method is developed for compressible two-phase multi-species flows with phase change and chemical reactions. The liquid–gas interface is represented by a sharp-interface model, whereas a diffuse-interface model treats the transport and chemical reactions of gas-phase species. Conservation is enforced by coupling the two phases through interfacial fluxes obtained from a multi-species phase-change Riemann problem. The original single-species four-wave Riemann solver is extended to multi-species gas mixtures by modifying the interfacial energy jump condition. Interfacial mass transfer is restricted to the condensable vapor species. Accordingly, both the interfacial energy jump condition and the gas-mixture energy-exchange flux are constructed using the internal energy of the phase-changing vapor species rather than the mixture internal energy. With this species-selective energy coupling, an approximate multi-species Riemann solver is constructed that retains the four-wave structure while avoiding the multidimensional nonlinear root-finding required by the exact solution. A series of numerical tests, including impulsive evaporation and condensation, reacting aluminum vaporization, shock-droplet interaction, and detonation-droplet interaction, are performed to assess the accuracy and robustness of the method. The numerical results agree well with reference solutions and benchmark data, demonstrating that the present method resolves the effects of phase change and chemical reactions in compressible multi-species multiphase flows while preserving conservative interfacial coupling.

Boiling heat transfer underpins many applications where large heat fluxes must be dissipated. Boiling is characterized by a wide range of coupled multiscale transport phenomena, making its accurate numerical prediction a long-standing challenge. In this context, interface-resolved simulation approaches - where the liquid-vapor interface is either explicitly or implicitly described - have undergone significant advancements, driven by improved numerical formulations, more complete thermodynamic and compressibility modeling, and the growing availability of computational resources. Here, we provide a comprehensive overview of the state of the art in interface-resolved simulations of boiling flows. We examine the different formulations governing the flow and temperature field, strategies for coupling heat and mass transfer at the interface, and current modeling approaches for small-scale physics such as nucleation, microlayer evaporation, and contact-line dynamics. By analyzing insights from recent high-fidelity simulations, a central observation is that interface-resolved simulations of boiling are hydrodynamically resolved but microscopically modeled: their predictive accuracy depends on the sub-grid closures for nucleation, microlayer, and contact-line physics no less than on the fidelity of the hydrodynamic solver. We discuss the strengths and limitations of available methods on this basis, together with the open challenges in the accurate description of boiling heat transfer.

Long-duration gravitational-wave modelling must resolve fast orbital motion together with slow dissipative evolution while preventing small numerical errors from accumulating into secular phase drift. Here we ask whether the finite-time evolution map itself can be learned as an explicit, differentiable, structure-preserving object and then repeatedly composed through a complete inspiral. We construct three neural-flow architectures: a symplectic and slimplectic flow on Galley's doubled phase space, [SINFONIA-J0]; a Taylor-anchored flow, [SINFONIA-J1]; and a Magnusian flow that learns the finite-time dissipative correction in the interaction picture, [SINFONIA-J2]. Applied to a 2.5PN neutron-star inspiral, all three expose the same controlling mechanism: long-time accuracy is governed not by pointwise map error alone, but by its signed projection onto a single secular channel fixed by energy–angular-momentum balance. Encoding this structure allows the learned maps to remain accurate through $10^{2}$–$10^{5}$ window compositions to coalescence at timesteps of a full orbital period and beyond, reaching chained phase errors orders of magnitude below a benchmark slimplectic integrator at lower cost. The same secular structure can also be exploited for physics inference: when the channel is left unconstrained, the accumulated phase retains enough information to recover an un-modelled dynamical-friction-like force, both parametrically and as a learned function of separation. Network-off controls isolate the contribution of learning from the analytic structure already built into each map. These results establish a proof of concept for structure-preserving learned evolution maps as tools for fast long-duration integration and physics inference in gravitational-wave source modelling.

Super-resolution machine learning methods hold promise for addressing the high computational costs associated with high-dimensional features in traditional transport simulations. This paper proposes a physics-enhanced neural network coupling algorithm for discrete ordinates (SN) transport calculations. Based on high- and low-accuracy data, we develop a predictor-corrector neural network (pcNN) to predict correction factors for coarse-grid solutions. Based on transport equations, local physical features containing subgrid-scale information are selected as network inputs. Dimensionless transformation of physical quantities reduces the input space dimensionality and narrows parameter distributions, facilitating network training. Physical constraints are incorporated into the network model, and the corrected solution retains its original conservation properties. pcNN and SN transport sweeps are internally coupled, and numerical solutions are corrected online. Numerical results demonstrate that this algorithm can effectively improve coarse-grid solutions to achieve a level of accuracy comparable to that of fine-grid results. The physics-based network design enables the model to demonstrate a certain degree of reusability under different computational conditions. Compared to mesh refinement, the pcNN-SN algorithm reduces the computation time for the three-dimensional test problem by more than 60%.

Nested sampling (NS) resolves the thermodynamics of an atomistic system from a single simulation, but its practical reach is limited by the Markov-chain updates needed to decorrelate walkers within each likelihood-constrained ensemble. Flow-based NS has reduced this bottleneck for gravitational-wave (GW) inference, yet its transfer to atomistic systems is not merely a change of application. Comparing a GW150914-like binary-black-hole likelihood with an eight-particle two-dimensional Lennard-Jones (LJ) system of comparable dimensionality, we show that the two landscapes differ fundamentally: atomistic multimodality is discrete and combinatorial, generated by particle permutations separated by hard collision walls, and its coordinate coupling is dense and collective, whereas the GW posterior exhibits smooth degeneracies and localized parameter coupling. Guided by this diagnosis, we introduce NS-Flows: a single conditional normalizing flow, conditioned on the NS energy bound and trained on a sliding window of recent live sets, that replaces MCMC by direct parallel draws corrected by importance-weighted rejection resampling. Live sets supply the data self-consistently, allowing flow training without structured priors or a pre-existing dataset. For LJ disks under periodic boundary conditions, the algorithm can reduce energy evaluations by two orders of magnitude and wall-clock time by about 30%, an advantage that becomes more favorable as the cost of the potential grows. The flow's generative efficiency further acts as a physical diagnostic: it varies non-monotonically along the annealing trajectory, is lowest in the dense disordered regime, and is quantitatively captured by the constrained ensemble's internal mode complexity together with target drift across the training window, identifying liquid-like ensembles, not prior-target separation, as the hard case for current flow architectures.

Second-order Moller–Plesset perturbation theory (MP2) is one of the simplest correlated wave-function methods, but its conventional $O(N^5)$ cost limits its application to large systems. Stochastic tensor contraction (STC) has recently appeared as a general technique to evaluate high-order tensor contractions in quantum chemistry. Here, we apply STC to the exchange contribution of Laplace-transformed MP2, which is the source of $O(N^5)$ scaling in the formulation. The resulting STC exchange algorithm has an $O(N^3)$ deterministic setup cost and an $O(N^2)$ stochastic cost at fixed absolute error. The estimator is unbiased and provides a way to specify the target stochastic error by estimating the number of required samples before the full calculation. We implement the algorithm using a hybrid deterministic–stochastic evaluation strategy, with grouped index sampling, to reduce the computational prefactor. Over a range of benchmark molecules containing up to $\sim 7000$ basis functions, the stochastic exchange evaluation takes as little as $1/270$ of the time of a complete DF-MP2 calculation on the same system. Within the Laplace-transformed formulation, the $O(N^4)$ scaling direct contribution is thus the only significant cost. Our results further substantiate the power of STC to serve as a general tensor-contraction engine for quantum chemistry.

We present a high-order multiphysics solver for the simulation of microwave-heated flows. The solver couples a discontinuous Petrov-Galerkin (DPG) finite element method for the time-harmonic Maxwell equations with continuous Galerkin finite element methods for the heat equation and the incompressible Navier-Stokes equations. We validate the electromagnetic solver against multiple benchmark problems: wave propagation in a rectangular waveguide, a cavity problem with a singular solution, and a microwave-heated obstacle problem, comparing our results against numerical and experimental data from the literature. The results confirm the validity of the implementation and demonstrate its ability to perform adaptive mesh refinement using the DPG method's built-in error estimator. The final part of the study showcases the capabilities of the multiphysics framework through simulations of microwave-heated flow around obstacles with singular geometric features. These results highlight the potential of the proposed framework for the simulation and optimization of microwave-assisted chemical processes. Finally, the developed high-order multiphysics solver has a low memory footprint, since the electromagnetic solver relies on a Conjugate Gradient (CG) iterative solver and the fluid solver is implemented in a matrix-free fashion, making the overall approach scalable and well-suited for large-scale parallel simulations.

Learning solution operators across broad parameter ranges can require substantial coverage of both input functions and physical parameters, particularly for purely data-driven parametric models. In addition, the resulting models may fail silently outside the training distribution. We introduce equation recast, which reformulates parametric operator learning as the learning of a single canonical operator. Parameter-induced operator variations are derived analytically from the governing equation and absorbed into effective sources, enabling zero-shot prediction across new parameter regimes. Across multi-parameter, nonlinear, and singular PDE settings, equation recast supports extrapolation, integrates sparse heterogeneous datasets in a shared canonical representation, and uses loss of convergence as an internal warning signal for failure of the recast iteration. In high-fidelity tokamak simulations for nuclear fusion, the framework unifies electron-temperature data across four device geometries through canonical-domain mapping within one jointly trained operator. Equation recast provides a route toward reusable neural PDE solvers combining equation-guided transfer, data efficiency, and monitorable inference.

We formulate a finite-temperature residual test in IDMate that bounds window-resolved electronic errors without a spectral-gap assumption. For a fixed Hamiltonian and exact electron number, strong convexity of the matrix Fermi entropy bounds the density-matrix distance and free-energy error within a selected window. The bound remains finite at spectral crossings and extends to weighted k points with a shared chemical potential. We also derive a distance correction for particle-number mismatch. Across $3{,}586$ stress trials in $70$ seeded perturbation ladders, $1{,}942$ proposals satisfy the screen with no observed violation of the $0.05$ window-distance criterion plus its numerical allowance. This criterion differs from the uncorrected exact-trace bound, which six of ten historical in-loop candidates exceed at the numerical-error scale. An accept-or-recover loop replaces ten reference-map evaluations while meeting terminal comparison criteria in three configurations that include oracle-subspace controls. Additional candidates built only from preceding-iteration orbitals yield two acceptances and one abstention. The silicon candidate has a window distance of $1.891\times10^{-13}$ but a normalized real-space density error of $3.754\%$. Analytic examples separate errors from complement occupations and interblock coupling. Window-level accuracy therefore does not imply full-state accuracy; the screen tests compressed proposal quality, independently of nonlinear SCF convergence or net acceleration.

Physical decoherence can preserve the microscopic strategic neutrality (i.e. zero effective field and equal potential of the two homogeneous strategic orientations) of a quantum game while changing the thermodynamic regime of the corresponding interacting population. We demonstrate this for an Eisert–Wilkens–Lewenstein (EWL) Stag Hunt embedded as independent nearest neighbor encounters on a square lattice. For the restricted strategies $\mathsf{Q}=i\mathbb{Z}$ and $\mathsf{D}=i\mathbb{Y}$, noisy two-player payoff matrices are determined for phase damping, depolarization, and amplitude damping and mapped exactly to channel dependent Ising parameters $\mathfrak{J}(\Gamma,p)$ and $\mathfrak{H}(\Gamma,p)$. Phase damping and depolarization show the clearest contrast: they share the same microscopic neutrality branch $\mathfrak{H}=0$, while only depolarization suppresses the interaction as $(1-p)^2$. At $\beta=1$, this produces an exact depolarization-driven square-lattice critical point at $p_{*}\approx 0.233460\ldots$, whereas phase damping remains in the ordered coexistence regime along the same neutrality branch. Monte Carlo finite size scaling is consistent with two-dimensional Ising criticality and distinguishes field driven coexistence below $p_{*}$ from a smooth crossover above it. Amplitude damping additionally reveals a strong dependence on channel placement: the post-strategy neutrality branch reaches $\Gamma=0$ at $p=1/3$ and then disappears. Resource negativity further shows that microscopic two-qubit entanglement and collective interaction strength are distinct quantities. The resulting extended lattice remains an ordinary classical Ising system.

Numerical methods for partial differential equations (PDEs) discretise differential operators, ideally reproducing the action of the continuous operators across all wavenumbers permitted by a given discretisation. Spectral-type methods approach this ideal, but rely on structured grids or high-order meshes that are hard to generate for complex geometries. In contrast, mesh-free methods are geometrically flexible, yet how faithfully they reproduce the operator across resolved scales is strongly influenced by a heuristically chosen kernel, which selects one of many weight sets satisfying the same consistency conditions without regard to the resulting spectral response. To address this, we introduce Spectrally optimised Neural Discretisations (SpeND), a framework that learns the map from local stencil geometry to discretisation weights on unstructured point clouds. A projection layer constrains every predicted stencil to the affine set defined by the discrete moment conditions, so polynomial consistency, and hence formal order of accuracy, holds exactly. Since consistency is enforced by the architecture, the weights can additionally be optimised for accuracy on a prescribed function space. Herein, we use Fourier modes and target the exact differentiation response over a chosen wavenumber band, so training is unsupervised. The loss function is a design interface: changing how it weights wavenumbers yields operators with distinct accuracy profiles. The trained discrete differential operators are PDE-agnostic and are applied without retraining to the Poisson, Burgers and Navier–Stokes equations, to near-boundary stencils, and across resolutions. At the same order and resolution, SpeND matches or improves on established mesh-free discretisations, and has been shown to reduce the wall-clock time between $3-20\times$ to achieve equivalent error as the baselines.

Polymeric materials are central to modern technologies, with applications ranging from energy to health and transportation. Although AI has made significant advances in materials discovery, the hierarchical structure of polymers across multiple length scales makes them inherently difficult to represent in a unified and physically meaningful way. Here we introduce HiPoly, a polymer-native AI framework that processes complete polymer descriptions through a three-level hierarchical graph architecture built on the G2RINS representation. HiPoly encodes stochastic inter-monomer connectivity, composition, and molecular weight directly within its architecture, using physically motivated design principles that mirror the multi-scale nature of polymeric systems. The framework establishes an end-to-end AI-driven workflow from experimental formulation data to property prediction, generative molecular design, and physics-based validation through molecular simulations, all unified by a single polymer representation. We demonstrate state-of-the-art prediction accuracy for thermophysical properties of multi-component polymer systems, with ablation studies confirming that each hierarchical design choice contributes independently to model performance. As an example, the generative design pathway is applied here to the discovery of sustainable alternatives to persistent fluorinated polymers, where it is possible to identify and independently validate PFAS-free candidates with target surface-energy properties. This work demonstrates how polymer-native AI can accelerate discovery by linking representation, prediction, and design across complex polymer chemistries.

Large-scale molecular dynamics simulations of particle systems on multi-GPU architectures are often constrained by the computational and communication costs of nonbonded force evaluation. We present RBMD 2.0, a major new release of the random batch molecular dynamics package designed for cross-node multi-GPU simulations of large-scale systems. It combines the improved random batch Ewald method with three-dimensional domain decomposition and ghost-particle communication to accelerate multi-GPU nonbonded force evaluation, while the DTK CUDA framework facilitates portability across heterogeneous accelerator architectures. Numerical experiments on multiple benchmark systems demonstrate both the accuracy and efficiency of simulations with RBMD 2.0. For simulations involving up to hundreds of millions of particles across multiple accelerator devices, one achieves speedups ranging from severalfold to approximately two orders of magnitude in nonbonded force evaluation while exhibiting over $97.5\%$ weak-scaling behavior. These results demonstrate the promising nature of RBMD 2.0 as a computational engine for future exascale molecular dynamics simulations.