Papers

We develop a Monte Carlo lattice Boltzmann method to compute statistical solutions to the three-dimensional incompressible Navier–Stokes and Euler equations. Entropic space-time adaptive relaxation of the higher order kinetic moments yields stable numerical solutions with decreasing viscosity. We provide a convergence analysis that is conditional on four explicitly stated assumptions regarding the discrete dynamics. Under diffusive scaling, the laws of the discrete ensemble converge along a subsequence to a limit satisfying the Foias–Temam Liouville formulation of the Navier–Stokes equations. Consequently, provided the structure function scaling holds uniformly, the vanishing viscosity limit of these measures satisfies the multi-point statistical Euler hierarchy of Fjordholm, Mishra, and Weber. The limit measures inherit the known weak-strong uniqueness principle on the interval of existence of a strong Euler solution. Under explicit scaling assumptions, a Kuznetsov-type argument yields a fractional 1-Wasserstein convergence rate. We present three-dimensional computations of time-dependent statistical solutions along the inviscid limit of the incompressible Navier–Stokes equations together with convergence measurements in the Wasserstein metric. Numerical experiments on a randomized Taylor–Green vortex with 24-dimensional initial uncertainty recover Kolmogorov's K41 scaling for energy spectra and structure functions, exhibit the failure of pathwise strong convergence, and yield Wasserstein convergence rates of about $0.5$ at the onset of turbulence. Finally, error measurements with respect to spectral hyperviscosity computations indicate that the computed limit measure is independent of the numerical regularization.

We prove that minimum Riesz $s$-energy subset selection in the Euclidean plane is NP-complete already for the fixed exponent $s=2$. To our knowledge, this is the first Euclidean hardness result for exact Riesz-energy subset selection in which both the ambient dimension and the exponent are fixed. The reduction uses Barahona's planar cubic Ising model with uniform field. A spin is encoded by one diagonal of a four-point square. Axis-aligned selector chains implement ferromagnetic consistency, while a $45^\circ$ terminal geometry yields an antiferromagnetic source interaction. Rational diagonal perturbations realize the magnetic field, and all remaining interactions are dominated by polynomial separation. Because $s=2$ and all coordinates are rational, every constructed energy and the decision threshold are rational exactly.

Ferromagnetic AT6X6 Kagome compounds are a popular class of systems in which quantum magnetism with topological features has been observed. These systems allow easy chemical substitution, creating an opportunity to fine-tune their properties. In this paper, we present electronic-structure and magnetic ground-state studies of several AT6X6 compounds with relatively low magnetic-ground-state stability. We find unusual magnetic orderings, including complex spin-spiral states and the formation of magnetic long-range superstructures. While LiFe6Ga6 and TiMn6Ge6 retain collinear AFM ground states with low-energy FM/AFM layer sequences, competing spin-spiral and long-period antiferromagnetic structures in MgFe6Ga6 and a double-spin-spiral ground state in TiFe6Ga6 were determined. Magnetism in all these systems appears local, with adiabatic energy profiles suggesting non-Heisenberg long-range interactions, including a strong biquadratic term. In TiMn6Ge6, we found the conditions for magnetic tunneling. Our results show that, in addition to traditional magnetic topological features in such FM Kagome systems, near-degenerate magnetic superstructures suitable for spintronic switching applications can form naturally. Overall, these systems represent a potentially rich playground for neutron diffraction and spintronics experimental studies.

In analogy to electron-phonon coupling (EPC), electron-magnon coupling (EMC) is expected to shape electronic structure, transport, and possibly unconventional superconductivity in magnetic materials. However, unlike EPC, which is now routinely treated within first-principles frameworks, a quantitative description of EMC, especially for transport, remains elusive because of the lack of theoretical formalism. Consequently, even for elemental iron, EPC-only calculations miss both the magnitude and the $T^2$ component of resistivity. This discrepancy has long been attributed to EMC, although direct computational evidence has been lacking and the underlying transport mechanism remains unresolved. Here we develop a unified first-principles formalism for EMC in collinear magnetic systems within many-body perturbation theory, complemented by machine-learning spinful Hamiltonians that supply quantities not directly accessible from conventional first-principles methods. Our framework enables ab initio transport calculations including EMC effects for the first time. Applied to ferromagnetic $\alpha$-Fe, our approach yields electron spectral functions consistent with previous studies. More importantly, we recover the full $T^2$ component of resistivity with a coefficient in quantitative agreement with measurement and reveal that the $T^2$ component cannot be attributed solely to EMC, as has long been assumed, but is dominated by the strong EPC-EMC interplay. Extending to antiferromagnetic K-doped $\mathrm{BaMn_2As_2}$, our method captures the ARPES-observed magnon-induced kink and a large EMC strength of $\sim 3$ comparable to experimental measurements, demonstrating the generality of the framework. Our work closes a longstanding gap in the quantitative understanding of transport in magnetic systems and provides a predictive foundation for examining magnon-mediated phenomena.

Precise targeting of pharmaceutical aerosols is critical to the efficacy and safety of inhaled therapies. This study focused on the influences of vortices and turbulent eddies on preferential concentration and deposition of pharmaceutical aerosols within the human respiratory tract. By reconstructing a high-fidelity respiratory tract geometry spanning the nasal cavity down to sequential bronchi from computed tomography (CT) images and assigning physiologically realistic transient breathing profiles, an unsteady Reynolds-averaged Navier-Stokes (URANS) framework using the shear stress transport (SST) k-w turbulence model and a stress-blended eddy simulation (SBES) framework of human respiratory tract were built. Beyond flow field analyses, Vorono diagrams and a set of newly-defined spatial accuracy metrics were adopted to quantitatively characterize particle distributions and localized prediction discrepancies. Spectral analysis revealed that the SBES simulations adequately recovered the prominent Kolmogorov -5/3 inertial scaling law. Such turbulent motion induces pronounced radial turbulent dispersion, forming particle clusters with higher cluster fractal dimensions D> 1.2 on the mid-plane of the laryngopharynx. Spatial accuracy metrics uncovered a critical dual deficiency of the URANS model: globally over-smears near-wall deposition by roughly 20%, simultaneously fails to resolve most high-concentration `hotspots' (the top 5% local extrema). These findings highlighted that the numerical resolution of transient vortices and turbulent eddies constitutes an indispensable prerequisite for accurately predicting of particle transport and deposition in the human respiratory tract.

Non-thermal carrier relaxation is routinely inferred from population dynamics or spectroscopic observables, yet neither class of quantity uniquely identifies the microscopic channels through which energy and coherence are redistributed. We introduce a pathway-resolved quantum-kinetic framework that simultaneously projects ultrafast relaxation onto orbital populations, directional inter-orbital transferes, coherence, spectroscopic visibility, and a hidden-pathway sector of the dynamical transfer network. Application to MXenes exposes strongly non-uniform orbital redistribution together with material-specific hierarchies of microscopic transfer channels. Temperature, excitation amplitude, and dissipative parameters modulate pathway competition and spectral amplitudes while leaving the identity of the dominant channels largely intact. Instantaneous transfer contributions, cumulative directional transfer, coherence, and spectroscopic visibility are shown to follow inequivalent hierarchical orderings. This non-equivalence isolates a set of hidden pathways that remain dynamically consequential despite weak conventional spectroscopic signatures. The resulting time energy coherence representation recasts nonthermal relaxation as a structured dynamical network comprising observable and hidden sectors, thereby providing a general methodology for resolving microscopic orbital transfer pathways in driven quantum materials.

Coherent terahertz (THz) emitters based on low dimensional quantum materials have attracted significant interest for compact broadband photonic technologies. However, theoretical descriptions that consistently connect microscopic quantum dynamics to emitted THz radiation remain limited for MXenes, whose electronic properties are governed by transition metal d orbitals and chemically tunable surface terminations. A multiscale density-matrix formalism for coherent THz generation in metallic MXenes driven by engineered three color femtosecond waveforms is developed. Material-specific electronic structures are described by parameterized multiband tight binding Hamiltonians, while ultrafast carrier dynamics are treated using a non-secular Redfield master equation that explicitly retains interband coherence, carrier populations, electron phonon interactions, impurity scattering, and environment-induced relaxation. The transient photocurrent is explicitly decomposed into population and coherence driven contributions and linked to the emitted THz field through its time derivative, establishing a direct connection between microscopic quantum dynamics and macroscopic radiation. The results show that environmental coupling does not merely attenuate THz emission, but redistributes coherent and population currents and reshapes the emitted waveform in both the time and frequency domains. Systematic investigations of optical waveform parameters, effective electronic structure, and open system relaxation identify physically grounded strategies for enhancing broadband THz generation. The proposed methodology establishes a transferable microscopic design platform for connecting material specific electronic structure, quantum coherence, open system relaxation, nonlinear carrier transport, and coherent THz emission across MXenes and related low dimensional quantum materials.

We present a method to calculate spin-phonon coupling parameters from first-principles perturbation theory by downfolding the electron-phonon coupling (EPC). We exploit the localized nature of magnetic moments and atomic displacements by working in the Wannier representation of the electronic Hamiltonian and the EPC matrix. The spin system is mapped to a classical Heisenberg Hamiltonian, whose parameters are obtained by treating local spin rotations as a perturbation within a Green's-function formalism. The spin and phonon perturbations are connected through the EPC parameters, which enter as lattice-induced perturbations to the tight-binding Hamiltonian. By combining these lattice perturbations with local spin rotations, we obtain real-space derivatives of magnetic exchange parameters without performing displaced magnetic supercell calculations. We illustrate the method on SrMnO$_3$ and show that it can be integrated directly into standard workflows.

The Vlasov–Poisson system provides the fundamental kinetic description of plasma and plays a central role in understanding collective phenomena such as Landau damping and wave–particle interactions. Efficient numerical simulation of these dynamics remains challenging because of the high dimensionality of phase space. In this work, we studied magnetized and non-magnetized plasma using a quantum simulation framework for the linearized Vlasov-Poisson equation by reformulating the discretized system as a Hermitian Hamiltonian suitable for gate-based quantum computation. The time evolution is implemented using first, second and fourth-order Trotter–Suzuki product formulas and the recently proposed Time-Resolved Interaction Framework (THRIFT). The performance of the different simulation methods is systematically evaluated through electric field evolution, state fidelity, convergence behavior, energy conservation, entanglement entropy and quantum resource requirements, including circuit depth and two-qubit gate complexity, for both magnetized and non-magnetized plasma models. To further reduce finite time step errors without increasing circuit depth, Richardson extrapolation is incorporated as a error-mitigation technique. The results provide a comprehensive comparison of Trotter and THRIFT approaches and establish practical guidelines for accurate and resource-efficient quantum simulation of plasma dynamics on gate-based quantum computers.

Bond-based peridynamics provides a non-local framework for modelling fracture without requiring spatial derivatives of the displacement field. However, when spatially varying horizons are used together with non-uniform discretisations, the classical single-horizon bond-based peridynamics formulation leads to asymmetric interactions between material points. These asymmetric interactions violate balance laws and can introduce non-physical artefacts such as ghost forces and spurious wave reflections. In this work, we develop a variational formulation for bond-based peridynamics with spatially varying horizons. Starting from the Lagrange-d'Alembert principle, we derive the governing equations of motion and show that the dual-horizon peridynamics formulation emerges naturally from the variation of the internal energy. Building on this variational structure, we construct asynchronous variational integrators that allow different time step sizes in different regions of the domain. This is particularly useful for dynamic fracture simulations with local refinement, where small time steps are required only near regions of high resolution or expected crack growth. Numerical examples involving wave propagation, a pre-cracked plate under tension, and the Kalthoff-Winkler impact experiment demonstrate that the proposed framework removes spurious reflections caused by non-uniform horizons, preserves physically consistent fracture patterns, and achieves results comparable to uniformly refined simulations. At the same time, the asynchronous variational integrator reduces the number of internal force evaluations compared to the standard velocity-Verlet method. The proposed approach therefore provides a consistent variational foundation and an efficient time-integration strategy for bond-based peridynamic simulations with spatially varying horizons.

Learned surrogates for expensive inner solver blocks are a widely pursued route to faster multiphysics simulation. We report a controlled, end-to-end negative result and identify three structural barriers, none of them a deficiency of the network we trained. The testbed is the implicit Newton solve coupling energy-dependent neutrino radiation to matter in a general-relativistic radiation-hydrodynamics code, its most expensive physics routine per call. First, per-call cost and share of runtime are different quantities, and only the second bounds acceleration. An exclusive self-time profile puts the target block at 16.9% of critical-rank wall clock, capping any surrogate at ~1.2x by Amdahl's law. A surrogate 5.8x cheaper per call merely ties the solver, and the configuration stable enough to run without fallback reaches only parity. Second, offline accuracy cannot rank surrogates for deployment: across fourteen networks the pooled Spearman error-versus-survival correlation (rho = +0.73) is a between-family confound that vanishes under control (rho = -0.04). Third, a correct out-of-distribution gate cannot accelerate a loop that leaves its training distribution. We give the break-even deferral fraction in closed form: because the visited states sit 73x off the data manifold, the gate defers 96.8 to 99.7% of cells, almost invariant to surrogate quality. Including its own cost, the gated loop is a 0.94 to 0.96x slowdown. We further separate stability from fidelity: a never-crashing gated run accumulates a linear -19.9% density bias over 6000 steps. The error is a directed, ballistically accumulating bias, not the variance-driven divergence the autoregressive literature targets.

Training large language models is costly. How low a loss the same compute can ultimately reach depends on how each step's gradient is converted into a weight update; the rule that performs this conversion is the optimizer. From SGD and AdamW to the recent Muon, effective update rules have mostly been shaped by engineering intuition and then selected on benchmarks. Muon semi-orthogonalizes the momentum matrix before applying the update and has kept breaking records on public training benchmarks; yet why the semi-orthogonalized direction works, and over how long a history the momentum should average, are two questions at present answered mainly by experience. Here we treat the weight matrix during training as a responsive medium with memory and build a physical model for it, in which both questions find answers: the semi-orthogonalized direction is the maximally dissipative response under an output-side safety budget, which explains why it works; momentum is the internal stress accumulated by the medium; how long it should average is set by the relaxation of this stress, and a real medium relaxes on more than one timescale, the simplest form being one fast and one slow. On this basis we propose the Bi-Maxwell optimizer. The framework further yields a testable consequence: gradient directions change fast early in training and more slowly later, so the optimal memory length should grow with training stage; step-by-step measurements of a proxy for it by a read-only probe across 8 independent training trajectories are consistent with this consequence. Replacing the memory kernel alone, from a single timescale to two, brings training to the target loss in noticeably fewer steps on a public large-language-model optimizer benchmark.

The collision operator for the Boltzmann equation is a nonlinear nonlocal operator. When lifted in the extended 2-particle space, it is viewed as the projection of a collisional linear operator. In this paper, we propose a particle method that samples the post-collision relative velocity directly from the Green's function of this operator (the transition probability of the generated time-continuous Markov chain). The normalizing flow amortized sampling is then proposed to reduce the sampling complexity. The resulted method takes $O(N)$ each time where $N$ is the particle number, and conserves momentum and energy exactly. This method does not require the boundedness of the kernel and, more importantly, it allows learning the Green's function directly from the scattering data without selecting the kernel in a specified family.

Developing physical neural network (PNN) hardwares is important to next generation artificial intelligence systems. Phononic devices-using heat current to encode and process information-is one of the solutions to neuromorphic computing. In this work, we back map an artificial neural network (ANN) into a PNN simulation model using polymer networked nanoparticles (PNNPs). Our atomistic simulation results demonstrate that the polymer linked nanoparticle networks can potentially realize information processing using heat current. Using high-throughput molecular dynamics (MD) simulations and the trust region Bayesian optimization (TuRBO) methods, we tune the plasticity of polymer linkers and the temperatures of nanoparticles to optimize the performance of the PNNP machines, which is similar to tune the weights and bias in ANNs. After 5 rounds of high-throughput MD simulations, we show that the PNNP machines have improved in performance. We also use a testing data set to verify the heat flow outputs from the top 5 PNNP machines in each round.

A recent experimental study reports the spontaneous formation of a three-dimensional woven ferroelectric domain fabric in bulk KTN:Li during sufficiently slow cooling through the ferroelectric transition. The present work develops a nondimensional phase-field framework to examine a physically plausible route by which such a state can emerge. A large-area two-dimensional model first resolves the cooling-rate-dependent formation of a frustrated crossing precursor by combining first-order ferroelectric thermodynamics, electrostatic and elastic interactions, compositional modulation, and effective charge screening. Slow cooling produces a persistent population of charge-associated crossings, whereas the corresponding fast-cooling pathway does not. A three-dimensional extension then incorporates cubic gradient anisotropy, flexoelectric coupling, and strain-gradient regularization to examine whether the planar precursor can develop a genuine woven topology. Within the explored nondimensional parameter regime, slow cooling produces a directly resolved geometrical separation and exchange of depth ordering between the intersecting wall families, whereas the corresponding fast-cooling pathway does not. This distinction is reproduced across independent realisations and remains robust to timestep refinement and changes in computational domain size. The simulations suggest that slow cooling provides a kinetic window for topological selection and that global charge relaxation can coexist with strong local charge concentration at surviving crossings. The model is not calibrated to material-specific KTN:Li coefficients and does not reproduce the experimentally observed low-temperature disappearance of the woven state.

A companion paper \cite{ItkinDF2026} introduced the Diagonal Frog (DF) positivity-preserving schemes for anisotropic Fokker–Planck equations, advancing each directional substep by a Krylov-computed matrix exponential, which dominates the cost. Replacing that exponential by a rational map $r(\gamma L)$ reduces the substep to a banded solve, but the positivity argument no longer applies. We prove that for eventually exponentially positive generators the entrywise sign of $r(\gamma L)$ at large steps is decided by a single number, the value $r(\infty)$ taken on infinitely stiff modes. Nonnegativity holds above a computable threshold when $0\le r(\infty)<1$, and at most on a bounded interval, empty or vanishingly narrow in all our tests, when $r(\infty)<0$. The criterion rejects the Crank–Nicolson (trapezoidal) method, where $r(\infty)=-1$, and selects the subdiagonal Padé$(0,2)$ method, which is second order, L-stable and provably positive above an explicit threshold. The resulting DF-ADI scheme costs $O(N)$ per step, keeps the implicit factorized mixed derivative unchanged, is second order in space and time, and conserves discrete mass exactly. In the strong cross-diffusion regime, however, the directional factors demand a step larger than the mixed derivative permits, so the composite second-order scheme is only empirically positive there, and the criterion serves to discriminate the well-behaved multiplicative factors from the stabilizing-correction schemes rather than to guarantee positivity. Against the Krylov exponential it runs ten to thirty-two times faster at matched accuracy in our tests with the gain growing with the mesh. We extend the construction to the backward Kolmogorov equation and to jump-diffusion models.

A downward fin thrust near a cohesive seabed lofts sediment. Whether this cloud settles or organizes into a self-sustaining down-slope current determines if a diver loses visibility briefly or catastrophically. We reduce the layer-averaged balances of fluid mass, sediment mass, and momentum to a temporal slab of fixed thickness in the weakly entraining limit. This yields an autonomous planar vector field in dimensionless near-bed speed and suspended load, governed by three dimensionless groups: drag against settling, erosion strength, and near-bed concentration. The field possesses a quiescent equilibrium at the origin and, above a critical bed slope obtained in closed form as the ratio of near-bed concentration times drag-settling number to erosion-strength number, an interior saddle equilibrium. The saddle's stable manifold partitions the state space into basins of decay and unbounded growth, establishing the exact threshold between self-limiting and igniting disturbances. On a flat bed, the origin attracts globally for all admissible erosion laws. For representative silt, the ignition threshold is near a 17-degree bed angle. The closed-form structure is confirmed numerically to machine precision. A closure study demonstrates the critical slope is robust in existence but closure-dependent in value, identifying the linear erosion law as the conservative choice. The model thus isolates bed slope as the controlling parameter for ignition.

The construction of a grid-based potential energy surface (PES) can be prohibitively expensive as the number of grid points grows exponentially with molecular size. Molecular symmetry can reduce this cost by eliminating symmetry-equivalent points. We present an algebraic symmetry-based grid reduction method, ASyBGR, that is capable of handling non-Abelian and higher-order cyclic symmetry groups. Non-coordinate-mixing operations are encoded into a vector space bit-string, where Gaussian elimination and closure can identify all symmetry-valid sign change patterns and the coordinate axes whose grids can be halved about the origin. In the presence of degenerate subspaces, we optimize the coordinate basis to maximize reduction. The method was validated by comparing vibrational configuration interaction (VCI) energies calculated using the full and symmetry-reduced fourth-order HDMR PESs for molecules spanning a broad range of symmetries. The number of grid points required to construct the PES was reduced by as much as 81%, while VCI energies deviated below 1 1/cm for all test cases on average. The relative root-mean-square deviation (RRMSD) between the full and symmetry-reduced potential energy and dipole moment surfaces were at most on the order of 10$^{-3}$ and 10$^{-2}$, respectively.

In EEG source imaging, the precision of the imaging of the brain activity depends on the accuracy of the forward head model which is, in turn, affected by the representation of tissue conductivity, including anisotropic compartments such as the skull and white matter. We introduce an EEG source imaging framework based on a hybrid volume-surface-wire integral formulation, enabling tract-aware modeling of anisotropic white matter contributions without a full volumetric head discretization. The proposed framework is assessed on a realistic MRI-derived head anatomy, showing close agreement with FEM reference solutions while avoiding full-volume meshing and providing a natural representation of white matter fiber tracts. We then integrate this model into a real-time pipeline that couples EEG processing with immersive visualization, enabling synchronized inspection of scalp potentials, cortical sources, and white matter fiber tracts-related quantities. The results support the proposed formulation as a tract-aware alternative to canonical formulations, combining robust localization performance with interactive visualization capabilities.

Deep learning surrogates have become powerful tools for simulating and forecasting complex dynamical systems, yet their utility remains limited by catastrophic error accumulation during long-term autoregressive rollouts. This behavior is partly tied to the nature of the underlying systems: chaotic spatiotemporal systems visit phase space unevenly, with dynamics dominated by recurrent, low-dimensional quiescent states and characterized by rare and dynamically complex regime transitions. Trained under a sample-wise uniform objective, standard neural surrogates allocate their finite capacity to the statistically more numerous low-dimensional quiescent states, systematically under-representing the transient regimes that trigger disproportionate, localized errors. Existing imbalanced-regression methods tackle this issue by reweighting samples according to target-space density. However, statistical target-space rarity does not coincide with the intrinsic dynamical rarity encoded in the recurrence geometry of the attractor. To address this, we introduce Dynamics-Aware Weighting (DAW), a data-centric objective reweighting framework. Using the local dimension $d$ from dynamical systems theory as an a priori measure of a state's dynamical complexity, DAW reshapes the loss landscape to allocate representational capacity toward the sparse, high-$d$ regimes where forecast errors are systematically large. On the chaotic KS equation, DAW consistently outperforms uniform training as well as weighting based on target-space rarity, and its randomly permuted ablation, reducing long-term autoregressive error relative to all baselines. Event-level analysis shows that DAW achieves this by suppressing the localized error amplifications incurred during sharp jumps in the local dimension $d$, which typically accompany complex physical processes such as wave-merging in the KS system.

This study proposes a well-balanced formulation of weakly compressible smoothed particle hydrodynamics (WCSPH) for free-surface flows, which preserves hydrostatic equilibrium exactly at the discrete level–a property essential for reliable long-term simulations. Although well-balanced schemes are well established for mesh-based methods, the property remains largely unaddressed in WCSPH, where the particle approximation of the pressure gradient fails to balance the gravitational force exactly. The imbalance stems from two difficulties: the nonlinearity of the pressure-gradient-over-density term, and the approximation error of gradients evaluated by particle summation. The first is resolved by introducing an auxiliary potential variable that recasts the nonlinear term as the gradient of a single scalar, which reduces to a linear function of position under hydrostatic conditions. The second is resolved by a Riemann-based gradient approximation with kernel correction, which is first-order consistent and recovers linear fields exactly. These two ingredients ensure that the discrete potential gradient balances gravitational force exactly. Widely used techniques, including $\delta-$SPH, particle shifting and tensile instability control, are readily incorporated. The formulation is further extended to three dimensions and implemented on GPU with architecture-tailored optimizations. Hydrostatic tests with rectangular, triangular and Gaussian bottom topographies show that the proposed formulation attains the well-balanced property to machine precision, reducing the spurious velocity error of conventional SPH from $10^{-3}$ to the order of $10^{-13}$. More complex benchmarks confirm its robustness, accuracy and low pressure oscillation, with simulations of up to 17.53 million particles performed on a single consumer-grade GPU.

Identifying atomic defects at elevated temperature is difficult because thermal fluctuations blur the local symmetry that both geometric heuristics and supervised classifiers rely on: trustworthy labels exist in low-temperature reference configurations, while the high-temperature regime where robust analysis matters most is effectively unlabeled. We cast this as a cross-temperature domain-shift problem and align the two domains at three levels: an equivariant denoiser at the input level, cross-temperature contrastive learning at the representation level, and a morphology-aware regularizer that steers predictions toward the compact geometry of physical defect structures. Because no atom-wise truth exists at temperature, we further introduce a label-free evaluation suite that scores predicted defect structures along five spatial and physics-based axes, enabling model assessment and selection without high-temperature labels. Near the melting point, the framework identifies vacancies and self-interstitial atoms across face-centered-cubic, body-centered-cubic, and hexagonal-close-packed iron systems with every interstitial localized and zero false detections in every vacancy system against Wigner-Seitz ground truth, with no high-temperature labels used in training. It sustains this fidelity on a million-atom, 2.5 ns trajectory, resolving single vacancy hops and complete Frenkel-pair recombination, and captures grain-boundary phase transformations in aluminum bicrystals, distinguishing two nucleation modes. Multi-level domain alignment thus offers a practical, label-efficient route to temperature-robust structural analysis of large-scale molecular dynamics.

We present a reduced-order semi-analytical model for reorientational nonlinearity in chiral nematic liquid crystals, showing that the chiral pitch acts as the dominant physical length scale governing the onset of nonlinear self-focusing and soliton formation. Starting from the full Frank-Oseen equation, we derive a closed-form expression for the optically induced molecular rotation that captures the essential saturable response of the medium while reducing computational cost by more than two orders of magnitude compared with standard relaxation-method solvers. Despite its simplicity, the model reproduces the essential features of the numerically obtained nonlinear refractive index, the onset of self-localization, and the transition from discrete to continuous solitons in one and two dimensions. It further predicts the formation of fully localized astigmatic nematicons with only minor shifts in the self-localization threshold due to the neglect of nonlocal effects. The proposed model provides direct physical insight into light-matter interactions with soft matter media and offers a computationally efficient tool for the design and optimization of nonlinear photonic devices.

We introduce a continuous data assimilation method for particle-in-cell simulations of the Vlasov-Poisson equation when only hydrodynamic moments are observed. The forecast state is an empirical measure on phase space, whereas the observed fields (density, bulk velocity, and temperature) constrain only a few velocity moments and leave the velocity-space shape of the distribution undetermined. We construct the moment feedback as a Wasserstein gradient flow of a moment-mismatch functional over phase-space measures. The resulting drift acts directly on particle positions and velocities, couples the density, momentum, and energy residuals through a single variational structure, and vanishes on the entire moment-compatible set. Under the standard Wasserstein metric, the energy residual produces a position correction that grows quadratically with the particle speed, and the particle system falls outside standard well-posedness theory. Our primary formulation pairs the quadratic moment mismatch with a velocity-weighted Wasserstein metric that penalizes spatial transport at large peculiar velocity relative to the observed bulk flow, which removes this growth. A direction-split variant retains the plain metric instead. Under the same weighted metric, an alternative moment-relative-entropy functional yields an affine, shape-preserving velocity correction and explicit global moment balances for the space-inhomogeneous system. We prove that the finite-particle scheme with linear Lenard-Bernstein collisions is globally well posed. In 1D1V and 2D2V experiments with several collision models, the nudged formulations reduce bulk-velocity and temperature errors by up to two orders of magnitude relative to an unassimilated run.

Representation quality is a central determinant of PINNs' performance, yet standard training leaves representations to emerge implicitly while fitting the final solution. We introduce representation curriculum, an ordered process in which representations are explicitly learned, transferred independently of their predictors, and progressively refined. We realize it with Staged Depth Training (SDT), which trains a shallow prefix under a temporary physics-informed head, discards the head, and freezes the learned prefix while adding depth, without equation-specific encodings or changes to the final architecture. Across the 20 default forward problems in PINNacle with three backbones, SDT improves 40 of 59 equal-budget problem–backbone cells by at least 5% and remains within that band in the rest, with a 32.8% geometric-mean error reduction on a PirateNet-style backbone. Mechanistic ablations suggest that the gain is not explained by optimizer restarts or shallow warm-starting alone. Representation visualizations and hyperparameter-basin analyses provide diagnostic evidence on representation geometry and local sensitivity to shared hyperparameters. On Poisson–Boltzmann 2D, SDT also more than doubles the fitted depth-scaling exponent for both backbones. These results support representation curriculum as a promising training strategy for improving PINNs while preserving the deployed architecture and inference cost.

Physics-informed neural networks (PINNs) are commonly evaluated via a single aggregate residual, assuming a smaller residual indicates a better solution. Testing this directly across three constrained PDE systems, I find this assumption can systematically fail. In matched pairs of solvers differing only in whether a defining structural identity is hard-wired or penalized, the penalized variant frequently attains a lower equation residual while violating that identity by several orders of magnitude, causing the exact variant to be falsely ranked worse. Over 64 matched pairs spanning two systems, four network variants, and eight seeds, this inversion occurs in 83% of cases (95% Wilson CI: 72–90%), with rates from 72% to 94% across systems. Testing across six architectures–MLP, cPINN, XPINN, hp-VPINN, and physics-informed DeepONet and FNO–inverts the ranking in 46 of 48 pairs, indicating that this variability is problem-dependent rather than specific to the approximator. A third, larger vorticity–streamfunction problem shows the same ordering: the residual-optimal solver violates its structural identity by over six orders above tolerance, despite a residual margin of only 9.37%. Because a scalar loss cannot expose this, I introduce a lexicographic admissibility gate spanning the structural identity, boundary trace, and a solvability integral that must vanish independently of the equation residual. All three must pass before residuals can compete. This gate catches three artifact classes but misses a fourth: a prescribed-structure prior yields fields that pass every single-run check, yet deleting the source term reveals that 97% of the reported structure survives removal of the physics. Reference data and figures accompany the paper.

Recent mesh-based simulation advances have, in no small part, relied on neural surrogates of two distinct families: global models that route information through a small set of latent tokens, and local models that perform message passing across mesh edges. Consistent with both classes is the inability to perform beyond low-dimensional problems and small-scale or oversimplified meshes, the simulation regimes where industrial problems reside. Our work shows this explicitly and presents a unified formulation. In global approaches, latent-token attention acts as a spatial low-pass filter, while local message passing lacks the global reach necessary to propagate information across large mesh spaces. Viewed through the error, the two operators are the halves of a multigrid cycle: one corrects errors at the lower end of the spectrum, the other at the higher end, and neither can do the other's job. We introduce Read-Write-Relax (RWR), which interleaves latent attention with message-passing relaxation under a unified formulation. The interleaved processor lowers error across the entire spectrum, making RWR the most accurate model in nearly every comparison across our industrial and public benchmarks. It is also markedly data-efficient in the scarce-data regimes, accurate on the engineering quantities of interest, and scales full-field predictions to challenging, large-scale problems.

We demonstrate an iterative approach to modeling a sparsely measured magnetic field in a large-bore solenoid. This approach uses a hybrid of traditional and machine learning techniques. The traditional technique is a linear least-squares fit using a series solution to Laplace's equation, while the machine learning technique involves the training of a physics-informed neural network (PINN) on the least-squares fit residuals. We use a newly defined activation function "DELTAsnake," a modification to the snake activation function proposed by Ziyin et al. that allows for stronger curvature and non-monotonicity. The combined model approximately obeys Maxwell's equations to a level sufficient for producing high quality physics simulations and analysis. Our approach is applied to a highly realistic calculation of the expected magnetic field in the Mu2e experiment's Detector Solenoid which includes a simple model for the expected statistical measurement uncertainties. Using ten toy measurement simulations, we demonstrate the capabilities of our model in comparison to the least-squares method alone; the least-squares method alone results in a reduced chi-squared statistic of ${2.15 \pm 0.01}$, while our approach improves the reduced chi-square to ${1.034 \pm 0.005}$. Furthermore, for an average toy simulation, we show that the range of the RMS of the three field component residuals reduces from ${0.07-0.37}$ Gauss to ${0.05-0.07}$ Gauss. We find that this novel method is robust against a realistic systematic uncertainty deriving from Hall probe calibration bias and can be used to significantly reduce the number of measurements required to achieve an accurate model.

Multilevel non-volatile memory technologies face recurring trade-offs among information density, endurance, retention, and switching energy. We investigate an alternative state variable based on the discrete vortex configuration of self-organized vortices in a boundary-driven electron fluid. A dissipative point-vortex model derived from magnetohydrodynamic dynamics yields six reproducible vortex codewords, corresponding to 2.585 bits per cell, whose write fidelity, noise sensitivity, 100-cycle endurance, and effective information capacity are quantified. The ordering of their finite-amplitude basin radii $r_{50}$ differs from that predicted by both fixed-circulation and fully coupled linear-stability spectra. A nonlinear saddle-point construction based on the reduced dynamics likewise does not recover the measured basin ordering. The discrepancy is associated with escape pathways involving coupled position–circulation dynamics that are absent from the fixed-circulation description. These results show that local stability alone does not determine the finite perturbation tolerance of the vortex states considered here. The proposed memory requires active hold power, and passive retention remains to be established experimentally.

Optical readout is a fundamental tool in atomic state measurement, yet the fidelity of optical readout is frequently limited by imperfect photon collection. This can be mitigated when readout occurs on a cycling transition which continuously fluoresces under resonant excitation, thus increasing signal and enabling single-shot readout. We present a method to extend the cyclicity of atomic transitions via coherent destructive interference between spurious decay paths. We describe the characteristics of atomic systems in which this method can be implemented and model several examples in which the number of emitted photons is increased by multiple orders of magnitude.