Computational Physics
BBun: an unsteady vortex-ring panel method for interacting lifting bodies, box wings and propellers
Daniele Peri
This report documents BBun (Blunt Body unsteady), a low-order code for the unsteady potential flow around one or more interacting three-dimensional bodies. The bodies are represented by
vortex rings (piecewise-constant doublets) with a Neumann boundary condition; free
vortex sheets are shed from the trailing edges and, optionally, from the tips, and convected in time, with an implicit unsteady Kutta condition. The report describes the choices that make the discretization consistent and convergent (a single desingularized kernel per wake line, a bordered factorization of the singular Neumann problem, interior velocity conditions for the nearly singular mode of ring-shaped bodies, the detection of the separation lines from the grid connectivity) and the extensions to several bodies, box wings, symmetric configurations (image method), non-lifting bodies, rigidly rotating bodies (propellers), the unsteady Bernoulli equation, a wake-body collision treatment and a strip-wise integral boundary layer. The verification and validation are reported in full: potential flow around a sphere, sensitivity and grid convergence, the two-dimensional limit, an independent
vortex-
lattice method, the NACA 0015 wing of McAlister and Takahashi (loads and chordwise pressures), the NACA 0012 profile drag, the biplane of Knight and Noyes, Prandtl's best wing system, Wagner's function and blade-element momentum theory for a propeller. A complete aircraft with counter-rotating tractor propellers illustrates the use of the code.
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Computational Physics · Cross-listed from cs.CE
A Bifurcation-Based Domain Decomposition Method with Neural Operators for Blood Flow Simulation
Yuzhou Zhao, Han Zhang, J. Matias Di Martino et al. (+2 more)
Fast and accurate simulation of hemodynamic behavior within vascular networks is essential for numerous clinical applications. However, obtaining high-quality and computationally efficient flow measurements across complex vascular networks remains challenging. To address this, we first decompose the vascular network into a set of bifurcation units and then develop an operator network capable of mapping unit-specific parameters to the local solution fields of each bifurcation unit. By lumping the Windkessel-model outlet parameters and incorporating inlet boundary conditions from the solution of parent units, the flow and pressure fields can be rapidly approximated. Subsequently, operator-network-driven Schwarz waveform relaxation is applied across bifurcation units to correct discontinuities and improve numerical accuracy. On 7-segment and 55-segment arterial tree models, the proposed method achieves $13\times$ to $17\times$ wall-clock speedups over conventional 1D numerical simulation, with relative $L^2$ errors of 1% in both pressure and velocity. The resulting pulse wave velocity biomarkers agree with the conventional reference to within 1–2%, and the same trained operator generalizes to different tree-like 1D vascular network
topologies.
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All authors Yuzhou Zhao, Han Zhang, J. Matias Di Martino, Jean-Michel Morel, Guillermo Sapiro
Computational Physics · Cross-listed from cs.CE
SHIFT-Truck: A High-Fidelity Aerodynamics Dataset and Benchmark for Pickup Trucks
Riddhiman Raut, Yin Yu, Aashwin Anand Mishra et al. (+4 more)
Pickup trucks account for 14% of new light-duty vehicles produced in the United States, yet are among the least aerodynamic. Their open cargo bed adds a flow absent from existing automotive aerodynamics
datasets such as DrivAerML and SHIFT-SUV: the shear layer leaving the cab roof passes over a recirculating bed flow before separating again at the tailgate. The resulting drag lowers fuel efficiency, raises emissions and limits the range of electric trucks. Scale-resolved Computational Fluid Dynamics (CFD) is too costly for broad design exploration; neural surrogates can predict flow features at a fraction of that cost, provided they are trained on large-scale, high-fidelity, domain-specific data. We introduce SHIFT-Truck, the first such
dataset for pickup trucks. It comprises 1,000 Spalart-Allmaras delayed detached-eddy simulations (SA-DDES) of a reference pickup geometry morphed across 17 shape parameters. Each case is run on a mesh of about 100 million
cells at a Reynolds number of $1.4 \times 10^7$ and released with time-averaged surface pressure, wall shear stress, volumetric pressure and velocity. The setup is verified by grid refinement and repeated runs, and checked against wind-tunnel measurements. We define geometry-grouped splits and
benchmark four neural surrogates, DoMINO, GeoTransolver, AB-UPT and SMART, on surface and volume tracks. SHIFT-Truck also introduces controlled distribution shifts in the operating point, the input surface discretization and the vehicle archetype. Models with strong in-distribution performance can degrade substantially under these shifts: operating-condition changes expose failures to infer speed dependence, while tessellation and cross-vehicle shifts reveal markedly different robustness across architectures. SHIFT-Truck is thus a
benchmark not only for surrogate accuracy but also for generalization across physical and numerical distributions.
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All authors Riddhiman Raut, Yin Yu, Aashwin Anand Mishra, Michael Emory, Thomas Economon, Peter Lyu, Juan J. Alonso
Computational Physics
Muhammad Idrees Khan
Reliable multistep
quantum lattice-Boltzmann
evolution requires controlling computational faults. When ideal collision preserves encoded mass and momentum exactly, changes in those charges can provide syndromes for selected faults at the post-collision checkpoint. A fault that shifts one population then leaves a unique mass-momentum residual labeled by the
lattice velocity. A coherent reference register stores the expected charges, so the same test remains valid while the physical fluid charges vary across the
lattice. Single bit flips on population number registers occupy disjoint syndrome sectors and satisfy the Knill-Laflamme condition. A state-vector demonstration on eighteen data
qubits of the two-dimensional nine-velocity
lattice (D2Q9) recovers that single-bit family to double-precision roundoff. Conservation still leaves a fifteen-dimensional kinetic nullspace on the three-dimensional nineteen-velocity
lattice (D3Q19). Exact multiple-relaxation-time (MRT) streaming analysis ranks those charge-preserving modes by the order at which they return to density or momentum. A classical D3Q19 decaying-flow simulation at moderate Reynolds number then injects about $1.75\times10^4$ selected single-population shifts per realization. Recovery of that alphabet returns the trajectory to floating-point roundoff. The
quantum statements assume an ideal charge-preserving collision and a reliable reference. The result is an inner recovery map for a stated charge-changing alphabet together with a kinetic classification of the unresolved sector.
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Computational Physics · Cross-listed from cs.CE
Neural topology optimization of ship structures under propulsion machinery vibrations
Shengyu Yan, Muhammad Muztahidul Hakim Zareer and Jasmin Jelovica
Ship structural vibrations contribute to noise, fatigue, and equipment damage, while dynamic-compliance
topology optimization can produce pathological designs near resonance. This study extends neural-reparameterized
topology optimization using a convolutional Kolmogorov-Arnold network (KATO) to forced-vibration design with active input power (AIP) as the objective. Applications include a 100 Hz engine-supporting deck panel and an 18 Hz thruster foundation frame. Helmholtz PDE filtering and Heaviside projection control feature sizes and manufacturing tolerance. Across both deck families, all eight optimized layouts reduce AIP relative to size-optimized references and, after finite-depth extrusion, also achieve lower static compliance. For unrestricted, manufacturing-aware, and stress-aware frame variants, KATO matches GCMMA in AIP within 0.5 dB while yielding 22-36x lower static compliance after matched-volume binary re-analysis. In a near-resonant 300 Hz case, both methods reduce initial AIP by more than 32 dB; KATO maintains a connected design, achieves 59x lower binary static compliance, and reduces maximum AIP over 1-500 Hz by 2.7 dB. KATO runs 6.4-10.4x faster than GCMMA for the implemented stress-aware formulations. The results demonstrate neural AIP-driven
topology optimization as an efficient approach for designing connected, feature-size-controlled ship structures with improved forced-vibration performance.
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Computational Physics · Cross-listed from cs.LG
A foundation model for energy and radiation systems built on heterogeneous scientific interfaces
Samrendra Roy, Tapas Tripura, Yoon Pyo Lee et al. (+2 more)
Scientific foundation models are commonly evaluated after heterogeneous physical problems have already been translated into a compatible gridded, tokenized or symbolic representation. This leaves the scientific interface outside both the pretrained model and the audit of what is actually reused. We study the complementary setting in which boundary histories, sparse monitor records and loading histories retain their native inference classes and their outputs remain on Cartesian, latitude-longitude and unstructured domains. GEODE couples task-specific scientific interfaces to a shared routed library of wavelet operators. A single jointly pretrained model represents cavity flow, radiation dose and elastoplastic stress, then acquires a heat exchanger and a reactor subchannel by training a private interface containing 2.1% of its parameters. Earlier predictions remain unchanged by parameter isolation, whereas unrestricted fine-tuning degrades them by factors of 14-29. Crucially, preservation alone does not establish reuse: norm-matched randomized-library controls show that the contribution of pretrained computation is conditional on the task and data regime. A separate decomposition shows that full-field relative L2 error can substantially understate error relative to spatial variation when field level dominates the norm. Task-specific operators remain more accurate on three of the five problems. These results distinguish multi-task coverage, preservation and pretrained reuse as separate properties that must be tested independently when scientific foundation models span heterogeneous interfaces.
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All authors Samrendra Roy, Tapas Tripura, Yoon Pyo Lee, Souvik Chakraborty, Syed Bahauddin Alam
Computational Physics · Cross-listed from physics.flu-dyn
A shape-similarity latent space for fluid interfaces: invertible reduced-order modelling of droplet morphology
Ali R. Hashemi, Mohammad R. Hashemi and Pavel B. Ryzhakov
A droplet breaks up in tens of microseconds, and a recording captures perhaps a dozen frames. The states in between cannot be recovered without repeating the experiment, and simulating them is too costly to sweep an operating envelope. Yet they are present in the corpus as a whole: a campaign spanning a device's actuation range produces morphologies resembling those any single recording missed. Exploiting that requires a representation that is low-dimensional, invertible, and faithful to shape rather than to sampling. Proper orthogonal decomposition supplies the first two but measures distance in sampled coordinates;
manifold learning supplies the third but no map back to a shape; elastic shape analysis supplies a shape metric but no reduced coordinates. SHROM composes all three. Interfaces are represented by their square-root velocity functions, a neighbour graph is built over that shape space, and an autoencoder is trained to reconstruct while penalising latents in which graph neighbours are not latent neighbours. The demonstration uses 301,539 inkjet droplet contours and four filmed break-up sequences. The graph term does not improve reconstruction. It determines whether position in the latent carries meaning: clustering the latent of an otherwise identical model recovers the shape-space partition at chance level (ARI = 0.063 +/- 0.059), and at 0.781 +/- 0.049 with the term active. Waveform parameters predict the full contour at R^2 = 0.878 +/- 0.026. Negative results are reported in the same terms. The graph metric proved immaterial across five choices, and interpolation error saturates at the reconstruction limit, so a plain autoencoder leads that task. The main limitation is interpolation across a
topology change: no component of the regularised latent holds both a single-component and a post-break-up shape, whereas an unregularised autoencoder mixes them freely.
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Computational Physics · Cross-listed from cond-mat.mtrl-sci
Irreducible Weyl Semimetals
Ke-Xin Pang and Yan Gao
A key objective in Weyl-semimetal (WSM) research is to identify phases built from minimal configurations of Weyl points (WPs), which provide the simplest settings for investigating the intrinsic physics of chiral topological charges. Pang et al. [Phys. Rev. Res. 8, 033304 (2026)] recently established that crystallographically realizable WSMs can be decomposed into linear combinations of 16 minimal "irreducible Weyl molecules" (IWMs). A fundamental question remains unresolved: which of these non-decomposable configurations can themselves form standalone crystalline phases? Here we introduce irreducible Weyl semimetals (IWSMs), in which two bands crossing near the Fermi level form an elementary
symmetry-compatible complex whose complete Weyl-node configuration is charge neutral and crystallographically indivisible. Combining all 1651
magnetic space groups with Weyl-orbit multiplicities and band-compatibility relations, we classify IWSMs formed by crystalline-
symmetry-protected twofold WPs. Only ten of the sixteen primitive inventories admit one-copy realizations, comprising four Pair, four Split, and two Mixed charge-node architectures. Remarkably, this classification uncovers five unconventional and previously unrecognized topological phases: the charge-three Pair IWSM {3, -3}; the Split IWSMs {3, -1, -1, -1}, and {4, -1, -1, -1, -1}; and the Mixed IWSMs {3, 1, -2, -2} and {3, 3, -2, -2, -2}. For all ten classes,
symmetry-constrained
lattice models verify the complete node inventories, Chern charges, and surface chiral-flow incidence. Our results establish crystalline irreducibility as a phase-level organizing principle beyond individual Weyl nodes and provide a
symmetry-resolved framework for identifying minimal Weyl complexes in electronic, phononic, and photonic systems.
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Computational Physics · Cross-listed from cs.LG
PHASE: Multi-Regime Modeling of Incompressible Magnetohydrodynamics
Radhika Achikanath Chirakkara, Rajdeep Haldar, Zezheng Song et al. (+1 more)
Magnetohydrodynamics (MHD) is central to
plasma modeling in astrophysics, space science, fusion, and engineering, but resolving multiscale MHD dynamics is computationally expensive. Machine-learning surrogates enable fast inference by learning reusable solution operators, yet existing models require separate training for each physical regime, limiting generalization across varying parameter settings. We introduce PHASE, a PHysics-Adaptive Scalable operator with residual Error correction, designed to model incompressible MHD across varying physical parameters with a single model. PHASE combines transfer learning, regime-aware adaptation, physics-centered learning, and residual refinement to improve both physical fidelity and generalization across MHD regimes. Together, these improvements achieve state-of-the-art prediction accuracy on two-dimensional MHD
turbulence by reducing relative $L_2$ errors on physical fields by more than an order of magnitude compared to prior MHD neural-operator baselines. Moreover, PHASE generalizes successfully to unseen parameter values without retraining, demonstrating the cross-regime adaptability expected from operator learning. We evaluate PHASE beyond point-wise prediction errors using derived physical fields, spectral analysis, and distribution statistics, consistently observing improved physical fidelity. We further show that our framework can accurately simulate MHD instabilities by testing it on the Kelvin–Helmholtz instability, demonstrating the robustness of our method.
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All authors Radhika Achikanath Chirakkara, Rajdeep Haldar, Zezheng Song, Jiequn Han
Computational Physics
Geometry-Controlled Chern transfer and Flat Band Reconstruction in distorted kagome lattices
Yu Zhu, Claudia Felser and Xiaolong Feng
Flat band formation and nontrivial
topology are central manifestations of kagome electronic structure, yet they are commonly discussed in idealized
lattice geometries. In distorted kagome materials, structural deformation reorganizes electronic propagation pathways, but a microscopic understanding of how such distortions govern flat band dispersion and band
topology is still lacking. Using a distorted kagome tight-binding model with rotated angle dependent long-range hopping and intrinsic
spin-orbit coupling, we show that distortion reconstructs both the dispersion and
topology of the kagome band
manifold. The flat band descendant develops distinct bandwidth regimes associated with a redistribution of its extrema in momentum space. Simultaneously,
symmetry-related band inversions generate quantized Chern number transfer whose parity is fixed by the multiplicity of the touching points, thereby determining the gap-resolved Z2
topology. The accompanying Berry
curvature evolution produces characteristic anomalous Hall and Nernst responses. These results identify
geometric deformation as a common microscopic origin of flat band and topological reconstruction in kagome systems.
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Computational Physics · Cross-listed from cond-mat.stat-mech
Accurate ground-state entropies from population Monte Carlo: The antiferromagnetic Ising model on the Shastry-Sutherland lattice
Denis Gessert, Wolfhard Janke and Martin Weigel
We demonstrate how the population annealing Monte Carlo simulation method can be used to compute the ground-state
entropy to high precision. This approach is tested for the classical antiferromagnetic Ising model on the Shastry-Sutherland
lattice with diagonal couplings chosen twice as strong as the nearest-neighbor interactions. In the absence of an external
magnetic field, the model is known to be disordered at all temperatures, with a macroscopically degenerate ground state. We find the ground-state
entropy to be $0.458\,777\,78(10)$ per site, which is in good agreement with the estimate of a recent study using the corner transfer
matrix renormalization group method. The sampled ground-state configurations are analyzed by considering the bond configurations, the local-energy configurations, and the
spin-
spin correlations. While all observations are consistent with the disordered nature of the ground state, the numerical data suggest a power-law decay of the size distribution of clusters of sites with local energies different from the ground-state level.
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Computational Physics · Cross-listed from hep-ex
Trace isotopes set the neutron horizon of liquid argon
Yasser Maghrbi
Near 57 keV, destructive interference makes argon-40 almost transparent to
neutrons. The 0.4% of argon-36 and argon-38 in natural argon then supply over 90% of its opacity, amplified 230-fold. Published transmission data rule out the argon-36 evaluation FLUKA uses by default, even with every other isotope made transparent, and bound its cross section in the window to 2-11 b. In a DUNE-scale detector, switching to the data-consistent evaluations moves the fiducial fraction of argon-41 calibration captures by 9-13% while the total yield changes by only 2%: the effect is on where captures occur, not how many.
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Computational Physics
From Bellissard's gap labeling to atomistic quasiperiodic bilayers
Thomas D. Kühne, Vladislav Efremkin and Emil Prodan
Bellissard's framework uses covariant observables to describe aperiodic solids. We examine how butterfly-like spectra in twisted bilayers can be related to bulk gap labels and topological response. A bulk gap permits a spectral projector and an integrated density of states. A topological response requires an additional pairing of that projector. In an illustrative finite honeycomb bilayer, an exact second-moment identity isolates the interlayer contribution to spectral variance. Angle-resolved spectra, finite state counts, an uncoupled reference, and size and broadening checks show how coupling redistributes spectral weight without assigning a bulk gap label. We then examine the requirements for atomistic electronic-structure calculations, including nonorthogonal orbitals, projected densities of states, and basis functions that move during relative sliding. The resulting framework specifies the steps needed to connect atomistic spectra with bulk state counting and topological response.
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Computational Physics · Cross-listed from cond-mat.mes-hall
Deep Learning GW Quasiparticle Hamiltonians for Many-Body Excited-State Electronic Structure at Scale
Xiaoxun Gong, Zechen Tang, Woochang Kim et al. (+4 more)
Accurate quasiparticle electronic structures are the foundation for understanding excited-state properties of materials and explaining optoelectronic,
quantum, and transport phenomena. First-principles GW calculations nevertheless remain computationally intensive for large or configurationally complex systems. Here we introduce DeepH-GW, a deep-learning framework that predicts an effective GW quasiparticle
Hamiltonian directly from atomic structure. Building on the local, equivariant message-passing architecture of DeepH, DeepH-GW is trained on high-fidelity plane-wave GW calculations through a real-space
Hamiltonian-reconstruction interface. This approach combines the systematic accuracy and broad chemical applicability of plane-wave methods with linear-scaling neural-network inference. Across the systems examined, DeepH-GW reproduces quasiparticle band structures with errors on the order of a few meV. Moreover, we show that, despite the intrinsic nonlocality of many-body interactions, DeepH-GW exhibits strong cross-scale transferability from relatively small training structures to substantially larger supercells. We demonstrate that the framework can accurately capture GW-level electron-
phonon band-gap renormalization through predictions in supercells with thermal displacements, illustrating the power of the approach. DeepH-GW therefore provides a practical route toward large-scale many-body simulations and foundation models for excited-state electronic structure.
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All authors Xiaoxun Gong, Zechen Tang, Woochang Kim, Yang Li, Wenhui Duan, Yong Xu, Steven G. Louie
Computational Physics · Cross-listed from physics.soc-ph
NuPaD: A Generative AI Framework for Fostering Deep Learning in Subatomic Physics
Chong Qi
The rapid adoption of generative artificial intelligence (GenAI) in higher education has introduced a critical pedagogical paradox: while these systems possess extraordinary capacity for information
retrieval and synthesis, their default operational mode of supplying immediate, unprompted answers actively undermines the cognitive processes upon which genuine scientific understanding is built. This paper presents NuPaD (Nuclear & Particle Physics – Deep Learning Tutor), a novel pedagogical framework designed for the graduate-level subatomic physics curriculum. For such advanced courses, instruction naturally shifts toward inquiry-driven, problem-based learning, making it an ideal environment to use GenAI to explore complex, open-ended physical questions rather than merely querying established facts. The framework consists of three tightly coupled and easy-to-use components: a primary
agent instruction file that enforces a structured problem-based learning protocol, a purpose-built textbook optimized for precise parsing by
privacy-preserving local GenAI, and a concise companion file that bridges the knowledge gap between the textbook and GenAI, alongside a comprehensive dynamic skill set for specialized tasks. We explain in detail the architectural principles of the modular NuPaD framework, the design philosophy of the Markdown-native textbook format, and the underlying GenAI regulation principles. By redefining the interaction loop between student and model, this framework transforms GenAI from a passive answer engine into an active, personalized tutor, ensuring that it accelerates rather than bypasses the development of deep learning and scientific
reasoning.
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Computational Physics
Label-Permutation Symmetry and Stability in Oscillator Potts Machines
E.M. Hasantha Ekanayake and Nikhil Shukla
Oscillator Potts machines (OPMs) provide a physics-inspired, energy-minimization framework for solving combinatorial optimization problems described by the $q$-state Potts
Hamiltonian. Although OPMs may be viewed as multistate extensions of oscillator Ising machines (OIMs), here, we show that they exhibit dynamical properties absent in the binary case. Specifically, we derive a configuration-dependent local-stability condition for a recently proposed multiharmonic OPM formulation and show that configurations with the same Potts energy need not be dynamically equivalent. In particular, for $q\geq4$, permutations of the Potts labels can alter the Jacobian spectrum and, consequently, the regularization strength required to locally stabilize a given Potts configuration. Thus, different phase encodings of the same Potts solution can exhibit different local stability properties despite having identical Potts energies.
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Computational Physics · Cross-listed from physics.chem-ph
Anomalous pressure-dependent viscosity of basaltic melts and its role in asthenosphere melt accumulation
Hongkun Zeng, Peiyu Zhang, Liang Yuan et al. (+3 more)
The asthenosphere's mechanical weakness enables plate tectonics, but its origin is debated. Partial melt has been proposed to cause this softening, yet recent studies suggest that the measured viscosity minimum in basaltic melts, an essential control on melt mobility, is an experimental artifact. Using
quantum mechanics-based, machine learning-accelerated molecular dynamics, we extend simulation timescales by more than a factor of 1000 and achieve percent-level precision. We show that basaltic melt exhibits a robust viscosity minimum (approximately 20% below 1-bar values) at approximately 3 GPa, driven by pressure-induced reorganization of aluminum coordination that facilitates shear relaxation while silicon-oxygen polyhedra remain structurally rigid. Our results reveal a depth-dependent rheological transition: melt mobility peaks below approximately 150 km, promoting efficient extraction, but declines sharply during ascent, causing melt to stagnate beneath the lithosphere. This mechanism provides a physical basis for the dual seismic signatures of a melt-depleted deep asthenosphere and a melt-enriched layer near the lithosphere-asthenosphere boundary.
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All authors Hongkun Zeng, Peiyu Zhang, Liang Yuan, Youjun Zhang, Xiang Wu, Junfeng Zhang
Computational Physics · Cross-listed from cs.LG
SCOPE: Observation-Conditioned Full-Target Prediction for Sparse PDE Inference
Ruichen Xu, Siyao Wang, Fang Wan et al. (+8 more)
Recovering complete physical fields from sparse observations is challenging because the measurements may not uniquely determine the underlying state.
Diffusion-based PDE solvers address this problem through iterative sampling whereas neural operators provide deterministic one-pass predictions. We propose SCOPE (Sparse-Context Observability-aware Predictive
Embeddings) to recover complete PDE fields from sparse observations by coupling full-field latent prediction with physical reconstruction. A shared decoder reconstructs fields from both predicted and complete-view representations so that representation learning is guided by both physical recovery and latent matching. We derive a quadratic risk decomposition at fixed teacher-decoder pairs showing why optimal latent prediction need not yield optimal field reconstruction. We also establish sufficient conditions for decoder improvements on complete inputs to transfer to recovery from partial observations. Experiments across five PDE settings show that SCOPE outperforms mask-aware neural operators on all ten forward and inverse tasks and achieves lower errors than those reported for
diffusion-based solvers including DiffusionPDE and FunDPS. Decoder-only adaptation further improves recovery without retraining the backbone while retaining deterministic single-pass inference.
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All authors Ruichen Xu, Siyao Wang, Fang Wan, Jiacheng Qiu, Wenhan Gao, Jiaxing Zhang, Linsey Pang, Ravid Shwartz-Ziv, Prakhar Mehrotra, Yann LeCun, Yuefan Deng
Computational Physics · Cross-listed from cs.LG
PDE-OBS: Controlled Evaluation Across Observation Patterns
Ruichen Xu, Siyao Wang, Fang Wan et al. (+7 more)
Physical-field reconstruction and forecasting depend on both measurement density and spatial layout, yet evaluation under a single observation pattern does not characterize performance when that pattern changes. We introduce PDE-OBS, an integrated benchmarking platform spanning numerical data generation, model training, and inference and evaluation under varying observation conditions. It combines 560,000 fields and trajectories from seven partial differential equation families with configurable observation operators and seven adapted baseline methods for stationary reconstruction and short-horizon forecasting. Separating observation construction from physical records allows users to specify parameterized patterns and deterministic mixtures for training and testing while preserving prediction targets and data splits. The evaluation protocol uses references trained for each test pattern to compare models on identical test observations and targets, alongside equal-count groups for spatial-layout comparisons. On a 14,000-record subset, we evaluate 441 trained models under nine test patterns, yielding 3,969 evaluations. Mean cross-pattern error exceeds mean matched-pattern error in all 49 PDE-method pairs, and this finding persists in a configuration-matched subset of 117 models. Denser test observations do not consistently reduce error for a fixed model. Mixed-pattern training on five completed pairs reduces large single-pattern transfer errors, although destination-trained references usually remain more accurate. Together, the
benchmark and findings support systematic evaluation of observation-pattern sensitivity and provide a reusable workflow for developing methods under changing measurement conditions. Code: https://github.com/ru1ch3n/PDE-OBS.
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All authors Ruichen Xu, Siyao Wang, Fang Wan, Jiacheng Qiu, Wenhan Gao, Jiaxing Zhang, Linsey Pang, Ravid Shwartz-Ziv, Yann LeCun, Yuefan Deng
Computational Physics
TT-FDTD: Tensor Train Accelerated Three-Dimensional FDTD With Logarithmic Cost of Spatial Operators
Chris Nguyen and Vladimir Okhmatovski
Quantized tensor-train (QTT) compression is incorporated into a full-vector three-dimensional scattered-field finite-difference time-domain (FDTD) formulation on uniform Yee grids. All six electromagnetic-field components, material-dependent update coefficients, equivalent-current sources, and staggered finite-difference operators are represented in compatible QTT form. Gaussian regularization of voxelized material interfaces is used to reduce the coefficient ranks generated by abrupt dielectric and conductivity transitions. The formulation is evaluated for an anatomically heterogeneous human-head model and a homogeneous dielectric sphere on grids containing up to $512^3$ spatial
cells. The reported results show that interface smoothing substantially reduces material-coefficient ranks and that the TT–FDTD solution reproduces the full-grid transient fields with pointwise absolute errors on the order of $10^{-4}$ in the examined slices. Compared with conventional FDTD, the tensor representation greatly reduces storage at fine discretizations, although tensor contractions and recompression introduce additional per-step computational cost. These results demonstrate the feasibility and
memory–time tradeoff of QTT-accelerated three-dimensional FDTD for large structured-grid simulations.
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