HS-FNO lifts the state to include history and decomposes updates into a learned future-slice predictor plus an exact shift-append transport, yielding lower rollout errors than standard or lag-stack FNO baselines on five non-Markovian PDE families.
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representative citing papers
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JanusPipe introduces SymFold and WaveK to enable efficient 3D-parallel training for conservative MLIPs, reporting 1.51x and 1.45x average throughput gains over 1F1B and Hanayo baselines on 32 GPUs.
A two-stage contrastive teacher-student framework learns and then projects latent dynamics onto port-Hamiltonian submanifolds from partial observations.
Port-Hamiltonian neural networks extended to PDEs recover the Hamiltonian and dissipation of nonlinear string dynamics from data and outperform non-physics-informed baselines.
Shock-centered scaling of DSMC fields in micro-nozzles reveals low-rank density structure, enabling DeepONet surrogates with mean errors reduced to 4.51% on hardest test cases.
A geometry-aligned bi-fidelity surrogate maps low- and high-fidelity wildfire solutions to a common domain for improved reduced-basis reconstruction, lower error near fronts, and practical uncertainty quantification.
Bayesian PINNs for elliptic PDEs have posteriors that contract around the true solution at near-optimal rates, with the prior adapting automatically to unknown smoothness.
A per-layer risk estimator for hybrid deep networks shows that replacing learned layers with known operators shrinks the bound and scales sample needs with the number of replaced parameters, validated on CT reconstruction.
DualTCN is the first deep-learning model for time-domain marine CSEM inversion that regresses four earth parameters, achieves high accuracy on simulated data, and runs up to 21,000 times faster than classical optimizers.
A video-to-PDE pipeline extracts the model u_t + v(t)·∇u = 9.005|∇u|^2 + 0.666Δu from grayscale ink-plume footage, outperforming advection-diffusion baselines on held-out frames and reducing to linear form via Cole-Hopf transformation.
TCD-Arena is a new customizable testing framework that runs millions of experiments to map how 33 different assumption violations affect time series causal discovery methods and shows ensembles can boost overall robustness.
Hybrid FNO-LBM accelerates porous media flow convergence by up to 70% via neural initialization and stabilizes unsteady simulations through embedded FNO rollouts, allowing small models to match larger ones in accuracy.
Quasi-equivariant metanetworks relax strict equivariance to preserve functional identity in weight-space learning while improving expressivity for feedforward, convolutional, and transformer networks.
A weighted FOSLS formulation for deep neural networks solves transmission problems robustly, with proofs that the loss aligns with the energy norm independently of material contrast and shows passive variance reduction.
A modified DCGAN with an auxiliary discriminator using the membrane factor generates stable, previously unseen funicular shells optimized for pure compression in three dimensions.
A deep energy method simulates fourth-order phase-field fracture in piezoresistive materials via one-way coupled electrical sensing after solving the mechanics-fracture problem.
Quantum PINNs using tensor-rank polynomials solve the Merton portfolio optimization PDE more accurately and with far fewer parameters than classical neural networks.
LJ-DSMC with VED collision selection from Chapman-Enskog viscosity matching and DeepONet scattering prediction is validated on shocks, Couette flows, and cylinders with 36% wall-time reduction.
A Kolosov-Muskhelishvili informed neural network satisfies plane elasticity equations by construction, achieves sub-1% errors on benchmarks, and uses transfer learning to predict crack paths under multiple criteria with over 70% less training time.
Shallow neural networks with time-frequency localized activations achieve dimension-independent Sobolev approximation rates of order N^{-1/2} for functions in weighted modulation spaces.
PVD-ONet combines multi-network DeepONet modules with Prandtl and Van Dyke matching conditions to map initial data to solution operators for families of singularly perturbed boundary-layer problems and to infer scaling exponents from sparse observations.
Input-convex neural networks in elementary polynomials of signed singular values provably approximate any frame-indifferent isotropic polyconvex hyperelastic energy.
citing papers explorer
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HS-FNO: History-Space Fourier Neural Operator for Non-Markovian Partial Differential Equations
HS-FNO lifts the state to include history and decomposes updates into a learned future-slice predictor plus an exact shift-append transport, yielding lower rollout errors than standard or lag-stack FNO baselines on five non-Markovian PDE families.