Extends structural identifiability analysis to functional components of differential equation models and characterizes conditions for unique recovery using differential algebra techniques.
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representative citing papers
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.
FactoryNet is the first universal pretraining corpus for industrial time-series data with a shared S-E-F-C schema that supports cross-embodiment transfer and competitive anomaly detection.
Proves a single a priori H1 error bound for consistent CutPINNs using discrete L^gamma interior loss (gamma = 1 + 1/log m_til) and discrete H^{1/2} boundary trace norm on curved level-set domains, with rate limited by cut-cell floor 1/(2 gamma).
Optimizing training data via a differentiable SCM yields climate emulators that outperform those trained on six standard ScenarioMIP pathways while using less data and isolating distinct forcing responses.
LiL-Q applies quasilinearization to nonlinear PDEs and solves each resulting linear problem by convex least-squares collocation on Linear-in-Learnables trial spaces, achieving fast convergence and high accuracy on multiple benchmarks.
A domain-validity rubric and MR-card format screen candidate metamorphic relations into auditable test assets for SciML surrogates, separating model violations from out-of-domain applications.
OGAS uses a parallel diffusion model to bias PDE configuration sampling toward high surrogate difficulty, reducing 99th-percentile errors and error variance versus uniform sampling across tested 2D PDEs.
The curvature-aware precision controller adapts between FP32 and FP64 during PINN training to match double-precision accuracy at reduced computational cost.
RRISE trains a surrogate against precomputed MC targets and uses conformal calibration to deliver certified radii matching fixed-budget MC accuracy within 0.84 points while using one forward pass instead of up to 10^4 evaluations.
SparseModesNet uses POD linear encoding with LassoNet-enforced sparse nonlinear NN decoding to select modes and reduce reconstruction error by 51-78% versus polynomial manifold methods on turbulent channel flow while preserving interpretability.
FLASH-MAX embeds exact Maxwell solutions as neurons in a neural network to reconstruct homogeneous EM fields from sparse data with guaranteed zero PDE residual and proven universal approximation on arbitrary domains.
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.
citing papers explorer
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From Video-to-PDE: Data-Driven Discovery of Nonlinear Dye Plume Dynamics
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.
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Robust Deep FOSLS for Transmission Problems
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.
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Physics-informed, Generative Adversarial Design of Funicular Shells
A modified DCGAN with an auxiliary discriminator using the membrane factor generates stable, previously unseen funicular shells optimized for pure compression in three dimensions.
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A multiphysics deep energy method for fourth-order phase-field fracture with piezoresistive self-sensing
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.
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A physics-informed neural network approach to solve the spatially inhomogeneous electron Boltzmann equation
A specialized PINN architecture solves the spatially inhomogeneous electron Boltzmann equation with high accuracy across gases and electric field strengths without case-specific tuning.
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Physics-Informed Neural Networks for Methane Sorption: Cross-Gas Transfer Learning, Ensemble Collapse Under Physics Constraints, and Monte Carlo Dropout Uncertainty Quantification
A PINN transfer learning framework for coal methane sorption reaches R²=0.932 on held-out data with 227% improvement over classical isotherms and identifies Monte Carlo Dropout as the best uncertainty method while ensembles degrade under shared physics constraints.
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A Statistical-AI Framework for Detecting Transient Flares in SDSS Stripe 82 Quasar Light Curves
A modular framework combining physics-informed neural networks, Ornstein-Uhlenbeck fitting, extreme value theory, and vision-language models detects 51 transient flares in 9,258 SDSS Stripe 82 quasar light curves.
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Cell-induced densification and tether formation in fibrous extracellular matrices with biomimetic physics-informed neural networks
Bio-PINNs with a near-to-far curriculum and deformation-uncertainty proxy recover cell-induced densified phases and tether morphologies more reliably than standard adaptive PINN baselines in single-cell and multicellular settings.
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Physics-Informed Neural Networks for Maximizing Quantum Fisher Information in Time-Dependent Many-Body Systems
PINNs combined with Magnus expansion learn scheduling functions and adiabatic gauge potentials that yield higher normalized QFI than Euler-Lagrange baselines in nearest-neighbor, dipolar, and trapped-ion spin models up to six qubits.
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Balance-Guided Sparse Identification of Multiscale Nonlinear PDEs with Small-coefficient Terms
BG-SINDy reformulates l0-constrained regression as term-level l2,0 regularization and uses progressive pruning guided by balance contributions to recover small-coefficient terms in multiscale PDEs.
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Curvature-Aware Optimization for High-Accuracy Physics-Informed Neural Networks
Curvature-aware optimizers such as natural gradient and self-scaling BFGS/Broyden accelerate PINN convergence and accuracy on PDEs including Helmholtz, Stokes, Burgers, and Euler equations plus stiff ODEs, with new model formulations and batched scaling.
- Learning PDEs for Portfolio Optimization with Quantum Physics-Informed Neural Networks