Extends structural identifiability analysis to functional components of differential equation models and characterizes conditions for unique recovery using differential algebra techniques.
Mixed citations
Physics-Informed Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations
Mixed citation behavior. Most common role is background (62%).
159
Pith papers citing it
14.7k
external citations · Crossref
Background
62% of classified citations
citation-role summary
background 22
method 12
citation-polarity summary
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.
Structural identifiability analysis shows point sources restore identifiability for inferring spatial stochastic dynamics parameters from static snapshots, unlike distributed sources, with limits depending on modeling choices.
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 linear POD encoding plus LassoNet-enforced sparse nonlinear neural decoding to select informative modes and cut reconstruction error on advection-dominated and turbulent flows.
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.
A variational physics-informed neural network using Kolosov-Muskhelishvili potentials is introduced for 2D linear elasticity and fracture problems, embedding crack conditions directly into the ansatz.
citing papers explorer
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Time-Frequency Analysis for Neural Networks
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.
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PVD-ONet: A Multi-scale Neural Operator Method for Singularly Perturbed Boundary Layer Problems
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.
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Input convex neural networks: universal approximation theorem and implementation for isotropic polyconvex hyperelastic energies
Input-convex neural networks in elementary polynomials of signed singular values provably approximate any frame-indifferent isotropic polyconvex hyperelastic energy.
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SuNeRF-CME: Physics-Informed Neural Radiance Fields for Tomographic Reconstruction of Coronal Mass Ejections
SuNeRF-CME uses physics-informed NeRFs with ray-tracing for Thomson scattering and constraints on plasma continuity, direction, and speed to enable tomographic 3D reconstruction of CMEs from as few as two viewpoints, validated on synthetic data with low parameter errors.
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MD-PNOP: Equation-Recast Neural Operators for Minimal-Data Extrapolation and PDE Solver Acceleration
MD-PNOP recasts parameter-induced operator differences as source terms to enable single-configuration neural operator training for extrapolation and acceleration of parametric PDE solvers.
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Physics-Informed Neural Networks for Device and Circuit Modeling: A Case Study of NeuroSPICE
NeuroSPICE uses PINNs to solve circuit DAEs via residual minimization, creating surrogate models for optimization and handling nonlinear emerging devices.
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Physics Priors Offer Useful Accuracy-Carbon Trade-Offs in Spatio-Temporal Forecasting
Stronger physics priors in neural networks for spatio-temporal shear flow forecasting yield substantially lower training carbon footprints than weak or no priors, though inference savings are less consistent.
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Process-Informed Forecasting of Complex Thermal Dynamics in Pharmaceutical Manufacturing
Process-Informed Forecasting models incorporating deterministic production recipe priors outperform ARIMA and deep learning baselines in accuracy, physical plausibility, and noise resilience for temperature forecasting in pharmaceutical lyophilization.
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Physics-informed neural network (PINN) modeling of charged particle multiplicity using the two-component framework in heavy-ion collisions: A comparison with data-driven neural networks
A PINN constrained by the two-component multiplicity model learns the hard-scattering fraction from Zr+Zr events and predicts N_ch more accurately than a data-driven NN on unseen Ru+Ru and Au+Au collisions.
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Time Series Forecasting Through the Lens of Dynamics
Proposes dynamics-based analysis of time series models showing partial dynamics learning and end-positioning as key to performance, plus a plug-and-play improvement method.
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Benchmarking Physics-Informed Neural Networks and Boundary Elements Methods for Wave Scattering
Side-by-side timing comparison finds BEM solves the scattering problem in ~0.01 s while PINN training takes ~100 s, but trained PINN evaluates interior points ~100x faster than BEM.
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A review of quantum machine learning and quantum-inspired applied methods to computational fluid dynamics
A survey of variational quantum algorithms, quantum neural networks, and tensor networks for addressing scalability challenges in computational fluid dynamics.