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.
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18 Pith papers cite this work, alongside 2,027 external citations. Polarity classification is still indexing.
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cs.LG 8 physics.comp-ph 2 physics.flu-dyn 2 quant-ph 2 cond-mat.mtrl-sci 1 cs.CE 1 math.NA 1 physics.app-ph 1years
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The curvature-aware precision controller adapts between FP32 and FP64 during PINN training to match double-precision accuracy at reduced computational cost.
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.
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.
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 physics-informed self-supervised framework learns detector calibration parameters and ionic charge-state predictions jointly from raw spectrometer data using iterative pseudo-labelling driven by physical constraints.
SPLIT-PINN infers drift fields in Liouville transport equations from data using marginal corrections and orthogonality constraints to enable probabilistic predictions of microstructural evolution across polycrystal realizations.
P-GONE applies generative ML to optimize Trotter-Suzuki decompositions, reporting up to 19.4x circuit depth reduction at F >= 0.95 versus Qiskit baselines on structured Hamiltonians.
AW-PINN uses dynamic wavelet basis adaptation in PINNs to solve PDEs with localized high-magnitude sources, outperforming prior methods on loss imbalances up to 10^10:1 while deriving a Gaussian process limit and NTK structure under assumptions.
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.
AutoSurrogate is a multi-agent LLM framework that autonomously constructs, tunes, and validates deep learning surrogates for subsurface flow from natural language, outperforming expert baselines on a 3D carbon storage task.
MI-VAE generates physics-constrained synthetic trajectories from scarce real data to improve offline RL policy performance on planetary lander tasks over standard VAEs.
HQPINNs reduce relative L2 error by roughly fourfold on Burgers' equation and fivefold on Allen-Cahn equation versus classical PINNs, with smoother training and largest gains in stiff regimes.
Systematic benchmark of PINN architectures on 1D stiff PNP system finds BRDR loss weighting competitive with NTK at lower wall-clock time.
PINN and adjoint-state methods reconstruct bottom topography and surface velocity from surface measurements in the shallow-water equations, with robustness to noise and sparsity on synthetic data.
Reviews linear and nonlinear SciML surrogates for coupled fluid flow and transport, with new PINN modeling of turbidity currents and β-VAE mode extraction from Rayleigh-Bénard convection.
PINNs for first-order plane-strain elastodynamics achieve higher accuracy with soft boundary enforcement over implicit geometries but require longer training than hard enforcement.
A scoping review of physics-informed machine learning for seismic wave propagation finds applications in forward and inverse problems with often comparable accuracy at lower cost, while identifying gaps in benchmarking, training cost, and 3D/experimental validation.
citing papers explorer
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A Convex Quasilinearization Method for Solving Nonlinear PDEs with Physics-Informed Neural Networks
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.
-
Curvature-aware dynamic precision approach for physics-informed neural networks
The curvature-aware precision controller adapts between FP32 and FP64 during PINN training to match double-precision accuracy at reduced computational cost.
-
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.
-
A Variational Kolosov--Muskhelishvili Network for Elasticity and Fracture
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.
-
Resolving Cryogenic and Hypersonic Rarefied Flows via Deep Learning-Accelerated Lennard-Jones DSMC
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.
-
Self-Supervised Calibration of Scientific Instruments Using Physical Consistency Constraints
A physics-informed self-supervised framework learns detector calibration parameters and ionic charge-state predictions jointly from raw spectrometer data using iterative pseudo-labelling driven by physical constraints.
-
SPLIT-PINN: Separable Probability Learning Technique via Physics-Informed Neural Networks for High-Dimensional Probabilistic Modeling
SPLIT-PINN infers drift fields in Liouville transport equations from data using marginal corrections and orthogonality constraints to enable probabilistic predictions of microstructural evolution across polycrystal realizations.
-
Physics Guided Generative Optimization for Trotter Suzuki Decomposition
P-GONE applies generative ML to optimize Trotter-Suzuki decompositions, reporting up to 19.4x circuit depth reduction at F >= 0.95 versus Qiskit baselines on structured Hamiltonians.
-
An adaptive wavelet-based PINN for problems with localized high-magnitude source
AW-PINN uses dynamic wavelet basis adaptation in PINNs to solve PDEs with localized high-magnitude sources, outperforming prior methods on loss imbalances up to 10^10:1 while deriving a Gaussian process limit and NTK structure under assumptions.
-
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.
-
AutoSurrogate: An LLM-Driven Multi-Agent Framework for Autonomous Construction of Deep Learning Surrogate Models in Subsurface Flow
AutoSurrogate is a multi-agent LLM framework that autonomously constructs, tunes, and validates deep learning surrogates for subsurface flow from natural language, outperforming expert baselines on a 3D carbon storage task.
-
Mitigating Data Scarcity in Spaceflight Applications for Offline Reinforcement Learning Using Physics-Informed Deep Generative Models
MI-VAE generates physics-constrained synthetic trajectories from scarce real data to improve offline RL policy performance on planetary lander tasks over standard VAEs.
-
Hybrid quantum-classical physics-informed neural networks for solving nonlinear PDEs: when and where hybridization is effective?
HQPINNs reduce relative L2 error by roughly fourfold on Burgers' equation and fivefold on Allen-Cahn equation versus classical PINNs, with smoother training and largest gains in stiff regimes.
-
A Systematic Benchmark of Physics-Informed Neural Network Architectures for the Stiff Poisson-Nernst-Planck System: Adaptive LossWeighting and Multi-Scale Resolution
Systematic benchmark of PINN architectures on 1D stiff PNP system finds BRDR loss weighting competitive with NTK at lower wall-clock time.
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Estimating bottom topography in shallow water flows
PINN and adjoint-state methods reconstruct bottom topography and surface velocity from surface measurements in the shallow-water equations, with robustness to noise and sparsity on synthetic data.
-
Advances in Scientific Machine Learning for Coupled Fluid Flow and Transport
Reviews linear and nonlinear SciML surrogates for coupled fluid flow and transport, with new PINN modeling of turbidity currents and β-VAE mode extraction from Rayleigh-Bénard convection.
-
Exact Boundary Enforcement Along Implicit Geometries for Physics-Informed, Deep Learning Problems in Continuum Mechanics
PINNs for first-order plane-strain elastodynamics achieve higher accuracy with soft boundary enforcement over implicit geometries but require longer training than hard enforcement.
-
A Scoping Review of Physics Informed Machine Learning for Wave Propagation Modeling in Seismology
A scoping review of physics-informed machine learning for seismic wave propagation finds applications in forward and inverse problems with often comparable accuracy at lower cost, while identifying gaps in benchmarking, training cost, and 3D/experimental validation.