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.
Canonical reference
Physics-informed machine learning
Canonical reference. 80% of citing Pith papers cite this work as background.
29
Pith papers citing it
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external citations · Crossref
Background
80% of classified citations
citation-role summary
background 12
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citation-polarity summary
representative citing papers
A cross-attention-based bipartite GNN predicts coupled nodal displacement increments and elemental thinning directly on their native mesh domains for sheet material forming.
TokaMind, pre-trained on MAST tokamak data, transfers to power grid PMU data for severe event classification with F1 0.837, where difficulty depends on grid topology and CSD indicators boost early-warning performance over CNN baselines.
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.
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 stability-derived CPINN framework for Oseen problems yields pressure-robust velocity approximations and optimal error rates in H^1 for velocity and L^2 for pressure under Besov regularity.
NHODE framework learns partially observed dynamical systems by combining Hamiltonian neural networks with neural ODEs, enforcing energy conservation and improving long-horizon stability over data-driven baselines on mass-spring and three-body problems.
A thermodynamics-constrained ML framework learns robust, consistent constitutive models for inelastic materials from macroscopic stress-strain data and generalizes to unseen paths.
PG-3DGS couples 3D Gaussian Splatting with differentiable physics so that optimized shapes satisfy both visual fidelity and physical objectives such as pouring and aerodynamic lift, with real-world 3D-printed validation.
ShardTensor is a domain-parallelism system for SciML that enables flexible scaling of extreme-resolution spatial datasets by removing the constraint of batch size one per device.
OGCVL integrates symbolic and numerical techniques to learn effective nonlinear controlled variables for scalable self-optimizing control in chemical processes.
An informed autoencoder estimates subject-specific motor unit parameters from surface EMG by reconstructing signals in a latent space that respects physical laws relating parameters to observed signals.
MuFiNNs integrates sparse experimental measurements with structured low-fidelity models via hierarchical construction and nonlinear correction to predict 3D flame wrinkling dynamics and turbulent mass burning velocity across fuels, pressures, and turbulence levels.
A specialized PINN architecture solves the spatially inhomogeneous electron Boltzmann equation with high accuracy across gases and electric field strengths without case-specific tuning.
A new scale-aware diagnostic framework shows that unconstrained diffusion generative models exhibit structural freezing and instability instead of smooth physical responses under multiscale perturbations.
K-STEMIT reduces RMSE by 21% for subsurface stratigraphy thickness estimation from radar data via a knowledge-informed spatio-temporal GNN with adaptive feature fusion and physical priors from the MAR weather model.
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.
PG-TMT couples a physics-aligned tri-branch encoder with EVT-calibrated decision rules to achieve higher PR-AUC and shorter detection times at controlled false-alarm rates across multiple bearing datasets.
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.
Analysis of the September 6, 2011 coronal wave with the SOLERwave multi-sector method reveals over 40% speed variation (750-1500 km/s) between northward and northwestward segments, attributed to differences in magnetosonic speed from an MHD solution.
A generative optimization loop using diffusion models, PINNs, and GNNs achieves 85.6% of fourth-order Qiskit fidelity at 21.8% circuit depth for transverse-field Ising model Trotter-Suzuki decomposition.
A two-stage PINN optimizes pulse sequences for silicon exchange-only spin qubits to achieve over 99% noise-averaged fidelity while shortening pulse durations by 20-40%.
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.
A multi-agent LLM framework autonomously completes the full computational mechanics pipeline from a photograph to a code-compliant engineering report on a steel L-bracket example.
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.
-
Cross-attention-based bipartite graph neural network for coupled nodal and elemental field prediction in large-deformation sheet material forming
A cross-attention-based bipartite GNN predicts coupled nodal displacement increments and elemental thinning directly on their native mesh domains for sheet material forming.
-
TokaMind for Power Grid: Cross-Domain Transfer from Fusion Plasma
TokaMind, pre-trained on MAST tokamak data, transfers to power grid PMU data for severe event classification with F1 0.837, where difficulty depends on grid topology and CSD indicators boost early-warning performance over CNN baselines.
-
A Deep Risk Estimator for Known Operator Learning
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.
-
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.
-
Structure-Preserving and Pressure-Robust PINNs for Incompressible Oseen Problems
A stability-derived CPINN framework for Oseen problems yields pressure-robust velocity approximations and optimal error rates in H^1 for velocity and L^2 for pressure under Besov regularity.
-
Learning partially observed systems with neural Hamiltonian ordinary differential equations
NHODE framework learns partially observed dynamical systems by combining Hamiltonian neural networks with neural ODEs, enforcing energy conservation and improving long-horizon stability over data-driven baselines on mass-spring and three-body problems.
-
Learning inelastic constitutive models from stress-strain data under hard thermodynamic constraints
A thermodynamics-constrained ML framework learns robust, consistent constitutive models for inelastic materials from macroscopic stress-strain data and generalizes to unseen paths.
-
PG-3DGS: Optimizing 3D Gaussian Splatting to Satisfy Physics Objectives
PG-3DGS couples 3D Gaussian Splatting with differentiable physics so that optimized shapes satisfy both visual fidelity and physical objectives such as pouring and aerodynamic lift, with real-world 3D-printed validation.
-
ShardTensor: Domain Parallelism for Scientific Machine Learning
ShardTensor is a domain-parallelism system for SciML that enables flexible scaling of extreme-resolution spatial datasets by removing the constraint of batch size one per device.
-
Generalized Global Self-Optimizing Control for Chemical Processes: Part II Objective-Guided Controlled Variable Learning Approach
OGCVL integrates symbolic and numerical techniques to learn effective nonlinear controlled variables for scalable self-optimizing control in chemical processes.
-
Estimation of Motor Unit Parameters from Surface Electromyograms using an Informed Autoencoder
An informed autoencoder estimates subject-specific motor unit parameters from surface EMG by reconstructing signals in a latent space that respects physical laws relating parameters to observed signals.
-
Hierarchical Multi-Fidelity Learning for Predicting Three-Dimensional Flame Wrinkling and Turbulent Burning Velocity
MuFiNNs integrates sparse experimental measurements with structured low-fidelity models via hierarchical construction and nonlinear correction to predict 3D flame wrinkling dynamics and turbulent mass burning velocity across fuels, pressures, and turbulence levels.
-
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.
-
Scale-Aware Adversarial Analysis: A Diagnostic for Generative AI in Multiscale Complex Systems
A new scale-aware diagnostic framework shows that unconstrained diffusion generative models exhibit structural freezing and instability instead of smooth physical responses under multiscale perturbations.
-
K-STEMIT: Knowledge-Informed Spatio-Temporal Efficient Multi-Branch Graph Neural Network for Subsurface Stratigraphy Thickness Estimation from Radar Data
K-STEMIT reduces RMSE by 21% for subsurface stratigraphy thickness estimation from radar data via a knowledge-informed spatio-temporal GNN with adaptive feature fusion and physical priors from the MAR weather model.
-
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.
-
Physics-Guided Tiny-Mamba Transformer for Reliability-Aware Early Fault Warning
PG-TMT couples a physics-aligned tri-branch encoder with EVT-calibrated decision rules to achieve higher PR-AUC and shorter detection times at controlled false-alarm rates across multiple bearing datasets.
-
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.
-
Investigation of the Two-Dimensional Velocity Field of the Large-Scale Coronal Wave from September 6, 2011 using the SOLERwave Tool
Analysis of the September 6, 2011 coronal wave with the SOLERwave multi-sector method reveals over 40% speed variation (750-1500 km/s) between northward and northwestward segments, attributed to differences in magnetosonic speed from an MHD solution.
-
Physics Guided Generative Optimization for Trotter Suzuki Decomposition
A generative optimization loop using diffusion models, PINNs, and GNNs achieves 85.6% of fourth-order Qiskit fidelity at 21.8% circuit depth for transverse-field Ising model Trotter-Suzuki decomposition.
-
Exchange-Only Silicon Based Spin Qubits: Charge Noise, PINN Optimised Pulse Sequences,and Gate-Level Fidelity
A two-stage PINN optimizes pulse sequences for silicon exchange-only spin qubits to achieve over 99% noise-averaged fidelity while shortening pulse durations by 20-40%.
-
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.
-
From Perception to Autonomous Computational Modeling: A Multi-Agent Approach
A multi-agent LLM framework autonomously completes the full computational mechanics pipeline from a photograph to a code-compliant engineering report on a steel L-bracket example.
-
FEDONet : Fourier-Embedded DeepONet for Spectrally Accurate Operator Learning
FEDONet augments DeepONet with Fourier-embedded trunk networks using random Fourier features, yielding lower L2 reconstruction errors than standard DeepONet on Burgers', 2D Poisson, Eikonal, Allen-Cahn, and Kuramoto-Sivashinsky equations across dataset sizes and noise levels.
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How it cools? Studying the heat flow out of a semi-infinite slab in welding: An analytical approach
Closed-form solutions for transient and steady-state heat flow out of a semi-infinite slab with Newton's cooling boundary conditions are derived for multiple heat source types.
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Amalgamation of Physics-Informed Neural Network and LBM for the Prediction of Unsteady Fluid Flows in Fractal-Rough Microchannels
A physics-informed neural network merges sparse LBM data with Navier-Stokes equations to predict unsteady flows in fractal-rough microchannels at 150-200 times lower data cost.
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Farm-wide virtual load monitoring for offshore wind structures via Bayesian neural networks
Bayesian neural networks enable farm-wide virtual load monitoring by predicting structural loads on non-instrumented offshore wind turbines from a fleet-leader's data while quantifying prediction uncertainty.
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AI-Powered Surrogate Modelling for Multiscale Combustion: A Critical Review and Opportunities
A critical review of AI surrogate models for multiscale combustion that compares supervised, unsupervised, and physics-guided methods, identifies transferability and consistency challenges, and outlines future opportunities.