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
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.
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.
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.
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.
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.
-
FactoryNet: A Large-Scale Dataset toward Industrial Time-Series Foundation Models
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.
-
Optimal scenario design for climate emulation
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.
-
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.
-
Domain-Validity-Gated Metamorphic Testing of Scientific ML Surrogates
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.
-
Learning Where to Simulate: Generative Active Sampling for Online PDE Surrogate Training
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.
-
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.
-
RRISE: Robust Radius Inference via a Surrogate Estimator
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.
-
Fast Reconstruction of Exact Maxwell Dynamics from Sparse Data
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: Efficient Pipeline Parallel Training for Machine Learning Interatomic Potentials
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.
-
Identify Then Project: Contrastive Learning of Latent Dynamics from Partial Observations with Port-Hamiltonian Structure
A two-stage contrastive teacher-student framework learns and then projects latent dynamics onto port-Hamiltonian submanifolds from partial observations.
-
Identifying the nonlinear string dynamics with port-Hamiltonian neural networks
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 Low-Rank Structure and Neural-Operator Representation of Rarefied Micro-Nozzle Flows
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 multi-fidelity framework for uncertainty quantification of wildfire spread
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.
-
Posterior Concentration of Bayesian Physics-Informed Neural Networks for Elliptic PDEs
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 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.
-
DualTCN: A Physics-Constrained Temporal Convolutional Network for 2 Time-Domain Marine CSEM Inversion
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.
-
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.
-
TCD-Arena: Assessing Robustness of Time Series Causal Discovery Methods Against Assumption Violations
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 Fourier Neural Operator-Lattice Boltzmann Method
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
Quasi-equivariant metanetworks relax strict equivariance to preserve functional identity in weight-space learning while improving expressivity for feedforward, convolutional, and transformer networks.
-
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.
-
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.
-
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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Learning PDEs for Portfolio Optimization with Quantum Physics-Informed Neural Networks
Quantum PINNs using tensor-rank polynomials solve the Merton portfolio optimization PDE more accurately and with far fewer parameters than classical neural networks.
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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.
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Transfer-learned Kolosov-Muskhelishvili Informed Neural Networks for Fracture Mechanics
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.
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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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Mosaic: A Benchmark Suite for Differentiable Physics Solvers
Mosaic is a benchmark suite evaluating 14 differentiable PDE solvers across fluids, structures, and heat transfer, showing large variations in cost and conditioning but similar convergence behavior.
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What Do Language Priors Contribute to Darcy-Flow Inversion? A Mechanistic Audit
Sentence embeddings reduce reconstruction error by 81% in Darcy-flow inversion by providing categorical geological constraints, with limited added value from within-class text detail.
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Topological Out-of-Domain Generalization in Dynamical Systems Reconstruction
Proposes feature splitting and a closed-form bound on extrapolation range to enable zero-shot topological out-of-domain generalization in dynamical systems reconstruction across tipping points.
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Constrained hybrid modelling to predict microbial dynamics and organic matter turnover in soil systems
Hybrid neural-process model derives biokinetic parameters from genomic traits for soil organic matter turnover, with ecological constraints, and outperforms baselines on synthetic and real data.
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INDEQS: Informed Neural controlled Differential EQuationS
INDEQS is a graph-informed NCDE variant that separates inner hidden-state mixing from outer vector-field mixing and reports lower MAE than uninformed NCDEs on synthetic advection data and real river/traffic tasks when the graph is known.
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Reconstructing Galactic Gravitational Potentials from Stellar Kinematics with Physics-Informed Neural Networks
A PINN approach learns galactic gravitational potentials from acceleration data, achieving sub-percent errors on simulations while outperforming analytic models and retaining interpretability via structured priors.
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A Diagnostic Software Suite for Auditing Learned PDE Simulators
Introduces an architecture-independent diagnostic software suite for auditing learned PDE simulators via checks like semigroup consistency and energy behavior, validated on five benchmark PDE tasks where L2 error alone proves insufficient.
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Joint reconstruction of $H(z)$ and $f\sigma_8(z)$ with physics informed neural networks
PINN-based joint reconstruction of H(z) and fσ8(z) coupled through the GR growth equation recovers the input H0 prior exactly, yields fσ8(z) below ΛCDM at all redshifts, and shows Om(z) departure from flat ΛCDM at low z.
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RepNN: Tackling spectral bias in deep neural networks via parameter reparameterization
RepNN reparameterizes the first hidden layer of DNNs to enable adaptive frequency scaling, improving accuracy on oscillatory and multiscale functions with minimal extra cost.
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Non-linear mechanical field reconstruction coupling recurrent neural networks with physics-informed graph neural networks
A coupled LSTM-GNN model reconstructs local elasto-plastic stress fields from macroscopic loading paths on a plate-with-hole microstructure, achieving 1000x speedup and mesh transferability with 1.9% error.
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A Physics-Informed B-Spline Framework for Continuous Approximation of Flow Data
PI-MFA optimizes tensor-product B-spline control points to balance data fidelity against PDE residuals, producing physically consistent continuous flow fields.
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Input-schema identifiability limits in physics-informed surrogates for mechanics-governed flow
The authors develop an input-schema identifiability certificate for physics-informed surrogates that decomposes lumen velocity in tubular flow into mesh-measurable tangent direction, boundary-condition-dependent magnitude, and signed-orientation ambiguity using a Cosserat-rod reduction.
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Self-Evolving Scientific Agent Discovers Generalizable Physically-Reasoned Fluid Control
An LLM-based self-evolving agent discovers a traveling-wave controller with body-frame guidance and yaw feedback that generalizes to unseen targets for an underactuated fluid swimmer.
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PDE-Agents: An LLM-Orchestrated Multi-Agent Framework for Automated Finite Element Simulations with Knowledge Graph-Augmented Reasoning
PDE-Agents shows a LangGraph-orchestrated multi-agent LLM framework with GraphRAG that reaches 100% task success and perfect material fidelity on novel materials in ablation tests, with 97.8% success across 1369 production runs.
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DAS-PINNs for high-dimensional partial differential equations: extending deep adaptive sampling to spacetime domains
DAS-PINNs uses normalizing flows to adaptively sample collocation points based on PDE residuals in unified spacetime domains for high-dimensional time-dependent PDEs.
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DiffSlack: Learning under Nonlinear Inequality Constraints via Learnable Slack Variables
DiffSlack introduces learnable slack variables and a damped Gauss-Newton projection to create a differentiable layer that enforces hard nonlinear inequality constraints in neural network outputs.
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Accelerating physics-informed neural networks for full waveform inversion using a hybrid quantum-classical finite-basis architecture
Hybrid quantum-classical FBPINN for acoustic FWI achieves lower L1 velocity error than classical baselines in ~8x fewer iterations with ~33% fewer parameters on anomaly and checkerboard benchmarks.
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MedGym:A Unified Continuous-Time Benchmark for Dynamic Medical Treatment Reinforcement Learning
MedGym introduces a continuous-time RL benchmark for medical treatment derived from clinical data via PINNs, supporting offline/online evaluation on personalization, safety, and discrete vs continuous methods.
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Oscillatory State-Space Models as Inductive Biases for Physics-Informed Neural PDE Solvers
Oscillatory state-space models with PDE-aware spectral bases are introduced as inductive biases for PINNs, yielding improved accuracy and lower memory on forward, inverse, and up to 100D PDE tasks.
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Scalable Bayesian Inference for Nonlinear Conservation Laws
Introduces a scalable Bayesian inference framework for nonlinear conservation laws using Gaussian process priors and sparse approximations, enabling accurate forward simulations with UQ and fast posterior recovery on inverse problems.