{"total":89,"rows":[{"id":"2308.05732","title":"PDE-Refiner: Achieving Accurate Long Rollouts with Neural PDE Solvers","created":"2023-08-10","cited_by_count":216,"area":"diffusion"},{"id":"2203.07404","title":"Respecting causality is all you need for training physics-informed neural networks","created":"2022-03-14","cited_by_count":156,"area":null},{"id":"2211.08064","title":"Physics-Informed Machine Learning: A Survey on Problems, Methods and Applications","created":"2022-11-15","cited_by_count":92,"area":null},{"id":"2407.07218","title":"Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations","created":"2024-07-09","cited_by_count":91,"area":null},{"id":"2201.01032","title":"Learning Operators with Coupled Attention","created":"2022-01-04","cited_by_count":90,"area":null},{"id":"2110.01654","title":"Improved architectures and training algorithms for deep operator networks","created":"2021-10-04","cited_by_count":86,"area":null},{"id":"2209.14855","title":"Continuous PDE Dynamics Forecasting with Implicit Neural Representations","created":"2022-09-29","cited_by_count":73,"area":null},{"id":"2205.11393","title":"Generic bounds on the approximation error for physics-informed (and) operator learning","created":"2022-05-23","cited_by_count":65,"area":null},{"id":"2203.09346","title":"Error estimates for physics informed neural networks approximating the Navier-Stokes equations","created":"2022-03-17","cited_by_count":63,"area":null},{"id":"2204.09157","title":"Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problems","created":"2022-04-19","cited_by_count":58,"area":null},{"id":"2107.01272","title":"Physics-Guided Deep Learning for Dynamical Systems: A Survey","created":"2021-07-02","cited_by_count":44,"area":null},{"id":"2206.00711","title":"Learning to Solve PDE-constrained Inverse Problems with Graph Networks","created":"2022-06-01","cited_by_count":37,"area":null},{"id":"2204.12670","title":"SVD Perspectives for Augmenting DeepONet Flexibility and Interpretability","created":"2022-04-27","cited_by_count":35,"area":null},{"id":"2210.00124","title":"Implicit Neural Spatial Representations for Time-dependent PDEs","created":"2022-09-30","cited_by_count":35,"area":null},{"id":"2110.13361","title":"A Metalearning Approach for Physics-Informed Neural Networks (PINNs): Application to Parameterized PDEs","created":"2021-10-26","cited_by_count":32,"area":null},{"id":"2303.02243","title":"Neural Operator Learning for Long-Time Integration in Dynamical Systems with Recurrent Neural Networks","created":"2023-03-03","cited_by_count":32,"area":null},{"id":"2207.08483","title":"wPINNs: Weak Physics informed neural networks for approximating entropy solutions of hyperbolic conservation laws","created":"2022-07-18","cited_by_count":29,"area":null},{"id":"2212.04663","title":"Transfer Learning Enhanced DeepONet for Long-Time Prediction of Evolution Equations","created":"2022-12-09","cited_by_count":28,"area":null},{"id":"2204.00997","title":"Bi-fidelity Modeling of Uncertain and Partially Unknown Systems using DeepONets","created":"2022-04-03","cited_by_count":27,"area":null},{"id":"2110.13297","title":"Fast PDE-constrained optimization via self-supervised operator learning","created":"2021-10-25","cited_by_count":25,"area":null},{"id":"2311.06483","title":"Stacked networks improve physics-informed training: applications to neural networks and deep operator networks","created":"2023-11-11","cited_by_count":21,"area":null},{"id":"2303.07127","title":"Improving physics-informed neural networks with meta-learned optimization","created":"2023-03-13","cited_by_count":19,"area":null},{"id":"2302.03598","title":"Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations","created":"2023-01-11","cited_by_count":16,"area":null},{"id":"2505.17341","title":"TI-DeepONet: Learnable Time Integration for Stable Long-Term Extrapolation","created":"2025-05-22","cited_by_count":14,"area":null},{"id":"2210.08095","title":"Bayesian Spline Learning for Equation Discovery of Nonlinear Dynamics with Quantified Uncertainty","created":"2022-10-14","cited_by_count":13,"area":null},{"id":"2301.12538","title":"On Approximating the Dynamic Response of Synchronous Generators via Operator Learning: A Step Towards Building Deep Operator-based Power Grid Simulators","created":"2023-01-29","cited_by_count":13,"area":null},{"id":"2304.03894","title":"A multifidelity approach to continual learning for physical systems","created":"2023-04-08","cited_by_count":13,"area":null},{"id":"2311.14131","title":"Exactly conservative physics-informed neural networks and deep operator networks for dynamical systems","created":"2023-11-23","cited_by_count":13,"area":null},{"id":"2501.06572","title":"Evolutionary Optimization of Physics-Informed Neural Networks: Evo-PINN Frontiers and Opportunities","created":"2025-01-11","cited_by_count":11,"area":null},{"id":"2110.01601","title":"NeuFENet: Neural Finite Element Solutions with Theoretical Bounds for Parametric PDEs","created":"2021-10-04","cited_by_count":10,"area":null},{"id":"2505.02308","title":"Enabling Local Neural Operators to perform Equation-Free System-Level Analysis","created":"2025-05-05","cited_by_count":10,"area":null},{"id":"2306.09478","title":"Understanding and Mitigating Extrapolation Failures in Physics-Informed Neural Networks","created":"2023-06-15","cited_by_count":9,"area":null},{"id":"2309.07899","title":"Improving physics-informed DeepONets with hard constraints","created":"2023-09-14","cited_by_count":9,"area":null},{"id":"2303.11577","title":"Feature-adjacent multi-fidelity physics-informed machine learning for partial differential equations","created":"2023-03-21","cited_by_count":8,"area":null},{"id":"2210.15799","title":"Adaptive physics-informed neural operator for coarse-grained non-equilibrium flows","created":"2022-10-27","cited_by_count":7,"area":null},{"id":"2303.16110","title":"Invariant preservation in machine learned PDE solvers via error correction","created":"2023-03-28","cited_by_count":7,"area":null},{"id":"2406.14715","title":"An Advanced Physics-Informed Neural Operator for Comprehensive Design Optimization of Highly-Nonlinear Systems: An Aerospace Composites Processing Case Study","created":"2024-06-20","cited_by_count":6,"area":null},{"id":"2208.03296","title":"Accelerating discrete dislocation dynamics simulations with graph neural networks","created":"2022-08-05","cited_by_count":5,"area":null},{"id":"2211.09928","title":"SMS: Spiking Marching Scheme for Efficient Long Time Integration of Differential Equations","created":"2022-11-17","cited_by_count":5,"area":null},{"id":"2410.05281","title":"Micrometer: Micromechanics Transformer for Predicting Mechanical Responses of Heterogeneous Materials","created":"2024-09-23","cited_by_count":5,"area":null},{"id":"2411.19125","title":"Advancing Generalization in PINNs through Latent-Space Representations","created":"2024-11-28","cited_by_count":5,"area":null},{"id":"2508.05190","title":"Physics-Informed Time-Integrated DeepONet: Temporal Tangent Space Operator Learning for High-Accuracy Inference","created":"2025-08-07","cited_by_count":5,"area":null},{"id":"2602.13616","title":"DiffusionRollout: Uncertainty-Aware Rollout Planning in Long-Horizon PDE Solving","created":"2026-02-14","cited_by_count":5,"area":"diffusion"},{"id":"2210.07880","title":"Tunable Complexity Benchmarks for Evaluating Physics-Informed Neural Networks on Coupled Ordinary Differential Equations","created":"2022-10-14","cited_by_count":4,"area":null},{"id":"2401.07888","title":"Multifidelity domain decomposition-based physics-informed neural networks and operators for time-dependent problems","created":"2024-01-15","cited_by_count":4,"area":null},{"id":"2404.10771","title":"TENG: Time-Evolving Natural Gradient for Solving PDEs With Deep Neural Nets Toward Machine Precision","created":"2024-04-16","cited_by_count":4,"area":null},{"id":"2405.02810","title":"Adaptive deep density approximation for stochastic dynamical systems","created":"2024-05-05","cited_by_count":4,"area":null},{"id":"2412.16787","title":"Symplectic Neural Flows for Modeling and Discovery","created":"2024-12-21","cited_by_count":4,"area":null},{"id":"2304.09070","title":"M-ENIAC: A machine learning recreation of the first successful numerical weather forecasts","created":"2023-04-18","cited_by_count":3,"area":null},{"id":"2308.06447","title":"A Sequential Meta-Transfer (SMT) Learning to Combat Complexities of Physics-Informed Neural Networks: Application to Composites Autoclave Processing","created":"2023-08-12","cited_by_count":3,"area":null},{"id":"2406.03407","title":"Physics and geometry informed neural operator network with application to acoustic scattering","created":"2024-06-02","cited_by_count":3,"area":null},{"id":"2411.18459","title":"What do physics-informed DeepONets learn? Understanding and improving training for scientific computing applications","created":"2024-11-27","cited_by_count":3,"area":null},{"id":"2503.17402","title":"Enhanced Vascular Flow Simulations in Aortic Aneurysm via Physics-Informed Neural Networks and Deep Operator Networks","created":"2025-03-19","cited_by_count":3,"area":null},{"id":"2602.05052","title":"Learning, Solving and Optimizing PDEs with TensorGalerkin: an efficient high-performance Galerkin assembly algorithm","created":"2026-02-04","cited_by_count":3,"area":null},{"id":"2308.09367","title":"On the Approximation of Bi-Lipschitz Maps by Invertible Neural Networks","created":"2023-08-18","cited_by_count":2,"area":null},{"id":"2310.04990","title":"Waveformer for modelling dynamical systems","created":"2023-10-08","cited_by_count":2,"area":null},{"id":"2409.02810","title":"A hybrid FEM-PINN method for time-dependent partial differential equations","created":"2024-09-04","cited_by_count":2,"area":null},{"id":"2501.14604","title":"Inverse Evolution Data Augmentation for Neural PDE Solvers","created":"2025-01-24","cited_by_count":2,"area":null},{"id":"2403.12764","title":"Neural Parameter Regression for Explicit Representations of PDE Solution Operators","created":"2024-03-19","cited_by_count":1,"area":null},{"id":"2404.17535","title":"Using Neural Implicit Flow To Represent Latent Dynamics Of Canonical Systems","created":"2024-04-26","cited_by_count":1,"area":null},{"id":"2408.10011","title":"PinnDE: Physics-Informed Neural Networks for Solving Differential Equations","created":"2024-08-19","cited_by_count":1,"area":null},{"id":"2409.00994","title":"Physics-informed DeepONet with stiffness-based loss functions for structural response prediction","created":"2024-09-02","cited_by_count":1,"area":null},{"id":"2410.15617","title":"Long-time Integration of Nonlinear Wave Equations with Neural Operators","created":"2024-10-21","cited_by_count":1,"area":null},{"id":"2503.23729","title":"Integral regularization PINNs for evolution equations","created":"2025-03-31","cited_by_count":1,"area":null},{"id":"2509.23975","title":"Equation-Free Coarse Control of Distributed Parameter Systems via Local Neural Operators","created":"2025-09-28","cited_by_count":1,"area":null},{"id":"2603.12676","title":"Parameterized Temporal Extrapolation of PDEs via Disentangled Latent Dynamics Manifold Fusion","created":"2026-03-13","cited_by_count":1,"area":null},{"id":"2606.01244","title":"Variation Spaces for Encoder--Decoder Neural Operators: Approximation and Generalization","created":"2026-05-31","cited_by_count":1,"area":null},{"id":"2606.06164","title":"On the training of physics-informed neural operators for solving parametric partial differential equations","created":"2026-06-04","cited_by_count":1,"area":null},{"id":"2304.06234","title":"Physics-informed radial basis network (PIRBN): A local approximating neural network for solving nonlinear PDEs","created":"2023-04-13","cited_by_count":0,"area":null},{"id":"2304.12188","title":"A Framework for Combustion Chemistry Acceleration with DeepONets","created":"2023-04-06","cited_by_count":0,"area":null},{"id":"2304.12609","title":"A Bi-fidelity DeepONet Approach for Modeling Uncertain and Degrading Hysteretic Systems","created":"2023-04-25","cited_by_count":0,"area":null},{"id":"2307.13869","title":"Number Theoretic Accelerated Learning of Physics-Informed Neural Networks","created":"2023-07-26","cited_by_count":0,"area":null},{"id":"2311.16860","title":"Data-efficient operator learning for solving high Mach number fluid flow problems","created":"2023-11-28","cited_by_count":0,"area":null},{"id":"2408.09756","title":"Parallel-in-Time Solutions with Random Projection Neural Networks","created":"2024-08-19","cited_by_count":0,"area":null},{"id":"2408.10458","title":"Transfer Operator Learning with Fusion Frame","created":"2024-08-20","cited_by_count":0,"area":null},{"id":"2409.02339","title":"Data-driven 2D stationary quantum droplets and wave propagations in the amended GP equation with two potentials via deep neural networks learning","created":"2024-09-04","cited_by_count":0,"area":null},{"id":"2409.05030","title":"Unified theoretical guarantees for stability, consistency, and convergence in neural PDE solvers from non-IID data to physics-informed networks","created":"2024-09-08","cited_by_count":0,"area":null},{"id":"2502.11504","title":"Accelerated Gradient-based Design Optimization Via Differentiable Physics-Informed Neural Operator: A Composites Autoclave Processing Case Study","created":"2025-02-17","cited_by_count":0,"area":null},{"id":"2506.13222","title":"NeuroPhysNet: A FitzHugh-Nagumo-Based Physics-Informed Neural Network Framework for Electroencephalograph (EEG) Analysis and Motor Imagery Classification","created":"2025-06-16","cited_by_count":0,"area":null},{"id":"2507.18346","title":"Low-rank adaptive physics-informed HyperDeepONets for solving differential equations","created":"2025-07-24","cited_by_count":0,"area":null},{"id":"2509.17293","title":"Physics-Informed Operator Learning for Hemodynamic Modeling","created":"2025-09-22","cited_by_count":0,"area":null},{"id":"2602.14853","title":"BEACONS: Bounded-Error, Algebraically-Composable Neural Solvers for Partial Differential Equations","created":"2026-02-16","cited_by_count":0,"area":null},{"id":"2602.21910","title":"The Error of Deep Operator Networks Is the Sum of Its Parts: Branch-Trunk and Mode Error Decompositions","created":"2026-02-25","cited_by_count":0,"area":null},{"id":"2603.00397","title":"TENG-BC: Unified Time-Evolving Natural Gradient for Neural PDE Solvers with General Boundary Conditions","created":"2026-02-28","cited_by_count":0,"area":null},{"id":"2603.17867","title":"RHYME-XT: A Neural Operator for Spatiotemporal Control Systems","created":"2026-03-18","cited_by_count":0,"area":null},{"id":"2607.23667","title":"No Free Lunch in Flow Surrogates under Time-Varying Boundary Conditions: A Two-Regime Study","created":"2026-07-26","cited_by_count":0,"area":null},{"id":"2608.13629","title":"Learning Unsteady Aneurysm Hemodynamics with Physics-Informed DeepONets","created":"2026-08-13","cited_by_count":0,"area":null},{"id":"2610.04405","title":"CEENs: Causality-enforced evolutional networks for solving time-dependent partial differential equations","created":"2026-10-03","cited_by_count":0,"area":null},{"id":"2610.20120","title":"A Bregman Proximal Viewpoint on Neural Operators","created":"2026-10-14","cited_by_count":0,"area":null}],"next_cursor":null}