{"total":44,"rows":[{"id":"2107.07871","title":"Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equations","created":"2021-07-16","cited_by_count":145,"area":null},{"id":"2402.01868","title":"Challenges in Training PINNs: A Loss Landscape Perspective","created":"2024-02-02","cited_by_count":113,"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":"2306.08827","title":"PINNacle: A Comprehensive Benchmark of Physics-Informed Neural Networks for Solving PDEs","created":"2023-06-15","cited_by_count":87,"area":null},{"id":"2112.14038","title":"DAS-PINNs: A deep adaptive sampling method for solving high-dimensional partial differential equations","created":"2021-12-28","cited_by_count":66,"area":null},{"id":"2109.09338","title":"Learning in Sinusoidal Spaces with Physics-Informed Neural Networks","created":"2021-09-20","cited_by_count":62,"area":null},{"id":"2211.08939","title":"Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology","created":"2022-11-16","cited_by_count":44,"area":null},{"id":"2103.11181","title":"Adaptive deep density approximation for Fokker-Planck equations","created":"2021-03-20","cited_by_count":28,"area":null},{"id":"2110.14121","title":"On Computing the Hyperparameter of Extreme Learning Machines: Algorithm and Application to Computational PDEs, and Comparison with Classical and High-Order Finite Elements","created":"2021-10-27","cited_by_count":26,"area":null},{"id":"2309.07049","title":"An Extreme Learning Machine-Based Method for Computational PDEs in Higher Dimensions","created":"2023-09-13","cited_by_count":21,"area":null},{"id":"2306.17648","title":"Enhancing training of physics-informed neural networks using domain-decomposition based preconditioning strategies","created":"2023-06-30","cited_by_count":20,"area":null},{"id":"2103.14629","title":"Hybrid analysis and modeling, eclecticism, and multifidelity computing toward digital twin revolution","created":"2021-03-26","cited_by_count":14,"area":null},{"id":"2312.14050","title":"Machine learning and domain decomposition methods -- a survey","created":"2023-12-21","cited_by_count":14,"area":null},{"id":"2106.06682","title":"Solving PDEs on Unknown Manifolds with Machine Learning","created":"2021-06-12","cited_by_count":12,"area":null},{"id":"2205.09833","title":"Learning Interface Conditions in Domain Decomposition Solvers","created":"2022-05-19","cited_by_count":11,"area":null},{"id":"2311.00224","title":"Domain decomposition-based coupling of physics-informed neural networks via the Schwarz alternating method","created":"2023-11-01","cited_by_count":9,"area":null},{"id":"2101.04879","title":"Bayesian neural networks for weak solution of PDEs with uncertainty quantification","created":"2021-01-13","cited_by_count":8,"area":null},{"id":"2112.03732","title":"A coarse space acceleration of deep-DDM","created":"2021-12-07","cited_by_count":8,"area":null},{"id":"2210.05837","title":"A composable machine-learning approach for steady-state simulations on high-resolution grids","created":"2022-10-11","cited_by_count":8,"area":null},{"id":"2502.07209","title":"Enhancing Physics-Informed Neural Networks Through Feature Engineering","created":"2025-02-11","cited_by_count":8,"area":null},{"id":"2301.05708","title":"A domain-decomposed VAE method for Bayesian inverse problems","created":"2023-01-09","cited_by_count":6,"area":null},{"id":"2504.00510","title":"Operator Learning with Domain Decomposition for Geometry Generalization in PDE Solving","created":"2025-04-01","cited_by_count":6,"area":null},{"id":"2508.00101","title":"Leveraging Operator Learning to Accelerate Convergence of the Preconditioned Conjugate Gradient Method","created":"2025-07-31","cited_by_count":6,"area":null},{"id":"2409.01433","title":"Domain Decomposition-based coupling of Operator Inference reduced order models via the Schwarz alternating method","created":"2024-09-02","cited_by_count":5,"area":null},{"id":"2302.01518","title":"LSA-PINN: Linear Boundary Connectivity Loss for Solving PDEs on Complex Geometry","created":"2023-02-03","cited_by_count":4,"area":null},{"id":"2305.12433","title":"ParticleWNN: a Novel Neural Networks Framework for Solving Partial Differential Equations","created":"2023-05-21","cited_by_count":4,"area":null},{"id":"2305.17387","title":"Learning from Integral Losses in Physics Informed Neural Networks","created":"2023-05-27","cited_by_count":4,"area":null},{"id":"2307.12435","title":"A Generalized Schwarz-type Non-overlapping Domain Decomposition Method using Physics-constrained Neural Networks","created":"2023-07-23","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":"2410.04668","title":"The role of interface boundary conditions and sampling strategies for Schwarz-based coupling of projection-based reduced order models","created":"2024-10-07","cited_by_count":4,"area":null},{"id":"2510.08924","title":"AB-PINNs: Adaptive-Basis Physics-Informed Neural Networks for Residual-Driven Domain Decomposition","created":"2025-10-10","cited_by_count":4,"area":null},{"id":"2511.20687","title":"Hybrid coupling with operator inference and the overlapping Schwarz alternating method","created":"2025-11-20","cited_by_count":4,"area":null},{"id":"2308.14258","title":"Breaking Boundaries: Distributed Domain Decomposition with Scalable Physics-Informed Neural PDE Solvers","created":"2023-08-28","cited_by_count":3,"area":null},{"id":"2310.16491","title":"TSONN: Time-stepping-oriented neural network for solving partial differential equations","created":"2023-10-25","cited_by_count":3,"area":null},{"id":"2409.13644","title":"Non-overlapping, Schwarz-type Domain Decomposition Method for Physics and Equality Constrained Artificial Neural Networks","created":"2024-09-20","cited_by_count":3,"area":null},{"id":"2503.10021","title":"DGNN: A Neural PDE Solver Induced by Discontinuous Galerkin Methods","created":"2025-03-13","cited_by_count":3,"area":null},{"id":"2211.12709","title":"SciAI4Industry -- Solving PDEs for industry-scale problems with deep learning","created":"2022-11-23","cited_by_count":2,"area":null},{"id":"2609.14841","title":"Tackling Failure Modes of PINNs and PIKANs Using Conflict-Free Gradients","created":"2026-09-13","cited_by_count":2,"area":null},{"id":"2509.12271","title":"A Variational Physics-Informed Neural Network Framework Using Petrov-Galerkin Method for Solving Singularly Perturbed Boundary Value Problems","created":"2025-09-13","cited_by_count":1,"area":null},{"id":"2402.08296","title":"Multi-Level GNN Preconditioner for Solving Large Scale Problems","created":"2024-02-13","cited_by_count":0,"area":null},{"id":"2408.12198","title":"Two-level deep domain decomposition method","created":"2024-08-22","cited_by_count":0,"area":null},{"id":"2511.13734","title":"Extended Physics Informed Neural Network for Hyperbolic Two-Phase Flow in Porous Media","created":"2025-11-05","cited_by_count":0,"area":null},{"id":"2606.16510","title":"Petrov-Galerkin Variational Physics-Informed Neural Network Framework for Two-Dimensional Singularly Perturbed Problems","created":"2026-06-15","cited_by_count":0,"area":null},{"id":"2608.02036","title":"Convex Neural Energy Elements: Monolithic Finite-Element Assembly of Geometry-Parameterized Neural Operators with Stability and Error Guarantees","created":"2026-08-03","cited_by_count":0,"area":null}],"next_cursor":null}