{"total":33,"rows":[{"id":"2410.13228","title":"From PINNs to PIKANs: Recent Advances in Physics-Informed Machine Learning","created":"2024-10-17","cited_by_count":73,"area":null},{"id":"2302.04107","title":"Can Physics-Informed Neural Networks beat the Finite Element Method?","created":"2023-02-08","cited_by_count":68,"area":null},{"id":"2309.15421","title":"Deep Learning in Deterministic Computational Mechanics","created":"2023-09-27","cited_by_count":21,"area":null},{"id":"2212.14319","title":"Gaussian Process Priors for Systems of Linear Partial Differential Equations with Constant Coefficients","created":"2022-12-29","cited_by_count":17,"area":null},{"id":"2302.05104","title":"Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation","created":"2023-02-10","cited_by_count":11,"area":null},{"id":"2403.03223","title":"Exact Enforcement of Temporal Continuity in Sequential Physics-Informed Neural Networks","created":"2024-02-15","cited_by_count":9,"area":null},{"id":"2404.17789","title":"BiLO: Bilevel Local Operator Learning for PDE Inverse Problems","created":"2024-04-27","cited_by_count":8,"area":null},{"id":"2408.13222","title":"An Overview on Machine Learning Methods for Partial Differential Equations: from Physics Informed Neural Networks to Deep Operator Learning","created":"2024-08-23","cited_by_count":6,"area":null},{"id":"2505.06549","title":"Good Things Come in Pairs: Paired Autoencoders for Inverse Problems","created":"2025-05-10","cited_by_count":5,"area":null},{"id":"2305.00250","title":"A Direct Sampling-Based Deep Learning Approach for Inverse Medium Scattering Problems","created":"2023-04-29","cited_by_count":4,"area":null},{"id":"2311.12528","title":"Inverse Problems with Learned Forward Operators","created":"2023-11-21","cited_by_count":4,"area":null},{"id":"2407.07375","title":"Stable Weight Updating: A Key to Reliable PDE Solutions Using Deep Learning","created":"2024-07-10","cited_by_count":4,"area":null},{"id":"2503.24092","title":"New universal operator approximation theorem for encoder-decoder architectures","created":"2025-03-31","cited_by_count":4,"area":null},{"id":"2308.11925","title":"Solving Elliptic Optimal Control Problems via Neural Networks and Optimality System","created":"2023-08-23","cited_by_count":3,"area":null},{"id":"2510.15651","title":"Deep Neural ODE Operator Networks for PDEs","created":"2025-10-17","cited_by_count":3,"area":null},{"id":"2303.16454","title":"Conductivity Imaging from Internal Measurements with Mixed Least-Squares Deep Neural Networks","created":"2023-03-29","cited_by_count":2,"area":null},{"id":"2310.18636","title":"Electrical Impedance Tomography: A Fair Comparative Study on Deep Learning and Analytic-based Approaches","created":"2023-10-28","cited_by_count":2,"area":null},{"id":"2405.08613","title":"GN-SINDy: Greedy Sampling Neural Network in Sparse Identification of Nonlinear Partial Differential Equations","created":"2024-05-14","cited_by_count":2,"area":null},{"id":"2409.04067","title":"Preconditioned FEM-based Neural Networks for Solving Incompressible Fluid Flows and Related Inverse Problems","created":"2024-09-06","cited_by_count":2,"area":null},{"id":"2508.21571","title":"Convergence of Stochastic Gradient Methods for Wide Two-Layer Physics-Informed Neural Networks for the Poisson Equation","created":"2025-08-29","cited_by_count":2,"area":null},{"id":"2605.25413","title":"Autoregression-Free Neural Operators for Time-Dependent PDEs","created":"2026-05-25","cited_by_count":2,"area":null},{"id":"2501.15186","title":"An Iterative Deep Ritz Method for Monotone Elliptic Problems","created":"2025-01-25","cited_by_count":1,"area":null},{"id":"2508.02537","title":"Solved in Unit Domain: JacobiNet for Differentiable Coordinate-Transformed PINNs","created":"2025-08-04","cited_by_count":1,"area":null},{"id":"2508.09655","title":"Noise-adapted Neural Operator for Robust Non-Line-of-Sight Imaging","created":"2025-08-13","cited_by_count":1,"area":null},{"id":"2512.14240","title":"Physically consistent model learning for reaction-diffusion systems","created":"2025-12-16","cited_by_count":1,"area":null},{"id":"2603.18331","title":"Understanding the Theoretical Foundations of Deep Neural Networks through Differential Equations","created":"2026-03-18","cited_by_count":1,"area":null},{"id":"2410.04299","title":"Dynamics-Encoded Deep Learning for Robust System Identification and Parameter Estimation","created":"2024-10-05","cited_by_count":0,"area":null},{"id":"2411.00463","title":"The learned range test method for the inverse inclusion problem","created":"2024-11-01","cited_by_count":0,"area":null},{"id":"2506.04256","title":"Estimating properties of a homogeneous bounded soil using machine learning models","created":"2025-06-02","cited_by_count":0,"area":null},{"id":"2507.07292","title":"Discretization-independent operator learning for partial differential equations","created":"2025-07-09","cited_by_count":0,"area":null},{"id":"2509.12483","title":"Benchmarking Physics-Informed Neural Networks and Boundary Elements Methods for Wave Scattering","created":"2025-09-15","cited_by_count":0,"area":null},{"id":"2602.15603","title":"Symbolic recovery of PDEs from measurement data","created":"2026-02-17","cited_by_count":0,"area":null},{"id":"2607.10200","title":"The Differential Neural Tangent Kernel and Its Positivity","created":"2026-07-11","cited_by_count":0,"area":null}],"next_cursor":null}