{"total":39,"rows":[{"id":"2503.17379","title":"Challenges and Advancements in Modeling Shock Fronts with Physics-Informed Neural Networks: A Review and Benchmarking Study","created":"2025-03-14","cited_by_count":11,"area":null},{"id":"2511.19980","title":"Operator Learning at Machine Precision","created":"2025-11-25","cited_by_count":7,"area":null},{"id":"2409.20264","title":"First Order System Least Squares Neural Networks","created":"2024-09-30","cited_by_count":5,"area":null},{"id":"2509.13717","title":"A Conformal Prediction Framework for Uncertainty Quantification in Physics-Informed Neural Networks","created":"2025-09-17","cited_by_count":5,"area":null},{"id":"2509.25311","title":"Aspects of holographic entanglement using physics-informed-neural-networks","created":"2025-09-29","cited_by_count":5,"area":null},{"id":"2508.07994","title":"Prediction error certification for PINNs: Theory, computation, and application to Stokes flow","created":"2025-08-11","cited_by_count":4,"area":null},{"id":"2508.00628","title":"Separated-Variable Spectral Neural Networks: A Physics-Informed Learning Approach for High-Frequency PDEs","created":"2025-08-01","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":"2503.18087","title":"HyperNOs: Automated and Parallel Library for Neural Operators Research","created":"2025-03-23","cited_by_count":2,"area":null},{"id":"2507.06967","title":"Noisy PDE Training Requires Bigger PINNs","created":"2025-07-09","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":"2509.09362","title":"Expressive Power of Deep Networks on Manifolds: Simultaneous Approximation","created":"2025-09-11","cited_by_count":2,"area":null},{"id":"2502.21033","title":"A data augmentation strategy for deep neural networks with application to epidemic modelling","created":"2025-02-28","cited_by_count":1,"area":null},{"id":"2503.10428","title":"Langevin Monte-Carlo Provably Learns Depth Two Neural Nets at Any Size and Data","created":"2025-03-13","cited_by_count":1,"area":null},{"id":"2505.11638","title":"Accelerating Natural Gradient Descent for PINNs with Randomized Numerical Linear Algebra","created":"2025-05-16","cited_by_count":1,"area":null},{"id":"2508.07559","title":"Barron Space Representations for Elliptic PDEs with Homogeneous Boundary Conditions","created":"2025-08-11","cited_by_count":1,"area":null},{"id":"2510.09192","title":"Augmented data and neural networks for robust epidemic forecasting: application to COVID-19 in Italy","created":"2025-10-10","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":"2508.17167","title":"Error analysis for the deep Kolmogorov method","created":"2025-08-23","cited_by_count":0,"area":null},{"id":"2509.19467","title":"THINNs: Thermodynamically Informed Neural Networks","created":"2025-09-23","cited_by_count":0,"area":null},{"id":"2509.21355","title":"Domain-Informed Genetic Superposition Programming: A Case Study on SFRC Beams","created":"2025-09-20","cited_by_count":0,"area":null},{"id":"2512.13217","title":"Rethinking Physics-Informed Regression Beyond Training Loops and Bespoke Architectures","created":"2025-12-15","cited_by_count":0,"area":null},{"id":"2602.00099","title":"Gauss-Newton Natural Gradient Descent for Shape Learning","created":"2026-01-24","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":"2603.15526","title":"Building Trust in PINNs: Error Estimation through Finite Difference Methods","created":"2026-03-16","cited_by_count":0,"area":null},{"id":"2603.18328","title":"A Family of Adaptive Activation Functions for Mitigating Failure Modes in Physics-Informed Neural Networks","created":"2026-03-18","cited_by_count":0,"area":null},{"id":"2604.04971","title":"A Theory-guided Weighted $L^2$ Loss for solving the BGK model via Physics-informed neural networks","created":"2026-04-04","cited_by_count":0,"area":null},{"id":"2604.18261","title":"DeepRitzSplit Neural Operator for Phase-Field Models via Energy Splitting","created":"2026-04-20","cited_by_count":0,"area":null},{"id":"2605.25057","title":"Random Neural Network Expressivity for Non-Linear Partial Differential Equations","created":"2026-05-24","cited_by_count":0,"area":null},{"id":"2606.03936","title":"Correcting Neural Operator Spectral Bias via Diffusion Posterior Sampling with Sparse Observations","created":"2026-06-02","cited_by_count":0,"area":null},{"id":"2606.19754","title":"Learning universal approximations for partial differential equations with Physics-Informed Broad Learning System","created":"2026-06-18","cited_by_count":0,"area":null},{"id":"2606.20417","title":"Neural network surrogates with uncertainty quantification for inverse problems in partial differential equations","created":"2026-06-18","cited_by_count":0,"area":null},{"id":"2607.06369","title":"Feature Learning for the High Dimensional Stationary Sch\\\"odinger Equation with Deep Ritz Method","created":"2026-07-07","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},{"id":"2608.08114","title":"Finite basis physics-informed neural networks with hard constraints for viscous fluid flow in highly perforated domains","created":"2026-08-08","cited_by_count":0,"area":null},{"id":"2608.10389","title":"Efficient Weak-Entropy PINN for Solving Hyperbolic Conservation Laws","created":"2026-08-11","cited_by_count":0,"area":null},{"id":"2608.11020","title":"Derivative Computation in PINNs: Automatic Differentiation, Finite Differences and Beyond","created":"2026-08-11","cited_by_count":0,"area":null},{"id":"2608.16473","title":"Reference-free logged energy-oracle recovery for neural approximations of symmetric coercive variational problems: conforming Riesz reconstruction and archive-level selection","created":"2026-08-17","cited_by_count":0,"area":null},{"id":"2610.10972","title":"Transferability of Learned States in Neural PDE Solvers","created":"2026-10-07","cited_by_count":0,"area":null}],"next_cursor":null}