Latest Research in Numerical Analysis

Top Research Topics in Numerical Analysis

• Machine Learning — 14 papers
• Numerical Analysis — 10 papers
• Model Reduction and Neural Networks — 8 papers
• Statistical Mechanics — 5 papers
• Neural dynamics and brain function — 3 papers
• Adaptation and Self-Organizing Systems — 2 papers
• Statistical Mechanics and Entropy — 1 papers
• Statistics Theory — 1 papers
• Dynamical Systems — 1 papers
• Pattern Formation and Solitons — 1 papers

Highest-Cited Papers

1. Stabilizing PDE–ML coupled systems
2. MERLIN SCIENCE — Phi-Scaled Vector Quantization of Neural Phase-Coherence — E8 Intelligence Research
3. Hard-constrained Physics-informed Neural Networks for Interface Problems
4. Topological Memory and Hysteresis in Reconfigurable Dusty Plasma Networks
5. Approximation Theorems for High-Dimensional Canonical U-Statistics: Gaussian Chaos and Phase Transition
6. GENERIC-FNO: Embedding Energy Conservation and Entropy Production into Fourier Neural Operators
7. Physics-Informed Neural Networks and Graph Neural Networks for the Numerical Modeling of the Vector Helmholtz Equation
8. Adaptive hybrid coupling with operator inference, the overlapping Schwarz alternating method and reinforcement learning
9. Trustworthy AI in numerics: On verification algorithms for neural network-based PDE solvers
10. Mixed precision solvers for the all-at-once Runge--Kutta discretization of the heat equation
11. DPG loss functions for learning parameter-to-solution maps by neural networks
12. PDEformer-2: A Versatile Foundation Model for Two-Dimensional Partial Differential Equations
13. PhysSAE: Mechanistic Interpretability of PINNs with Sparse Autoencoders
14. CyFM: Cylindrical Optimal Transport for Few-Step Complex-Valued Flow Matching
15. Characterizing resonant solitary states as relative equilibria via normal form reduction
16. Machine Learning of Nonlinear Waves: Data-Driven Methods for Computer-Assisted Discovery of Equations, Symmetries, Conservation Laws, and Integrability
17. Nonperturbative functional renormalization group for Higgs-singlet models with physics-informed neural networks
18. Scientific machine learning meets semi-analytical computation: a hybrid NIM-PINN approach for nonlinear PDEs
19. On the Shared Mathematics of Dynamical Systems and Neural Computation
20. On the Shared Mathematics of Dynamical Systems and Neural Computation