Latest Research in Numerical Analysis

Top Research Topics in Numerical Analysis

• Numerical Analysis — 11 papers
• Model Reduction and Neural Networks — 5 papers
• Machine Learning — 3 papers
• Dynamical Systems — 2 papers
• Statistical Mechanics — 2 papers
• Evolutionary Algorithms and Applications — 1 papers
• Probability — 1 papers
• Chaos control and synchronization — 1 papers
• Numerical methods for differential equations — 1 papers
• Complex Systems and Time Series Analysis — 1 papers

Highest-Cited Papers

1. A Parallel-in-Time Combination Method for Parabolic Problems
2. Pattern formation: reactivity is not necessary for chemotaxis--driven instabilities
3. Multi-level neural networks for high-dimensional parametric obstacle problems
4. A semi-smooth Newton method for efficient evaluation of the inverse hysteresis operator
5. Geometric Generalization of Neural Operators from a Kernel Integral Perspective
6. DFSC: Error-Controlled Differentiable Mittag-Leffler Propagation for Fractional Scientific Machine Learning
7. A Pseudo-time Data-Driven Framework for Model Reduction of Linear Operator Equations
8. Resolution-Induced Collapse in Quantized Nonlinear Dynamics: A Finite-Horizon Structural Framework
9. Spectral Basis Interpretable Unit: A Learned Orthogonal Projection Module for Interpretable Function Approximation and Unsupervised Regime Discovery
10. Learning Dynamically Inspired Bases for Koopman and Transfer Operator Approximation
11. Learning the Helmholtz equation operator with DeepONet for non-parametric 2D geometries
12. Neural network-based method for exact solutions of Burgers-type equations
13. On Analytically Tractable Multidimensional Diffusions via Doob h-Transforms, with Resetting and Applications to Wiener and Ornstein--Uhlenbeck Processes
14. Finite-Time Chaos Diagnostics and Noise-Induced Basin Merging in a Two-Dimensional Map
15. HORSES3D-GPU: A high-order discontinuous Galerkin solver for multi-GPU systems
16. Physics-informed token transformer methodology for nonlinear balance laws. I. Schwarzschild--Burgers fluid flows
17. Markov state models revisited: Principles and algorithms for unbiased observables
18. Feigenbaum's Universal Constants: δ and α Govern Nonlinear Period-Doubling Cascades — E8 Intelligence Research
19. Data-driven Reverse Engineering of Physical Laws: Extracting Unknown Interactions via Hierarchical Basis Expansion
20. ETDRK4–Chebyshev Collocation for the Generalized Burgers–Huxley Equation: Machine-Precision Benchmarks and a Corrected Exact Solution