Allen-Cahn equation

The Allen-Cahn equation is a partial differential equation used to model phase separation and interface dynamics, and it serves as a benchmark to evaluate the performance of Physics-Informed Neural Networks (PINNs) in solving such problems.

Papers using Allen-Cahn equation (14)

Neural Tangent Kernel Analysis to Probe Convergence in Physics-informed Neural Solvers: PIKANs vs. PINNs2025 · 8 citesEnabling Local Neural Operators to perform Equation-Free System-Level Analysis2025 · 1 citesStabilized Adaptive Loss and Residual-Based Collocation for Physics-Informed Neural Networks2026PIP$^2$ Net: Physics-informed Partition Penalty Deep Operator Network2025Real-time physics-informed reconstruction of transient fields using sensor guidance and higher-order time differentiation2025Causality-Respecting Adaptive Refinement for PINNs: Enabling Precise Interface Evolution in Phase Field Modeling2024A Framework Based on Symbolic Regression Coupled with eXtended Physics-Informed Neural Networks for Gray-Box Learning of Equations of Motion from Data2023 · 26 citesInvestigating Guiding Information for Adaptive Collocation Point Sampling in PINNs2024 · 6 citesMultifidelity domain decomposition-based physics-informed neural networks and operators for time-dependent problems2024 · 3 citesDensely Multiplied Physics Informed Neural Networks2024 · 1 citesCausality-guided adaptive sampling method for physics-informed neural networks2024 · 1 citesFB-HyDON: Parameter-Efficient Physics-Informed Operator Learning of Complex PDEs via Hypernetwork and Finite Basis Domain Decomposition2024 · 1 citesEfficient Error Certification for Physics-Informed Neural Networks2023TENG: Time-Evolving Natural Gradient for Solving PDEs With Deep Neural Nets Toward Machine Precision2024