Deadline Date: 31 December 2027
Partial differential equations (PDEs) serve as a cornerstone in modeling, analyzing, and predicting complex phenomena across scientific and engineering disciplines. Their ability to capture essential dynamics of processes in physics, biology, chemistry, finance, and materials science has made them indispensable in both theoretical and applied research.
In recent years, significant progress has been made in the study of partial PDEs through three complementary approaches: analytical methods, numerical schemes, and neural network–based techniques. Analytical methods provide deep insights into the structure, well-posedness, and qualitative behavior of solutions. Numerical methods, such as finite difference, finite element, and spectral methods, enable efficient approximation of solutions for complex geometries and boundary conditions. Meanwhile, neural network techniques, including physics-informed neural networks and deep learning–based solvers offer powerful data-driven tools for solving high-dimensional and ill-posed inverse problems, even when limited data are available. Together, these three paradigms not only enhance analytical tractability but also enable robust and scalable computational solutions for highly nonlinear and real-world PDE systems.
This Special Issue, “Advances in PDEs: Analytical, Numerical, and Neural Network Approaches,” seeks to present recent progress and innovative contributions in this evolving field. We invite high-quality research papers, comprehensive reviews, and methodological studies addressing theoretical, computational, or applied aspects of PDEs.
Topics of interest but not limited to:
Applications of PDEs in real-world modeling and simulation;
Scalable high-performance algorithms for large-scale PDE simulations;
Convergence, stability, and error analysis of hybrid computational methods;
Analytical, semi-analytical, and numerical techniques for PDEs;
Neural network and deep learning approaches for solving or approximating PDEs;
PDEs involving fractional derivatives and memory effects;
Hybrid computational methods combining analytical theory with AI techniques;
Pattern formation, bifurcation, and nonlinear wave propagation in PDE systems;
Emerging applications of hybrid numerical and deep learning methods in computational engineering and applied sciences.
Partial differential equations (PDEs) serve as a cornerstone in modeling, analyzing, and predicting complex phenomena across scientific and engineering disciplines. Their ability to capture essential dynamics of processes in physics, biology, chemistry, finance, and materials science has made them indispensable in both theoretical and applied research.
In recent years, significant progress has been made in the study of partial PDEs ... show more
Editorial board
