The field of physics-informed neural networks (PINNs) is rapidly advancing, with significant developments in improving the accuracy and efficiency of solving partial differential equations (PDEs). Recent research has focused on addressing challenges such as balancing competing loss terms, adapting to complex geometries, and capturing sharp gradients. Innovations include the proposal of PDE-aware optimizers, quasi-random sampling methods, and adaptive feature capture techniques. These advancements have led to improved performance in solving high-dimensional PDEs, nonlinear lattice systems, and thermodynamically consistent models. Noteworthy papers include the introduction of a PDE-aware optimizer that achieves smoother convergence and lower absolute errors, and the proposal of Quasi-Random Physics-Informed Neural Networks (QRPINNs) that significantly outperform traditional PINNs in high-dimensional PDEs. Overall, the field is moving towards more efficient, accurate, and scalable methods for solving complex PDEs, with potential applications in various scientific and engineering disciplines.
Advances in Physics-Informed Neural Networks for Solving Partial Differential Equations
Sources
PDE-aware Optimizer for Physics-informed Neural Networks
Quasi-Random Physics-informed Neural Networks
Computational algorithm for downward continuation of gravity anomalies
On the under-reaching phenomenon in message-passing neural PDE solvers: revisiting the CFL condition
Energy Dissipation Rate Guided Adaptive Sampling for Physics-Informed Neural Networks: Resolving Surface-Bulk Dynamics in Allen-Cahn Systems
Physics-informed neural networks for high-dimensional solutions and snaking bifurcations in nonlinear lattices
Compliance Minimization via Physics-Informed Gaussian Processes
Kernel-Adaptive PI-ELMs for Forward and Inverse Problems in PDEs with Sharp Gradients
Norm-Stabilized Imaginary-Time Evolution via Feedback Control
Structured First-Layer Initialization Pre-Training Techniques to Accelerate Training Process Based on $\varepsilon$-Rank
Physics-Informed Linear Model (PILM): Analytical Representations and Application to Crustal Strain Rate Estimation
Layer Separation Deep Learning Model with Auxiliary Variables for Partial Differential Equations
Adaptive feature capture method for solving partial differential equations with low regularity solutions
Stability of lattice Boltzmann schemes for initial boundary value problems in raw formulation