The field of physics-informed neural networks (PINNs) and partial differential equations (PDEs) is rapidly evolving, with a focus on improving the accuracy, efficiency, and interpretability of these models. Recent developments have led to the creation of novel frameworks, such as the discrete physics-informed neural network (dPINN) and the physics-informed temporal alignment (PITA) method, which aim to address the challenges of solving complex PDEs. Additionally, research has highlighted the importance of sufficient arithmetic precision in PINNs, with the use of FP64 precision shown to rescue optimization and enable reliable PDE solving. The development of dual-balancing techniques for PINNs has also been proposed, which dynamically adjusts loss weights to alleviate imbalance issues and improve convergence. Furthermore, the integration of physics-informed neural networks with other methods, such as reinforcement learning and equivariant neural networks, has shown promise in solving complex PDEs and improving the accuracy of predictions. Noteworthy papers in this area include the proposal of physics-informed reduced order modeling and the introduction of equivariant eikonal neural networks for scalable travel-time prediction. Overall, these advancements demonstrate the potential of PINNs and PDEs to tackle complex problems in various fields, from fluid dynamics to materials science.
Advancements in Physics-Informed Neural Networks and Partial Differential Equations
Sources
Enforced Interface Constraints for Domain Decomposition Method of Discrete Physics-Informed Neural Networks
Physics-informed Temporal Alignment for Auto-regressive PDE Foundation Models
FP64 is All You Need: Rethinking Failure Modes in Physics-Informed Neural Networks
Dual-Balancing for Physics-Informed Neural Networks
Reinforcement Learning Closures for Underresolved Partial Differential Equations using Synthetic Data
Potential failures of physics-informed machine learning in traffic flow modeling: theoretical and experimental analysis
Surrogate Modeling of 3D Rayleigh-Benard Convection with Equivariant Autoencoders
Collapsing Taylor Mode Automatic Differentiation
Convergence Guarantees for Gradient-Based Training of Neural PDE Solvers: From Linear to Nonlinear PDEs
Hybrid Adaptive Modeling in Process Monitoring: Leveraging Sequence Encoders and Physics-Informed Neural Networks
Physics-Guided Learning of Meteorological Dynamics for Weather Downscaling and Forecasting
Electrostatics from Laplacian Eigenbasis for Neural Network Interatomic Potentials
Physics-informed Reduced Order Modeling of Time-dependent PDEs via Differentiable Solvers
Machine learning-based parameter optimization for M\"untz spectral methods
Towards Identifiability of Interventional Stochastic Differential Equations
Locally Subspace-Informed Neural Operators for Efficient Multiscale PDE Solving
Equivariant Eikonal Neural Networks: Grid-Free, Scalable Travel-Time Prediction on Homogeneous Spaces
Mesh-free sparse identification of nonlinear dynamics
A finite element solver for a thermodynamically consistent electrolyte model
Implicit Neural Shape Optimization for 3D High-Contrast Electrical Impedance Tomography
Towards Coordinate- and Dimension-Agnostic Machine Learning for Partial Differential Equations
PICT -- A Differentiable, GPU-Accelerated Multi-Block PISO Solver for Simulation-Coupled Learning Tasks in Fluid Dynamics
A Unified Framework for Simultaneous Parameter and Function Discovery in Differential Equations