Advancements in Physics-Informed Neural Networks

The field of physics-informed neural networks (PINNs) is rapidly advancing, with a focus on improving efficiency, accuracy, and interpretability. Recent developments have explored the use of sparse and small models, reactive transport modeling, and influence functions for resampling data. Additionally, there have been advancements in high-precision training of PINNs in unbounded domains, stabilization of PDE-ML coupled systems, and application of PINNs in industrial gas turbines.

Notable papers include:

S$^2$GPT-PINNs, which proposes a sparse and small model for solving parametric partial differential equations, achieving high efficiency via knowledge distillation and judicious down-sampling.
Causal Operator Discovery in Partial Differential Equations, which develops a framework for discovering causal structure in partial differential equations using physics-informed neural networks and counterfactual perturbations, demonstrating improved structural fidelity and interpretability.

Sources

S$^2$GPT-PINNs: Sparse and Small models for PDEs

Reactive Transport Modeling with Physics-Informed Machine Learning for Critical Minerals Applications

Leveraging Influence Functions for Resampling Data in Physics-Informed Neural Networks

High precision PINNs in unbounded domains: application to singularity formulation in PDEs

Stabilizing PDE--ML Coupled System

Physics-Informed Neural Networks for Industrial Gas Turbines: Recent Trends, Advancements and Challenges

Convolution-weighting method for the physics-informed neural network: A Primal-Dual Optimization Perspective

A parametric tensor ROM for the shallow water dam break problem

Causal discovery in deterministic discrete LTI-DAE systems

Causal Operator Discovery in Partial Differential Equations via Counterfactual Physics-Informed Neural Networks

Stochastic particle method with birth-death dynamics

M\'ethode de quadrature pour les PINNs fond\'ee th\'eoriquement sur la hessienne des r\'esiduels

Physics-Informed Machine Learning Regulated by Finite Element Analysis for Simulation Acceleration of Laser Powder Bed Fusion

Boundary integral equation analysis for spheroidal suspensions

Robust and efficient pre-processing techniques for particle-based methods including dynamic boundary generation