The field of physics-informed neural networks (PINNs) is rapidly advancing, with a focus on solving complex systems and modeling real-world phenomena. Recent developments have shown significant improvements in scalability, generalization, and adaptability to varying boundary conditions. Researchers are exploring new architectures and training paradigms to address challenges in solving nonlinear partial differential equations (PDEs) and estimating parameters from noisy data. Notable advancements include the use of neural operators to compute equilibria in mean-field games and the development of constrained PINNs for accurate parameter estimation. Noteworthy papers include: PIONM, which proposes a generalized framework for solving density-constrained mean-field games equilibrium under modified boundary conditions. PINNverse, which introduces a training paradigm that addresses convergence issues and stability problems in PINNs. Other notable papers, such as AM-PIRN and Online Traffic Density Estimation, demonstrate the effectiveness of PINNs in solving nonlinear option pricing models and estimating traffic density in real-time.
Advances in Physics-Informed Neural Networks for Complex Systems
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PIONM: A Generalized Approach to Solving Density-Constrained Mean-Field Games Equilibrium under Modified Boundary Conditions
On the Connection Between Diffusion Models and Molecular Dynamics
Adaptive Movement Sampling Physics-Informed Residual Network (AM-PIRN) for Solving Nonlinear Option Pricing models
Online Traffic Density Estimation using Physics-Informed Neural Networks
PINNverse: Accurate parameter estimation in differential equations from noisy data with constrained physics-informed neural networks
Estimation of Heat Transfer Coefficient in Heat Exchangers from closed-loop data using Neural Networks
A structure-preserving LDG discretization of the Fisher-Kolmogorov equation for modeling neurodegenerative diseases
Physics informed neural network for forward and inverse modeling of low grade brain tumors