Advances in Physics-Informed Neural Networks for Complex Systems

The field of physics-informed neural networks (PINNs) is rapidly advancing, with a focus on developing innovative methods for solving complex problems in various scientific and engineering domains. Recent research has explored the application of PINNs to problems involving nonlinear material modeling, dynamic loading, and inverse problems in spectroscopy. A key direction in this field is the development of new architectures and techniques that can effectively incorporate physical constraints and handle sparse or incomplete data. Notable advances include the introduction of monotone peridynamic neural operators, physics-encoded spectral attention networks, and perception-informed neural networks, which have shown promising results in modeling complex systems and discovering new forms of differential equations.

Noteworthy papers in this area include the introduction of the Spatiotemporal Super-Resolution Physics-Informed Operator (ST-SRPINN) for global stress generation and spatiotemporal super-resolution in two-phase random materials, and the development of the Perception-Informed Neural Networks (PrINNs) framework, which allows for the integration of diverse forms of perception precisiation into neural networks. The Set Operator Network (SetONet) is another significant contribution, as it enables the learning of mappings between function spaces with permutation-invariant variable input sampling. These advances have the potential to significantly improve the accuracy and robustness of PINNs in a wide range of applications, from materials science to biomedical engineering.

Sources

A Parameter-Driven Physics-Informed Neural Network Framework for Solving Two-Parameter Singular Perturbation Problems Involving Boundary Layers

Monotone Peridynamic Neural Operator for Nonlinear Material Modeling with Conditionally Unique Solutions

Transforming physics-informed machine learning to convex optimization

Global Stress Generation and Spatiotemporal Super-Resolution Physics-Informed Operator under Dynamic Loading for Two-Phase Random Materials

PeSANet: Physics-encoded Spectral Attention Network for Simulating PDE-Governed Complex Systems

A Deep Learning Scheme of Electromagnetic Scattering From Scatterers With Incomplete Profiles

Inverse Modeling of Dielectric Response in Time Domain using Physics-Informed Neural Networks

Physics-informed neural network estimation of active material properties in time-dependent cardiac biomechanical models

Neural Integral Operators for Inverse problems in Spectroscopy

A general physics-constrained method for the modelling of equation's closure terms with sparse data

Perception-Informed Neural Networks: Beyond Physics-Informed Neural Networks

SetONet: A Deep Set-based Operator Network for Solving PDEs with permutation invariant variable input sampling

Physics-informed solution reconstruction in elasticity and heat transfer using the explicit constraint force method

Neural network methods for power series problems of Perron-Frobenius operators

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