CENN: conservative energy method based on neural networks with subdomains for solving variational problems involving heterogeneous and complex geometries

Phase-field DeepONet: physics-informed deep operator neural network for fast simulations of pattern formation governed by gradient flows of free-energy functionals, BINN: a deep learning approach for computational mechanics problems based on boundary integral equations, Solving multi-material problems in solid mechanics using physics-informed neural networks based on domain decomposition technology

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The Deep Ritz Method: a deep learning-based numerical algorithm for solving variational problems
\textit{hp}-VPINNs: variational physics-informed neural networks with domain decomposition
A physics-informed deep learning framework for inversion and surrogate modeling in solid mechanics
Non-invasive inference of thrombus material properties with physics-informed neural networks
Exact imposition of boundary conditions with distance functions in physics-informed deep neural networks
PFNN: a penalty-free neural network method for solving a class of second-order boundary-value problems on complex geometries
Parallel physics-informed neural networks via domain decomposition
When and why PINNs fail to train: a neural tangent kernel perspective
Physics-informed neural networks for high-speed flows
Conservative physics-informed neural networks on discrete domains for conservation laws: applications to forward and inverse problems
A mesh-free method for interface problems using the deep learning approach
Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
Unsupervised discovery of interpretable hyperelastic constitutive laws
A physics-guided neural network framework for elastic plates: comparison of governing equations-based and energy-based approaches
On the eigenvector bias of Fourier feature networks: from regression to solving multi-scale PDEs with physics-informed neural networks
Physics-informed neural network for modelling the thermochemical curing process of composite-tool systems during manufacture
Parametric deep energy approach for elasticity accounting for strain gradient effects
A deep energy method for finite deformation hyperelasticity
Radial basis function approximations: comparison and applications
An energy approach to the solution of partial differential equations in computational mechanics via machine learning: concepts, implementation and applications
Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Neural algorithm for solving differential equations
Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks
DeepXDE: A Deep Learning Library for Solving Differential Equations
Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks
Extended Physics-Informed Neural Networks (XPINNs): A Generalized Space-Time Domain Decomposition Based Deep Learning Framework for Nonlinear Partial Differential Equations
Approximation by superpositions of a sigmoidal function