A comprehensive and fair comparison of two neural operators (with practical extensions) based on fair data
Neural operators can learn nonlinear mappings between function spaces and offer a new
simulation paradigm for real-time prediction of complex dynamics for realistic diverse …
simulation paradigm for real-time prediction of complex dynamics for realistic diverse …
Learning the solution operator of parametric partial differential equations with physics-informed DeepONets
Partial differential equations (PDEs) play a central role in the mathematical analysis and
modeling of complex dynamic processes across all corners of science and engineering …
modeling of complex dynamic processes across all corners of science and engineering …
Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations
N McGreivy, A Hakim - Nature Machine Intelligence, 2024 - nature.com
One of the most promising applications of machine learning in computational physics is to
accelerate the solution of partial differential equations (PDEs). The key objective of machine …
accelerate the solution of partial differential equations (PDEs). The key objective of machine …
Physics-informed machine learning: A survey on problems, methods and applications
Recent advances of data-driven machine learning have revolutionized fields like computer
vision, reinforcement learning, and many scientific and engineering domains. In many real …
vision, reinforcement learning, and many scientific and engineering domains. In many real …
Reliable extrapolation of deep neural operators informed by physics or sparse observations
Deep neural operators can learn nonlinear mappings between infinite-dimensional function
spaces via deep neural networks. As promising surrogate solvers of partial differential …
spaces via deep neural networks. As promising surrogate solvers of partial differential …
Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport
Deep neural operators can learn operators mapping between infinite-dimensional function
spaces via deep neural networks and have become an emerging paradigm of scientific …
spaces via deep neural networks and have become an emerging paradigm of scientific …
Learning operators with coupled attention
Supervised operator learning is an emerging machine learning paradigm with applications
to modeling the evolution of spatio-temporal dynamical systems and approximating general …
to modeling the evolution of spatio-temporal dynamical systems and approximating general …
Deep learning in computational mechanics: a review
L Herrmann, S Kollmannsberger - Computational Mechanics, 2024 - Springer
The rapid growth of deep learning research, including within the field of computational
mechanics, has resulted in an extensive and diverse body of literature. To help researchers …
mechanics, has resulted in an extensive and diverse body of literature. To help researchers …
Novel DeepONet architecture to predict stresses in elastoplastic structures with variable complex geometries and loads
A novel deep operator network (DeepONet) with a residual U-Net (ResUNet) as the trunk
network is devised to predict full-field highly nonlinear elastic–plastic stress response for …
network is devised to predict full-field highly nonlinear elastic–plastic stress response for …
Interfacing finite elements with deep neural operators for fast multiscale modeling of mechanics problems
Multiscale modeling is an effective approach for investigating multiphysics systems with
largely disparate size features, where models with different resolutions or heterogeneous …
largely disparate size features, where models with different resolutions or heterogeneous …