Deep Learning Applied to Computational Mechanics: A Comprehensive Review, State of the Art, and the Classics

Abstract

A classic never dies."We must welcome the future, for it soon will be the past, and we must respect the past, for it was once all that was humanly possible."

Enhanced physics‐informed neural networks for efficient modelling of hydrodynamics in river networks

“…To enhance the robustness of the training procedure, we modify the initial phase by substituting the traditional Adam optimizer with its more advanced variant, the AdamW optimizer (Loshchilov & Hutter, 2017). This modification is guided by the increasing recognition of decoupled weight decay regularization in AdamW within the deep‐learning research community (Vu‐Quoc & Humer, 2023). Specifically, AdamW aids in mitigating overfitting by incorporating a penalty term into the loss function, based on the magnitude of the model's weights.…”

Neural networks for the approximation of Euler's elastica

“…Examples comprise virtually any problem where approximation of functions is required, but also efficient reduced order modelling e.g. in fluid mechanics, the deep Ritz method, or more specific numerical tasks such as optimisation of the quadrature rule for the computation of the finite element stiffness matrix, acceleration of simulations on coarser meshes by learning appropriate collocation points, and replacing expensive numerical computations with data-driven predictions [9,12,[25][26][27]. This recent literature is evidence that neural networks can be used successfully as surrogate models for the solution operators of various differential equations.…”