Related papers: Physically recurrent neural networks for path-depe…

We propose a surrogate model for two-scale computational homogenization of elastostatics at finite strains. The macroscopic constitutive law is made numerically available via an explicit formulation of the associated macro-energy density.…

Constitutive modeling based on continuum mechanics theory has been a classical approach for modeling the mechanical responses of materials. However, when constitutive laws are unknown or when defects and/or high degrees of heterogeneity are…

Compared to conventional projection-based model-order-reduction, its neural-network acceleration has the advantage that the online simulations are equation-free, meaning that no system of equations needs to be solved iteratively.…

Many important multi-component crystalline solids undergo mechanochemical spinodal decomposition: a phase transformation in which the compositional redistribution is coupled with structural changes of the crystal, resulting in dynamically…

Correctly capturing intraoperative brain shift in image-guided neurosurgical procedures is a critical task for aligning preoperative data with intraoperative geometry for ensuring accurate surgical navigation. While the finite element…

Neural networks (NNs) are often used as surrogates or emulators of partial differential equations (PDEs) that describe the dynamics of complex systems. A virtually negligible computational cost of such surrogates renders them an attractive…

Physics-informed neural networks (PINNs) are capable of finding the solution for a given boundary value problem. We employ several ideas from the finite element method (FEM) to enhance the performance of existing PINNs in engineering…

Recently, physics informed neural networks have successfully been applied to a broad variety of problems in applied mathematics and engineering. The principle idea is to use a neural network as a global ansatz function to partial…

Crash simulations play an essential role in improving vehicle safety, design optimization, and injury risk estimation. Unfortunately, numerical solutions of such problems using state-of-the-art high-fidelity models require significant…

Surrogate testing techniques have been used widely to investigate the presence of dynamical nonlinearities, an essential ingredient of deterministic chaotic processes. Traditional surrogate testing subscribes to statistical hypothesis…

We present a finite element-inspired hypergraph neural network framework for predicting flow-induced vibrations in freely oscillating cylinders. The surrogate architecture transforms unstructured computational meshes into node-element…

We present a scalable framework for learning deterministic and probabilistic neural surrogates for high-resolution 3D physics simulations. We introduce a hybrid CNN-Transformer backbone architecture targeted for 3D physics simulations,…

The major challenge in determining a hyperelastic model for a given material is the choice of invariants and the selection how the strain energy function depends functionally on these invariants. Here we introduce a new data-driven…

Machine learning methods are increasingly used to build computationally inexpensive surrogates for complex physical models. The predictive capability of these surrogates suffers when data are noisy, sparse, or time-dependent. As we are…

Surrogate neural network-based models have been lately trained and used in a variety of science and engineering applications where the number of evaluations of a target function is limited by execution time. In cell phone camera systems,…

Random microstructures of heterogeneous materials play a crucial role in the material macroscopic behavior and in predictions of its effective properties. A common approach to modeling random multiphase materials is to develop so-called…

Neural networks are powerful function estimators, leading to their status as a paradigm of choice for modeling structured data. However, unlike other structured representations that emphasize the modularity of the problem -- e.g., factor…

The discovery of constitutive models for hyperelastic materials is essential yet challenging due to their nonlinear behavior and the limited availability of experimental data. Traditional methods typically require extensive stress-strain or…

Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…

Recurrent Neural Networks (RNNs) have emerged as an interesting alternative to conventional material modeling approaches, particularly for nonlinear path dependent materials. Remarkable computational enhancements are obtained using RNNs…