Related papers: An approach to encode divergence-free stress field…

We propose a very general framework for deriving rigorous bounds on the approximation error for physics-informed neural networks (PINNs) and operator learning architectures such as DeepONets and FNOs as well as for physics-informed operator…

This work presents a machine learning approach to predict peak-stress clusters in heterogeneous polycrystalline materials. Prior work on using machine learning in the context of mechanics has largely focused on predicting the effective…

We introduce MENO (''Matrix Exponential-based Neural Operator''), a hybrid surrogate modeling framework for efficiently solving stiff systems of ordinary differential equations (ODEs) that exhibit a sparse nonlinear structure. In such…

Neural operators aim to approximate the solution operator of a system of differential equations purely from data. They have shown immense success in modeling complex dynamical systems across various domains. However, the occurrence of…

Data-Driven Continuum Mechanics -- the continuous counterpart of Data-Driven Computational Mechanics -- is a modern paradigm that enhances classical continuum mechanics by incorporating finite sets of experimental material data directly,…

Spiking Neural Networks (SNNs) offer a biologically plausible framework for energy-efficient neuromorphic computing. However, it is a challenge to train SNNs due to their non-differentiability, efficiently. Existing gradient approximation…

Classical sequential models employed in time-series prediction rely on learning the mappings from the past to the future instances by way of a hidden state. The Hidden states characterise the historical information and encode the required…

The numerical approximation of solutions to the compressible Euler and Navier-Stokes equations is a crucial but challenging task with relevance in various fields of science and engineering. Recently, methods from deep learning have been…

Ensuring neural networks adhere to domain-specific constraints is crucial for addressing safety and trustworthiness while also enhancing inference accuracy. Despite the nonlinear nature of most real-world tasks, the majority of existing…

The neural operator has emerged as a powerful tool in learning mappings between function spaces in PDEs. However, when faced with real-world physical data, which are often highly non-uniformly distributed, it is challenging to use…

One of the obstacles hindering the scaling-up of the initial successes of machine learning in practical engineering applications is the dependence of the accuracy on the size of the database that "drives" the algorithms. Incorporating the…

Accurately modeling and forecasting complex systems governed by partial differential equations (PDEs) is crucial in various scientific and engineering domains. However, traditional numerical methods struggle in real-world scenarios due to…

Neuro-encoded expression programming(NEEP) that aims to offer a novel continuous representation of combinatorial encoding for genetic programming methods is proposed in this paper. Genetic programming with linear representation uses…

Neural operators have emerged as cost-effective surrogates for expensive fluid-flow simulators, particularly in computationally intensive tasks such as permeability inversion from time-lapse seismic data, and uncertainty quantification. In…

Energy efficiency remains a critical challenge in deploying physics-informed operator learning models for computational mechanics and scientific computing, particularly in power-constrained settings such as edge and embedded devices, where…

In this work, we present the feedforward neural network based on the conservative approximation to the derivative from point values, for the weighted essentially non-oscillatory (WENO) schemes in solving hyperbolic conservation laws. The…

Physics-informed neural networks (PINNs) offer a promising framework by embedding partial differential equations (PDEs) into the loss function together with measurement data, making them well-suited for inverse problems. However, standard…

Physics-informed neural networks have emerged as an alternative method for solving partial differential equations. However, for complex problems, the training of such networks can still require high-fidelity data which can be expensive to…

The precise measurement of mechanical stress at the nanoscale is of fundamental and technological importance. In principle, all six independent variables of the stress tensor, which describe the direction and magnitude of…

A new penalty-free neural network method, PFNN-2, is presented for solving partial differential equations, which is a subsequent improvement of our previously proposed PFNN method [1]. PFNN-2 inherits all advantages of PFNN in handling the…