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Analyzing the worst-case performance of deep neural networks against input perturbations amounts to solving a large-scale non-convex optimization problem, for which several past works have proposed convex relaxations as a promising…

We explore the potential of the deep Ritz method to learn complex fracture processes such as quasistatic crack nucleation, propagation, kinking, branching, and coalescence within the unified variational framework of phase-field modeling of…

Neural operators have been applied in various scientific fields, such as solving parametric partial differential equations, dynamical systems with control, and inverse problems. However, challenges arise when dealing with input functions…

The predictive accuracy of operator learning frameworks depends on the quality and quantity of available training data (input-output function pairs), often requiring substantial amounts of high-fidelity data, which can be challenging to…

Solving nonlinear partial differential equations (PDEs) with multiple solutions using neural networks has found widespread applications in various fields such as physics, biology, and engineering. However, classical neural network methods…

Predicting the microstructural and morphological evolution of materials through phase-field modelling is computationally intensive, particularly for high-throughput parametric studies. While neural operators such as the Fourier neural…

The calibration and training of a neural network is a complex and time-consuming procedure that requires significant computational resources to achieve satisfactory results. Key obstacles are a large number of hyperparameters to select and…

Interfacial dynamics underlie a wide range of phenomena, including phase transitions, microstructure coarsening, pattern formation, and thin-film growth, and are typically described by stiff, time-dependent nonlinear partial differential…

Neural operators have achieved strong performance in learning solution operators of partial differential equations (PDEs), but their inherently continuous representations struggle to capture discontinuities and sharp transitions. Existing…

Phase-field modeling reformulates fracture problems as energy minimization problems and enables a comprehensive characterization of the fracture process, including crack nucleation, propagation, merging, and branching, without relying on…

The recent success of deep learning applications has coincided with those widely available powerful computational resources for training sophisticated machine learning models with huge datasets. Nonetheless, training large models such as…

Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…

Microstructural evolution, particularly grain growth, plays a critical role in shaping the physical, optical, and electronic properties of materials. Traditional phase-field modeling accurately simulates these phenomena but is…

Edge AI has been recently proposed to facilitate the training and deployment of Deep Neural Network (DNN) models in proximity to the sources of data. To enable the training of large models on resource-constraint edge devices and protect…

This paper presents a new method for pre-training neural networks that can decrease the total training time for a neural network while maintaining the final performance, which motivates its use on deep neural networks. By partitioning the…

Neural ordinary differential equations (NODEs), one of the most influential works of the differential equation-based deep learning, are to continuously generalize residual networks and opened a new field. They are currently utilized for…

Neural operators (NO) are discretization invariant deep learning methods with functional output and can approximate any continuous operator. NO have demonstrated the superiority of solving partial differential equations (PDEs) over other…

This paper introduces a data-driven operator learning method for multiscale partial differential equations, with a particular emphasis on preserving high-frequency information. Drawing inspiration from the representation of multiscale…

Accurate prediction of machining deformation in structural components is essential for ensuring dimensional precision and reliability. Such deformation often originates from residual stress fields, whose distribution and influence vary…

Parametric differential equations of the form du/dt = f(u, x, t, p) are fundamental in science and engineering. While deep learning frameworks such as the Fourier Neural Operator (FNO) can efficiently approximate solutions, they struggle…