Related papers: Deep Operator Learning-based Surrogate Models with…

Parametric PDEs power modern simulation, design, and digital-twin systems, yet their many-query workloads still hinge on repeatedly solving large finite-element systems. Existing operator-learning approaches accelerate this process but…

Phase-field modeling is an effective but computationally expensive method for capturing the mesoscale morphological and microstructure evolution in materials. Hence, fast and generalizable surrogate models are needed to alleviate the cost…

Optimization and uncertainty quantification have been playing an increasingly important role in computational hemodynamics. However, existing methods based on principled modeling and classic numerical techniques have faced significant…

Kinetic simulations excel at capturing microscale plasma physics phenomena with high accuracy, but their computational demands make them impractical for modeling large-scale space and astrophysical systems. In this context, we build a…

In the paper, a multi-objective evolutionary surrogate-assisted approach for the fast and effective generative design of coastal breakwaters is proposed. To approximate the computationally expensive objective functions, the deep…

A deep-learning-based surrogate model capable of predicting flow and geomechanical responses in CO2 storage operations is presented and applied. The 3D recurrent R-U-Net model combines deep convolutional and recurrent neural networks to…

In Bayesian inverse problems, surrogate models are often constructed to speed up the computational procedure, as the parameter-to-data map can be very expensive to evaluate. However, due to the curse of dimensionality and the nonlinear…

Failure trajectories, identifying the probable failure zones, and damage statistics are some of the key quantities of relevance in brittle fracture applications. High-fidelity numerical solvers that reliably estimate these relevant…

Focused ultrasound (FUS) therapy is a promising tool for optimally targeted treatment of spinal cord injuries (SCI), offering submillimeter precision to enhance blood flow at injury sites while minimizing impact on surrounding tissues.…

Deep Operator Networks (DeepOnets) have revolutionized the domain of scientific machine learning for the solution of the inverse problem for dynamical systems. However, their implementation necessitates optimizing a high-dimensional space…

Efficiently predicting the flowfield and load in aerodynamic shape optimisation remains a highly challenging and relevant task. Deep learning methods have been of particular interest for such problems, due to their success for solving…

Modern power systems require fast and accurate dynamic simulations for stability assessment, digital twins, and real-time control, but classical ODE solvers are often too slow for large-scale or online applications. We propose a…

For computational efficiency, surrogate models have been used to emulate mathematical simulators for physical or biological processes. High-speed simulation is crucial for conducting uncertainty quantification (UQ) when the simulation is…

The deep operator network (DeepONet) is a popular neural operator architecture that has shown promise in solving partial differential equations (PDEs) by using deep neural networks to map between infinite-dimensional function spaces. In the…

This paper proposes a technique for training a neural network by minimizing a surrogate loss that approximates the target evaluation metric, which may be non-differentiable. The surrogate is learned via a deep embedding where the Euclidean…

Developing the proper representations for simulating high-speed flows with strong shock waves, rarefactions, and contact discontinuities has been a long-standing question in numerical analysis. Herein, we employ neural operators to solve…

This study proposes a new discrete neural operator for surrogate modeling of transient Darcy flow fields in heterogeneous porous media with random parameters. The new method integrates temporal encoding, operator learning and UNet to…

Numerical simulation for climate modeling resolving all important scales is a computationally taxing process. Therefore, to circumvent this issue a low resolution simulation is performed, which is subsequently corrected for bias using…

Operator learning has the potential to strongly impact scientific computing by learning solution operators for differential equations, potentially accelerating multi-query tasks such as design optimization and uncertainty quantification by…

To speed-up the solution to parametrized differential problems, reduced order models (ROMs) have been developed over the years, including projection-based ROMs such as the reduced-basis (RB) method, deep learning-based ROMs, as well as…