Related papers: Reduced-Basis Deep Operator Learning for Parametri…

In numerous contexts, high-resolution solutions to partial differential equations are required to capture faithfully essential dynamics which occur at small spatiotemporal scales, but these solutions can be very difficult and slow to obtain…

Physics-Informed Neural Networks (PINNs) have emerged as powerful tools for solving partial differential equations (PDEs). However, training PINNs from scratch is often computationally intensive and time-consuming. To address this problem,…

Deep learning based approaches like Physics-informed neural networks (PINNs) and DeepONets have shown promise on solving PDE constrained optimization (PDECO) problems. However, existing methods are insufficient to handle those PDE…

In this paper, we evaluate the effectiveness of deep operator networks (DeepONets) in solving both forward and inverse problems of partial differential equations (PDEs) on unknown manifolds. By unknown manifolds, we identify the manifold by…

This work introduces a new approach for accelerating the numerical analysis of time-domain partial differential equations (PDEs) governing complex physical systems. The methodology is based on a combination of a classical reduced-order…

Accurately modeling crack propagation is critical for predicting failure in engineering materials and structures, where small cracks can rapidly evolve and cause catastrophic damage. The interaction of cracks with discontinuities, such as…

Deep learning models deployed on edge devices frequently encounter resource variability, which arises from fluctuating energy levels, timing constraints, or prioritization of other critical tasks within the system. State-of-the-art machine…

Operator learning for complex nonlinear systems is increasingly common in modeling multi-physics and multi-scale systems. However, training such high-dimensional operators requires a large amount of expensive, high-fidelity data, either…

Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…

In this paper, we propose an equation-based parametric Reduced Order Model (ROM), whose accuracy is improved with data-driven terms added into the reduced equations. These additions have the aim of reintroducing contributions that in…

Materials discovery is crucial for making scientific advances in many domains. Collections of data from experiments and first-principle computations have spurred interest in applying machine learning methods to create predictive models…

The computational overhead of traditional numerical solvers for partial differential equations (PDEs) remains a critical bottleneck for large-scale parametric studies and design optimization. We introduce a Minimal-Data Parametric Neural…

Deep learning has gained broad interest in remote sensing image scene classification thanks to the effectiveness of deep neural networks in extracting the semantics from complex data. However, deep networks require large amounts of training…

Industrial design evaluation often relies on high-fidelity simulations of governing partial differential equations (PDEs). While accurate, these simulations are computationally expensive, making dense exploration of design spaces…

In this paper, we consider the design of model predictive control (MPC) algorithms based on deep operator neural networks (DeepONets). These neural networks are capable of accurately approximating real and complex valued solutions of…

Thermal analysis is crucial in 3D-IC design due to increased power density and complex heat dissipation paths. Although operator learning frameworks such as DeepOHeat~\cite{liu2023deepoheat} have demonstrated promising preliminary results…

Deep neural networks are powerful tools for solving nonlinear problems in science and engineering, but training highly accurate models becomes challenging as problem complexity increases. Non-convex optimization and sensitivity to…

Coherent nonlinear wave dynamics are often strongly shaped by a compact set of physically meaningful descriptors of the initial state. Traditional neural operators typically treat the input-output mapping as a largely black-box…

Improving diesel engine efficiency, reducing emissions, and enabling robust health monitoring have been critical research topics in engine modelling. While recent advancements in the use of neural networks for system monitoring have shown…

Deep neural networks (DNNs) recently emerged as a promising tool for analyzing and solving complex differential equations arising in science and engineering applications. Alternative to traditional numerical schemes, learning-based solvers…