Related papers: SVD Perspectives for Augmenting DeepONet Flexibili…

Singular Value Decomposition (SVD) has recently seen a surge of interest as a simple yet powerful tool for large language models (LLMs) compression, with a growing number of works demonstrating 20-80% parameter reductions at minimal…

Neural operators are capable of capturing nonlinear mappings between infinite-dimensional functional spaces, offering a data-driven approach to modeling complex functional relationships in classical density functional theory (cDFT). In this…

We use Deep Operator Networks (DeepONets) to perform super-resolution reconstruction of the solutions of two types of partial differential equations and compare the model predictions with the results obtained using conventional…

Burn injuries present a significant global health challenge. Among the most severe long-term consequences are contractures, which can lead to functional impairments and disfigurement. Understanding and predicting the evolution of post-burn…

We introduce a novel deep operator network (DeepONet) framework that incorporates generalised variational inference (GVI) using R\'enyi's $\alpha$-divergence to learn complex operators while quantifying uncertainty. By incorporating…

In linear models, visualizing a weight vector naturally reveals the model's preferred input direction, but extending this intuition to deep networks via gradients or gradient ascent often yields brittle or adversarial-looking features. We…

Physics-informed neural networks (PINNs) have achieved notable success in modeling dynamical systems governed by partial differential equations (PDEs). To avoid computationally expensive retraining under new physical conditions,…

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…

Design and optimal control problems are among the fundamental, ubiquitous tasks we face in science and engineering. In both cases, we aim to represent and optimize an unknown (black-box) function that associates a performance/outcome to a…

AI for science (AI4Science) models often suffer from discretization: learned representations remain tied to the training grid, limiting transfer across resolutions, solvers and applications. We introduce Neural Proper Orthogonal…

In the pursuit of accurate experimental and computational data while minimizing effort, there is a constant need for high-fidelity results. However, achieving such results often requires significant computational resources. To address this…

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…

Nested dropout is a variant of dropout operation that is able to order network parameters or features based on the pre-defined importance during training. It has been explored for: I. Constructing nested nets: the nested nets are neural…

Low-rank approximation methods such as singular value decomposition (SVD) and its variants (e.g., Fisher-weighted SVD, Activation SVD) have recently emerged as effective tools for neural network compression. In this setting, decomposition…

FNO and DeepONet are by far the most popular neural operator learning algorithms. FNO seems to enjoy an edge in popularity due to its ease of use, especially with high dimensional data. However, a lesser-acknowledged feature of DeepONet is…

There is a critical need for efficient and reliable active flow control strategies to reduce drag and noise in aerospace and marine engineering applications. While traditional full-order models based on the Navier-Stokes equations are not…

Dynamic mode decomposition (DMD) has recently become a popular tool for the non-intrusive analysis of dynamical systems. Exploiting Proper Orthogonal Decomposition (POD) as a dimensionality reduction technique, DMD is able to approximate a…

Accurate temporal extrapolation remains a fundamental challenge for neural operators modeling dynamical systems, where predictions must extend far beyond the training horizon. Conventional DeepONet approaches rely on two limited paradigms:…

Tensor network decomposition, originated from quantum physics to model entangled many-particle quantum systems, turns out to be a promising mathematical technique to efficiently represent and process big data in parsimonious manner. In this…

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…