Related papers: Ensemble and Mixture-of-Experts DeepONets For Oper…

Fast and accurate predictions for complex physical dynamics are a significant challenge across various applications. Real-time prediction on resource-constrained hardware is even more crucial in real-world problems. The deep operator…

Larger networks generally have greater representational power at the cost of increased computational complexity. Sparsifying such networks has been an active area of research but has been generally limited to static regularization or…

Deep Operator Network (DeepONet), a recently introduced deep learning operator network, approximates linear and nonlinear solution operators by taking parametric functions (infinite-dimensional objects) as inputs and mapping them to…

Deep operator networks (DeepONets) represent a powerful class of data-driven methods for operator learning, demonstrating strong approximation capabilities for a wide range of linear and nonlinear operators. They have shown promising…

Mixture-of-Experts (MoE) enhances model performance while maintaining computational efficiency, making it well-suited for large-scale applications. Conventional mixture-of-experts (MoE) architectures suffer from suboptimal coordination…

DeepONet has recently been proposed as a representative framework for learning nonlinear mappings between function spaces. However, when it comes to approximating solution operators of partial differential equations (PDEs) with…

DeepONets have recently been proposed as a framework for learning nonlinear operators mapping between infinite dimensional Banach spaces. We analyze DeepONets and prove estimates on the resulting approximation and generalization errors. In…

Operator learning enables fast surrogate modeling of high-dimensional dynamical systems, but existing approaches face two fundamental limitations: quadratic inference complexity and unreliable uncertainty quantification in safety-critical…

Traditional numerical methods, such as the finite element method and finite volume method, adress partial differential equations (PDEs) by discretizing them into algebraic equations and solving these iteratively. However, this process is…

Operator learning has emerged as a promising paradigm for developing efficient surrogate models to solve partial differential equations (PDEs). However, existing approaches often overlook the domain knowledge inherent in the underlying PDEs…

A new data-driven method for operator learning of stochastic differential equations(SDE) is proposed in this paper. The central goal is to solve forward and inverse stochastic problems more effectively using limited data. Deep operator…

Mixture-of-Experts (MoE) is a neural network architecture that adds sparsely activated expert blocks to a base model, increasing the number of parameters without impacting computational costs. However, current distributed deep learning…

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…

Mixture-of-Experts (MoE) architectures enable efficient scaling of large language models by activating only a subset of parameters per input. However, existing MoE models suffer from two critical limitations: (1) inefficient token-to-expert…

Large language models are typically deployed as monolithic systems, requiring the full model even when applications need only a narrow subset of capabilities, e.g., code, math, or domain-specific knowledge. Mixture-of-Experts (MoEs)…

Pre-training has proven effective in addressing data scarcity and performance limitations in solving PDE problems with neural operators. However, challenges remain due to the heterogeneity of PDE datasets in equation types, which leads to…

Mixture of Experts (MoE) models enable parameter-efficient scaling through sparse expert activations, yet optimizing their inference and memory costs remains challenging due to limited understanding of their specialization behavior. We…

The Deep Operator Networks~(DeepONet) is a fundamentally different class of neural networks that we train to approximate nonlinear operators, including the solution operator of parametric partial differential equations (PDE). DeepONets have…

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…

Deep Operator Networks (DeepONets) provide a branch-trunk neural architecture for approximating nonlinear operators acting between function spaces. In the classical operator approximation framework, the input is a function $u\in C(K_1)$…