Related papers: Multiple Neural Operators Achieve Near-Optimal Rat…

This work studies the sampling complexity of learning with ReLU neural networks and neural operators. For mappings belonging to relevant approximation spaces, we derive upper bounds on the best-possible convergence rate of any learning…

We introduce a novel Multimodal Neural Operator (MNO) architecture designed to learn solution operators for multi-parameter nonlinear boundary value problems (BVPs). Traditional neural operators primarily map either the PDE coefficients or…

Background: Traumatic brain injury modeling requires integrating volumetric neuroimaging, demographic parameters, and acquisition metadata. Finite element solvers are too computationally expensive for clinical settings. Neural operators…

Neural operators (NOs) employ deep neural networks to learn mappings between infinite-dimensional function spaces. Deep operator network (DeepONet), a popular NO architecture, has demonstrated success in the real-time prediction of complex…

We study computational and statistical aspects of learning Latent Markov Decision Processes (LMDPs). In this model, the learner interacts with an MDP drawn at the beginning of each epoch from an unknown mixture of MDPs. To sidestep known…

In multi-task learning, multiple tasks are solved jointly, sharing inductive bias between them. Multi-task learning is inherently a multi-objective problem because different tasks may conflict, necessitating a trade-off. A common compromise…

While it is widely known that neural networks are universal approximators of continuous functions, a less known and perhaps more powerful result is that a neural network with a single hidden layer can approximate accurately any nonlinear…

An important application of neural networks to scientific computing has been the learning of non-linear operators. In this framework, a neural network is trained to fit a non-linear map between two infinite dimensional spaces, for example,…

This paper introduces an operator-based neural network, the mirror-padded Fourier neural operator (MFNO), designed to learn the dynamics of stochastic systems. MFNO extends the standard Fourier neural operator (FNO) by incorporating mirror…

We design a low complexity decentralized learning algorithm to train a recently proposed large neural network in distributed processing nodes (workers). We assume the communication network between the workers is synchronized and can be…

We present a distributed algorithm that enables a group of robots to collaboratively optimize the parameters of a deep neural network model while communicating over a mesh network. Each robot only has access to its own data and maintains…

Finding multiple solutions of non-convex optimization problems is a ubiquitous yet challenging task. Most past algorithms either apply single-solution optimization methods from multiple random initial guesses or search in the vicinity of…

While many approaches exist in the literature to learn low-dimensional representations for data collections in multiple modalities, the generalizability of multi-modal nonlinear embeddings to previously unseen data is a rather overlooked…

Operator learning has been highly successful for continuous mappings between infinite-dimensional spaces, such as PDE solution operators. However, many operators of interest-including differential operators-are discontinuous or set-valued,…

Singularly perturbed problems present inherent difficulty due to the presence of a thin boundary layer in its solution. To overcome this difficulty, we propose using deep operator networks (DeepONets), a method previously shown to be…

This paper surveys recent developments at the intersection of operator learning, statistical learning theory, and approximation theory. First, it reviews error bounds for empirical risk minimization with a focus on holomorphic operators and…

This paper introduces the Kernel Neural Operator (KNO), a provably convergent operator-learning architecture that utilizes compositions of deep kernel-based integral operators for function-space approximation of operators (maps from…

Compact neural network offers many benefits for real-world applications. However, it is usually challenging to train the compact neural networks with small parameter sizes and low computational costs to achieve the same or better model…

On the one hand, the framework of mixed norm spaces has potential applications in different areas of mathematics. On the other hand, neural network (NN) operators are well established as approximators, attracting significant attention in…

Multi-task learning (MTL) has emerged as a pivotal paradigm in machine learning by leveraging shared structures across multiple related tasks. Despite its empirical success, the development of likelihood-based efficiently solvable…