Related papers: A Deep Learning Framework for Multi-Operator Learn…
We present Basis-to-Basis (B2B) operator learning, a novel approach for learning operators on Hilbert spaces of functions based on the foundational ideas of function encoders. We decompose the task of learning operators into two parts:…
We study the computational complexity of (deterministic or randomized) algorithms based on point samples for approximating or integrating functions that can be well approximated by neural networks. Such algorithms (most prominently…
Training deep neural networks is a highly nontrivial task, involving carefully selecting appropriate training algorithms, scheduling step sizes and tuning other hyperparameters. Trying different combinations can be quite labor-intensive and…
Deep reinforcement learning has achieved remarkable performance in various domains by leveraging deep neural networks for approximating value functions and policies. However, using neural networks to approximate value functions or policy…
The classical development of neural networks has been primarily for mappings between a finite-dimensional Euclidean space and a set of classes, or between two finite-dimensional Euclidean spaces. The purpose of this work is to generalize…
The aim of this paper is twofold. First, we show that a certain concatenation of a proximity operator with an affine operator is again a proximity operator on a suitable Hilbert space. Second, we use our findings to establish so-called…
We consider the learning of algorithmic tasks by mere observation of input-output pairs. Rather than studying this as a black-box discrete regression problem with no assumption whatsoever on the input-output mapping, we concentrate on tasks…
Deep learning has achieved remarkable success across a wide range of tasks, but its models often suffer from instability and vulnerability: small changes to the input may drastically affect predictions, while optimization can be hindered by…
Operator learning provides methods to approximate mappings between infinite-dimensional function spaces. Deep operator networks (DeepONets) are a notable architecture in this field. Recently, an extension of DeepONet based on model…
Learning maps between function spaces with a strong inductive bias is a central challenge in soft computing, especially when training data are scarce and standard deep architectures overfit. We introduce a \emph{neural integral operator}…
The field of deep learning has witnessed a remarkable shift towards extremely compute- and memory-intensive neural networks. These newer larger models have enabled researchers to advance state-of-the-art tools across a variety of fields.…
Robust optimization is becoming increasingly important in machine learning applications. In this paper, we study a unified framework of robust submodular optimization. We study this problem both from a minimization and maximization…
This paper presents novel generalization bounds for vector-valued neural networks and deep kernel methods, focusing on multi-task learning through an operator-theoretic framework. Our key development lies in strategically combining a…
Multiscale modeling is an effective approach for investigating multiphysics systems with largely disparate size features, where models with different resolutions or heterogeneous descriptions are coupled together for predicting the system's…
Real-world problems are often multi-objective with decision-makers unable to specify a priori which trade-off between the conflicting objectives is preferable. Intuitively, building machine learning solutions in such cases would entail…
In this paper, we propose to provide a general ensemble learning framework based on deep learning models. Given a group of unit models, the proposed deep ensemble learning framework will effectively combine their learning results via a…
At its core, machine learning seeks to train models that reliably generalize beyond noisy observations; however, the theoretical vacuum in which state-of-the-art universal approximation theorems (UATs) operate isolates them from this goal,…
Multitask learning, i.e. learning several tasks at once with the same neural network, can improve performance in each of the tasks. Designing deep neural network architectures for multitask learning is a challenge: There are many ways to…
Machine Learning algorithms have had a profound impact on the field of computer science over the past few decades. These algorithms performance is greatly influenced by the representations that are derived from the data in the learning…
Pretraining for partial differential equation (PDE) modeling has recently shown promise in scaling neural operators across datasets to improve generalizability and performance. Despite these advances, our understanding of how pretraining…