Related papers: Generalizability of local neural operator: example…
Generalizability of Reinforcement Learning (RL) agents (ability to perform on environments different from the ones they have been trained on) is a key problem as agents have the tendency to overfit to their training environments. In order…
Neural networks can be powerful function approximators, which are able to model high-dimensional feature distributions from a subset of examples drawn from the target distribution. Naturally, they perform well at generalizing within the…
Despite the tremendous empirical success of deep learning models to solve various learning tasks, our theoretical understanding of their generalization ability is very limited. Classical generalization bounds based on tools such as the VC…
We propose a novel data-lean operator learning algorithm, the Reduced Basis Neural Operator (ReBaNO), to solve a group of PDEs with multiple distinct inputs. Inspired by the Reduced Basis Method and the recently introduced Generative…
Neural operators learn mappings between function spaces, which is practical for learning solution operators of PDEs and other scientific modeling applications. Among them, the Fourier neural operator (FNO) is a popular architecture that…
Data-driven methods have emerged as powerful tools for modeling the responses of complex nonlinear materials directly from experimental measurements. Among these methods, the data-driven constitutive models present advantages in physical…
As an alternative to classical numerical solvers for partial differential equations (PDEs) subject to boundary value constraints, there has been a surge of interest in investigating neural networks that can solve such problems efficiently.…
Laplace Neural Operators (LNOs) have recently emerged as a promising approach in scientific machine learning due to the ability to learn nonlinear maps between functional spaces. However, this framework often requires substantial amounts of…
A central theme in distributed network algorithms concerns understanding and coping with the issue of locality. Inspired by sequential complexity theory, we focus on a complexity theory for distributed decision problems. In the context of…
Ordinary differential equations (ODEs) can provide mechanistic models of temporally local changes of processes, where parameters are often informed by external knowledge. While ODEs are popular in systems modeling, they are less established…
Learning system dynamics from observations is a critical problem in many applications over various real-world complex systems, e.g., climate, ecology, and fluid systems. Recently, neural dynamics modeling method have become a prevalent…
We apply the network Lasso to classify partially labeled data points which are characterized by high-dimensional feature vectors. In order to learn an accurate classifier from limited amounts of labeled data, we borrow statistical strength,…
There exist many forms of deep latent variable models, such as the variational autoencoder and adversarial autoencoder. Regardless of the specific class of model, there exists an implicit consensus that the latent distribution should be…
Deep neural operators are recognized as an effective tool for learning solution operators of complex partial differential equations (PDEs). As compared to laborious analytical and computational tools, a single neural operator can predict…
Learning to Optimize (L2O), a technique that utilizes machine learning to learn an optimization algorithm automatically from data, has gained arising attention in recent years. A generic L2O approach parameterizes the iterative update rule…
Accurate modeling of complex physical problems, such as fluid-structure interaction, requires multiphysics coupling across the interface, which often has intricate geometry and dynamic boundaries. Conventional numerical methods face…
Recently there has been substantial interest in spectral methods for learning dynamical systems. These methods are popular since they often offer a good tradeoff between computational and statistical efficiency. Unfortunately, they can be…
Many well-established anomaly detection methods use the distance of a sample to those in its local neighbourhood: so-called `local outlier methods', such as LOF and DBSCAN. They are popular for their simple principles and strong performance…
A core issue with learning to optimize neural networks has been the lack of generalization to real world problems. To address this, we describe a system designed from a generalization-first perspective, learning to update optimizer…
We apply the network Lasso to solve binary classification and clustering problems for network-structured data. To this end, we generalize ordinary logistic regression to non-Euclidean data with an intrinsic network structure. The resulting…