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Recently, many studies have shed light on the high adaptivity of deep neural network methods in nonparametric regression models, and their superior performance has been established for various function classes. Motivated by this…

Diffusion-based generative models have achieved promising results recently, but raise an array of open questions in terms of conceptual understanding, theoretical analysis, algorithm improvement and extensions to discrete, structured,…

This paper introduces a new Convolutional Neural Network (ConvNet) architecture inspired by a class of partial differential equations (PDEs) called quasi-linear hyperbolic systems. With comparable performance on the image classification…

We present ConDiff, a novel dataset for scientific machine learning. ConDiff focuses on the parametric diffusion equation with space dependent coefficients, a fundamental problem in many applications of partial differential equations…

The representation of nonlinear sub-grid processes, especially clouds, has been a major source of uncertainty in climate models for decades. Cloud-resolving models better represent many of these processes and can now be run globally but…

The configuration model was originally defined for undirected networks and has recently been extended to directed networks. Many empirical networks are however neither undirected nor completely directed, but instead usually partially…

A novel global energy model for multi-class semantic image segmentation is proposed that admits very efficient exact inference and derivative calculations for learning. Inference in this model is equivalent to MAP inference in a particular…

It is well known that building analytical performance models in practice is difficult because it requires a considerable degree of proficiency in the underlying mathematics. In this paper, we propose a machine-learning approach to derive…

This article summarizes principles and ideas from the emerging area of applying \textit{conditional computation} methods to the design of neural networks. In particular, we focus on neural networks that can dynamically activate or…

In this paper, we consider a class of convection-diffusion equations with memory effects. These equations arise as a result of homogenization or upscaling of linear transport equations in heterogeneous media and play an important role in…

In this paper, we examine an important problem of learning neural networks that certifiably meet certain specifications on input-output behaviors. Our strategy is to find an inner approximation of the set of admissible policy parameters,…

Simulations of complex physical systems are typically realized by discretizing partial differential equations (PDEs) on unstructured meshes. While neural networks have recently been explored for surrogate and reduced order modeling of PDE…

Understanding theoretical properties of deep and locally connected nonlinear network, such as deep convolutional neural network (DCNN), is still a hard problem despite its empirical success. In this paper, we propose a novel theoretical…

Diffusion and flow-based generative models have achieved remarkable success in domains such as image synthesis, video generation, and natural language modeling. In this work, we extend these advances to weight space learning by leveraging…

A physics-informed neural network is developed to solve conductive heat transfer partial differential equation (PDE), along with convective heat transfer PDEs as boundary conditions (BCs), in manufacturing and engineering applications where…

Complex biological systems have been successfully modeled by biochemical and genetic interaction networks, typically gathered from high-throughput (HTP) data. These networks can be used to infer functional relationships between genes or…

Diffusion processes are instrumental to describe the movement of a continuous quantity in a generic network of interacting agents. Here, we present a probabilistic framework for diffusion in networks and propose to classify agent…

We generalize the scattering transform to graphs and consequently construct a convolutional neural network on graphs. We show that under certain conditions, any feature generated by such a network is approximately invariant to permutations…

Dynamic neural network is an emerging research topic in deep learning. Compared to static models which have fixed computational graphs and parameters at the inference stage, dynamic networks can adapt their structures or parameters to…

A fully-convolutional neural-network model is used to predict the streamwise velocity fields at several wall-normal locations by taking as input the streamwise and spanwise wall-shear-stress planes in a turbulent open channel flow. The…