Related papers: Learning Constitutive Relations from Indirect Obse…
We present a general numerical approach for learning unknown dynamical systems using deep neural networks (DNNs). Our method is built upon recent studies that identified the residue network (ResNet) as an effective neural network structure.…
Physics models typically contain adjustable parameters to reproduce measured data. While some parameters correspond directly to measured features in the data, others are unobservable. These unobservables can, in some cases, cause…
This paper investigates the learnability of the nonlinearity property of Boolean functions using neural networks. We train encoder style deep neural networks to learn to predict the nonlinearity of Boolean functions from examples of…
We present a numerical framework for deep neural network (DNN) modeling of unknown time-dependent partial differential equations (PDE) using their trajectory data. Unlike the recent work of [Wu and Xiu, J. Comput. Phys. 2020], where the…
Neural networks (NNs) are currently changing the computational paradigm on how to combine data with mathematical laws in physics and engineering in a profound way, tackling challenging inverse and ill-posed problems not solvable with…
Deep neural networks can empirically perform efficient hierarchical learning, in which the layers learn useful representations of the data. However, how they make use of the intermediate representations are not explained by recent theories…
Network structures underlie the dynamics of many complex phenomena, from gene regulation and foodwebs to power grids and social media. Yet, as they often cannot be observed directly, their connectivities must be inferred from observations…
Deep learning and convolutional neural networks in particular are powerful and promising tools for cosmological analysis of large-scale structure surveys. They are already providing similar performance to classical analysis methods using…
Visual scene understanding often requires the processing of human-object interactions. Here we seek to explore if and how well Deep Neural Network (DNN) models capture features similar to the brain's representation of humans, objects, and…
Perceptual learning enables humans to recognize and represent stimuli invariant to various transformations and build a consistent representation of the self and physical world. Such representations preserve the invariant physical relations…
While deep networks have been enormously successful over the last decade, they rely on flat-feature vector representations, which makes them unsuitable for richly structured domains such as those arising in applications like social network…
This paper is the first work to propose a network to predict a structured uncertainty distribution for a synthesized image. Previous approaches have been mostly limited to predicting diagonal covariance matrices. Our novel model learns to…
Interacting systems are prevalent in nature, from dynamical systems in physics to complex societal dynamics. The interplay of components can give rise to complex behavior, which can often be explained using a simple model of the system's…
This work investigates the framework and performance issues of the composite neural network, which is composed of a collection of pre-trained and non-instantiated neural network models connected as a rooted directed acyclic graph for…
Deep neural networks are a powerful tool for the characterization of quantum states. Existing networks are typically trained with experimental data gathered from the specific quantum state that needs to be characterized. But is it possible…
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…
Despite the huge success of deep neural networks (NNs), finding good mechanisms for quantifying their prediction uncertainty is still an open problem. Bayesian neural networks are one of the most popular approaches to uncertainty…
This paper integrates deep neural networks (DNNs) into structural economic models to increase flexibility and capture rich heterogeneity while preserving interpretability. Economic structure and machine learning are complements in empirical…
When agents devise plans for execution in the real world, they face two important forms of uncertainty: they can never have complete knowledge about the state of the world, and they do not have complete control, as the effects of their…
We propose a neural network based approach for extracting models from dynamic data using ordinary and partial differential equations. In particular, given a time-series or spatio-temporal dataset, we seek to identify an accurate governing…