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Many physics-informed machine learning methods for PDE-based problems rely on Gaussian processes (GPs) or neural networks (NNs). However, both face limitations when data are scarce and the dimensionality is high. Although GPs are known for…

Spiking neural networks (SNN) are a biologically inspired model of neural networks with certain brain-like properties. In the past few decades, this model has received increasing attention in computer science community, owing also to the…

Many communities have researched the application of novel network architectures such as Content-Centric Networking (CCN) and Software-Defined Networking (SDN) to build the future Internet. Another emerging technology which is big data…

Neural operators have recently become popular tools for designing solution maps between function spaces in the form of neural networks. Differently from classical scientific machine learning approaches that learn parameters of a known…

Large-scale numerical simulations are used across many scientific disciplines to facilitate experimental development and provide insights into underlying physical processes, but they come with a significant computational cost. Deep neural…

Recent efforts have shown machine learning to be useful for the prediction of nonlinear fluid dynamics. Predictive accuracy is often a central motivation for employing neural networks, but the pattern recognition central to the network…

Spiking neural networks (SNNs) are well known as the brain-inspired models with high computing efficiency, due to a key component that they utilize spikes as information units, close to the biological neural systems. Although spiking based…

Standard infinite-width limits of neural networks sacrifice the ability for intermediate layers to learn representations from data. Recent work (A theory of representation learning gives a deep generalisation of kernel methods, Yang et al.…

Turbulence plays an important role in astrophysical phenomena, including core-collapse supernovae (CCSN), but current simulations must rely on subgrid models since direct numerical simulation (DNS) is too expensive. Unfortunately, existing…

Deep neural networks (DNNs) have been widely applied to solve real-world regression problems. However, selecting optimal network structures remains a significant challenge. This study addresses this issue by linking neuron selection in DNNs…

The recent development of artificial intelligence (AI) technology, especially the advance of deep neural network (DNN) technology, has revolutionized many fields. While DNN plays a central role in modern AI technology, it has been rarely…

We propose Deep Kronecker Network (DKN), a novel framework designed for analyzing medical imaging data, such as MRI, fMRI, CT, etc. Medical imaging data is different from general images in at least two aspects: i) sample size is usually…

Digital twins require computationally-efficient reduced-order models (ROMs) that can accurately describe complex dynamics of physical assets. However, constructing ROMs from noisy high-dimensional data is challenging. In this work, we…

Tensorial neural networks (TNNs) combine the successes of multilinear algebra with those of deep learning to enable extremely efficient reduced-order models of high-dimensional problems. Here, I describe a deep neural network architecture…

In recent years, Deep Reinforcement Learning has made impressive advances in solving several important benchmark problems for sequential decision making. Many control applications use a generic multilayer perceptron (MLP) for non-vision…

Turbulence modeling is a classical approach to address the multiscale nature of fluid turbulence. Instead of resolving all scales of motion, which is currently mathematically and numerically intractable, reduced models that capture the…

We propose a novel method to explain trained deep neural networks (DNNs), by distilling them into surrogate models using unsupervised clustering. Our method can be applied flexibly to any subset of layers of a DNN architecture and can…

Machine learning has shown significant breakthroughs in quantum science, where in particular deep neural networks exhibited remarkable power in modeling quantum many-body systems. Here, we explore how the capacity of data-driven deep neural…

Control of a dynamical system without the knowledge of dynamics is an important and challenging task. Modern machine learning approaches, such as deep neural networks (DNNs), allow for the estimation of a dynamics model from control inputs…

Neural networks have become an increasingly popular tool for solving many real-world problems. They are a general framework for differentiable optimization which includes many other machine learning approaches as special cases. In this…