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Machine learning has made important headway in helping to improve the treatment of quantum many-body systems. A domain of particular relevance are correlated inhomogeneous systems. What has been missing so far is a general, scalable…
Scattering networks are a class of designed Convolutional Neural Networks (CNNs) with fixed weights. We argue they can serve as generic representations for modelling images. In particular, by working in scattering space, we achieve…
Reliable estimation of the raindrop size distribution (RSD) is important for applications including quantitative precipitation estimation, soil erosion modelling, and wind turbine blade erosion. While in situ instruments such as…
Heterogeneous materials such as biological tissue scatter light in random, yet deterministic, ways. Wavefront shaping can reverse the effects of scattering to enable deep-tissue microscopy. Such methods require either invasive access to the…
In this manuscript, we study the learning of deep attention neural networks, defined as the composition of multiple self-attention layers, with tied and low-rank weights. We first establish a mapping of such models to sequence multi-index…
Visual inspection of x-ray scattering images is a powerful technique for probing the physical structure of materials at the molecular scale. In this paper, we explore the use of deep learning to develop methods for automatically analyzing…
In Hezaveh et al. 2017 we showed that deep learning can be used for model parameter estimation and trained convolutional neural networks to determine the parameters of strong gravitational lensing systems. Here we demonstrate a method for…
We develop a machine-learning method for coarse-graining condensed-phase molecular systems using anisotropic particles. The method extends currently available high-dimensional neural network potentials by addressing molecular anisotropy. We…
We introduce general scattering transforms as mathematical models of deep neural networks with l2 pooling. Scattering networks iteratively apply complex valued unitary operators, and the pooling is performed by a complex modulus. An…
We present a technique for efficiently synthesizing images of atmospheric clouds using a combination of Monte Carlo integration and neural networks. The intricacies of Lorenz-Mie scattering and the high albedo of cloud-forming aerosols make…
The automated construction of coarse-grained models represents a pivotal component in computer simulation of physical systems and is a key enabler in various analysis and design tasks related to uncertainty quantification. Pertinent methods…
Modeling and controlling complex spatiotemporal dynamical systems driven by partial differential equations (PDEs) often necessitate dimensionality reduction techniques to construct lower-order models for computational efficiency. This paper…
Across numerous applications, forecasting relies on numerical solvers for partial differential equations (PDEs). Although the use of deep-learning techniques has been proposed, actual applications have been restricted by the fact the…
Unsupervised dimensionality reduction is one of the commonly used techniques in the field of high dimensional data recognition problems. The deep autoencoder network which constrains the weights to be non-negative, can learn a low…
We study the theoretical behavior of denoising score matching--the learning task associated to diffusion models--when the data distribution is supported on a low-dimensional manifold and the score is parameterized using a random feature…
An image-based deep learning framework is developed in this paper to predict damage and failure in microstructure-dependent composite materials. The work is motivated by the complexity and computational cost of high-fidelity simulations of…
As deep learning applications continue to deploy increasingly large artificial neural networks, the associated high energy demands are creating a need for alternative neuromorphic approaches. Optics and photonics are particularly compelling…
Deep neural networks are widely used for classification. These deep models often suffer from a lack of interpretability -- they are particularly difficult to understand because of their non-linear nature. As a result, neural networks are…
Coherent imaging through scatter is a challenging task in computational imaging. Both model-based and data-driven approaches have been explored to solve the inverse scattering problem. In our previous work, we have shown that a deep…
This work presents a variational physics-informed deep learning framework for phase-field modelling of brittle crack propagation in anisotropic media. Previous Deep Ritz Method (DRM) approaches have focused on second-order, isotropic…