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We introduce physics informed neural networks -- neural networks that are trained to solve supervised learning tasks while respecting any given law of physics described by general nonlinear partial differential equations. In this second…
In this article we review computational aspects of Deep Learning (DL). Deep learning uses network architectures consisting of hierarchical layers of latent variables to construct predictors for high-dimensional input-output models. Training…
We propose a hybrid method combining the deep long short-term memory (LSTM) model with the inexact empirical model of dynamical systems to predict high-dimensional chaotic systems. The deep hierarchy is encoded into the LSTM by…
The unfolding of detector effects is crucial for the comparison of data to theory predictions. While traditional methods are limited to representing the data in a low number of dimensions, machine learning has enabled new unfolding…
Incorporating a priori physics knowledge into machine learning leads to more robust and interpretable algorithms. In this work, we combine deep learning techniques and classic numerical methods for differential equations to address two…
Grassmannian manifold offers a powerful carrier for geometric representation learning by modelling high-dimensional data as low-dimensional subspaces. However, existing approaches predominantly rely on static single-subspace…
Inversion of gravity data is an important method for investigating subsurface density variations relevant to mineral exploration, geothermal assessment, carbon storage, natural hydrogen, groundwater resources, and tectonic evolution. Here…
Manifold learning builds on the "manifold hypothesis," which posits that data in high-dimensional datasets are drawn from lower-dimensional manifolds. Current tools generate global embeddings of data, rather than the local maps used to…
The world is moving towards clean and renewable energy sources, such as wind energy, in an attempt to reduce greenhouse gas emissions that contribute to global warming. To enhance the analysis and storage of wind data, we introduce a deep…
We propose an empirical approach centered on the spectral dynamics of weights -- the behavior of singular values and vectors during optimization -- to unify and clarify several phenomena in deep learning. We identify a consistent bias in…
In this proceeding, we will briefly review our recent progress on implementing deep learning to relativistic hydrodynamics. We will demonstrate that a successfully designed and trained deep neural network, called {\tt stacked U-net}, can…
We introduce a quantum-informed machine learning (QIML) framework for modelling the long-term behaviour of high-dimensional chaotic systems. QIML combines a one-time, offline-trained quantum generative model with a classical autoregressive…
Multimodal deep learning methods capture synergistic features from multiple modalities and have the potential to improve accuracy for stress detection compared to unimodal methods. However, this accuracy gain typically comes from high…
Our goal is to provide a review of deep learning methods which provide insight into structured high-dimensional data. Rather than using shallow additive architectures common to most statistical models, deep learning uses layers of…
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…
Deep neural networks have become the main work horse for many tasks involving learning from data in a variety of applications in Science and Engineering. Traditionally, the input to these networks lie in a vector space and the operations…
Interpretation and diagnosis of machine learning models have gained renewed interest in recent years with breakthroughs in new approaches. We present Manifold, a framework that utilizes visual analysis techniques to support interpretation,…
Manifold learning-based encoders have been playing important roles in nonlinear dimensionality reduction (NLDR) for data exploration. However, existing methods can often fail to preserve geometric, topological and/or distributional…
Deep metric learning maps visually similar images onto nearby locations and visually dissimilar images apart from each other in an embedding manifold. The learning process is mainly based on the supplied image negative and positive training…
Deep learning (DL) is a high dimensional data reduction technique for constructing high-dimensional predictors in input-output models. DL is a form of machine learning that uses hierarchical layers of latent features. In this article, we…