FWI seeks to achieve a high-resolution model of the subsurface through the application of multi-variate optimization to the seismic inverse problem. Although now a mature technology, FWI has limitations related to the choice of the appropriate solver for the forward problem in challenging environments requiring complex assumptions, and very wide angle and multi-azimuth data necessary for full reconstruction are often not available. Deep Learning techniques have emerged as excellent optimization frameworks. These exist between data and theory-guided methods. Data-driven methods do not impose a wave propagation model and are not exposed to modelling errors. On the contrary, deterministic models are governed by the laws of physics. Application of seismic FWI has recently started to be investigated within Deep Learning. This has focussed on the time-domain approach, while the pseudo-spectral domain has not been yet explored. However, classical FWI experienced major breakthroughs when pseudo-spectral approaches were employed. This work addresses the lacuna that exists in incorporating the pseudo-spectral approach within Deep Learning. This has been done by re-formulating the pseudo-spectral FWI problem as a Deep Learning algorithm for a data-driven pseudo-spectral approach. A novel DNN framework is proposed. This is formulated theoretically, qualitatively assessed on synthetic data, applied to a two-dimensional Marmousi dataset and evaluated against deterministic and time-based approaches. Inversion of data-driven pseudo-spectral DNN was found to outperform classical FWI for deeper and over-thrust areas. This is due to the global approximator nature of the technique and hence not bound by forward-modelling physical constraints from ray-tracing.

In this work we develop a novel approach using deep neural networks to reconstruct the conductivity distribution in elliptic problems from one measurement of the solution over the whole domain. The approach is based on a mixed reformulation of the governing equation and utilizes the standard least-squares objective, with deep neural networks as ansatz functions to approximate the conductivity and flux simultaneously. We provide a thorough analysis of the deep neural network approximations of the conductivity for both continuous and empirical losses, including rigorous error estimates that are explicit in terms of the noise level, various penalty parameters and neural network architectural parameters (depth, width and parameter bound). We also provide multiple numerical experiments in two- and multi-dimensions to illustrate distinct features of the approach, e.g., excellent stability with respect to data noise and capability of solving high-dimensional problems.

This paper introduces a method based on a deep neural network (DNN) that is perfectly capable of processing radar data from extremely thinned radar apertures. The proposed DNN processing can provide both aliasing-free radar imaging and super-resolution. The results are validated by measuring the detection performance on realistic simulation data and by evaluating the Point-Spread-function (PSF) and the target-separation performance on measured point-like targets. Also, a qualitative evaluation of a typical automotive scene is conducted. It is shown that this approach can outperform state-of-the-art subspace algorithms and also other existing machine learning solutions. The presented results suggest that machine learning approaches trained with sufficiently sophisticated virtual input data are a very promising alternative to compressed sensing and subspace approaches in radar signal processing. The key to this performance is that the DNN is trained using realistic simulation data that perfectly mimic a given sparse antenna radar array hardware as the input. As ground truth, ultra-high resolution data from an enhanced virtual radar are simulated. Contrary to other work, the DNN utilizes the complete radar cube and not only the antenna channel information at certain range-Doppler detections. After training, the proposed DNN is capable of sidelobe- and ambiguity-free imaging. It simultaneously delivers nearly the same resolution and image quality as would be achieved with a fully occupied array.

We propose in this work the gradient-enhanced deep neural networks (DNNs) approach for function approximations and uncertainty quantification. More precisely, the proposed approach adopts both the function evaluations and the associated gradient information to yield enhanced approximation accuracy. In particular, the gradient information is included as a regularization term in the gradient-enhanced DNNs approach, for which we present similar posterior estimates (by the two-layer neural networks) as those in the path-norm regularized DNNs approximations. We also discuss the application of this approach to gradient-enhanced uncertainty quantification, and present several numerical experiments to show that the proposed approach can outperform the traditional DNNs approach in many cases of interests.

From esoteric tech to AI, visual analysis and deep learning systems are now transforming the innovation of intelligent products and devices, making enterprises more competitive and jobs more efficient. MIT Technology Review Editor at Large, David Rotman, and Max Versace, Cofounder and CEO of Neurala, discuss what this means within the enterprise space and how it translates into worksite and process efficiency. Dr. Massimiliano Versace is the CEO and cofounder of AI-powered visual inspection company, Neurala. Max is a pioneer in non-traditional DNN approaches and a leader in the movement to bring AI beyond the hype and apply it in real-world, tangible use cases. As a cofounder of Neurala, Max has been instrumental in innovating AI technologies that enable customers in the industrial, drone, robotics, and smart device verticals efficiently and cost-effectively deploy AI for real-world impact.