Inverse problems are pervasive mathematical methods in inferring knowledge from observational and experimental data by leveraging simulations and models. Unlike direct inference methods, inverse problem approaches typically require many forward model solves usually governed by Partial Differential Equations (PDEs). This a crucial bottleneck in determining the feasibility of such methods. While machine learning (ML) methods, such as deep neural networks (DNNs), can be employed to learn nonlinear forward models, designing a network architecture that preserves accuracy while generalizing to new parameter regimes is a daunting task. Furthermore, due to the computation-expensive nature of forward models, state-of-the-art black-box ML methods would require an unrealistic amount of work in order to obtain an accurate surrogate model. On the other hand, standard Reduced-Order Models (ROMs) accurately capture supposedly important physics of the forward model in the reduced subspaces, but otherwise could be inaccurate elsewhere. In this paper, we propose to enlarge the validity of ROMs and hence improve the accuracy outside the reduced subspaces by incorporating a data-driven ML technique. In particular, we focus on a goal-oriented approach that substantially improves the accuracy of reduced models by learning the error between the forward model and the ROM outputs. Once an ML-enhanced ROM is constructed it can accelerate the performance of solving many-query problems in parametrized forward and inverse problems. Numerical results for inverse problems governed by elliptic PDEs and parametrized neutron transport equations will be presented to support our approach.

Volvo has created a new business unit for its growing range of autonomous transport solutions. The new business area, Volvo Autonomous Solutions, will accelerate the development, commercialization and sales of autonomous transport solutions. Volvo says this will enable the company to meet "a growing demand" and to offer "the best possible solutions" to customers in such segments as mining, ports and transport between logistics centers, as a complement to today's products and services. With global developments that are characterized by higher demand for transportation, increasingly congested roads and major environmental challenges, the industry needs to provide transport solutions that are safer, have a lower environmental impact and are more efficient. Autonomous transport solutions, based on self-driving and connectivity technologies are well-suited for applications where there is a need to move large volumes of goods and material on pre-defined routes, in repetitive flows.

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